This is weird! (math thing)

[MuniAddict]

It recently occured to me that only the number *2*, either added to itself or multiplied by itself, yields the exact same number. So in this case, there is ZERO difference between adding or multiplying. Does this happen with any other number? :confused:

2+2=4 (but of course 1+1=2 and 1x1=1. 2+3=5, and 2x3=6, and so on.)
and:
2x2=4

[yoopers]

It recently occured to me that only the number *2*, either added to itself or multiplied by itself, yields the exact same number. So in this case, there is ZERO difference between adding or multiplying. Does this happen with any other number? :confused:

2+2=4 (but of course 1+1=2 and 1x1=1. 2+3=5, and 2x3=6, and so on.)
and:
2x2=4
There is another number. You mentioned it in your post.

[dudewithasock]

Zero and infinite both do the same thing, though they aren't really numbers.

[yoopers]

Zero and infinite both do the same thing, though they aren't really numbers.
Zero is a number.

[wickedbob]

Zero and infinite both do the same thing, though they aren't really numbers.

Yeah, I was told they were abstract concepts.

edit^^

Yoopers is zero really a number? I was always taught it wasn't anything, but an abstract concept used to represent nothing at all.

[dudewithasock]

Zero is a number.

Zero is a lack of number/quantity, much like black is an absence of color.

[MuniAddict]

I figured someone might mention *zero*, but to clarify, it's 1 and over, lol.

[peleschramm]

eh, zero is definitely a number guys...

infinite is the concept.

There are actually several different values of infinite.

[MuniAddict]

eh, zero is definitely a number guys...

infinite is the concept.

There are actually several different values of infinite.That's the old argument that "nothing" is something. Forget zero! 1 or more please.:D :p :cool:

[wickedbob]

eh, zero is definitely a number guys...

infinite is the concept.

There are actually several different values of infinite.

A number means there is something there, like say 1 book. If there are 0 books there is no books at all. So how can the lack of something be represented by something? I'm pretty sure it is not a number.

[catinabag1]

there are imaginary numbers that equal the same if you add them or multiply them.

[Tyler_N]

If i have six classes with zero zero's how many zero's do i have?

[peleschramm]

A number means there is something there, like say 1 book. If there are 0 books there is no books at all. So how can the lack of something be represented by something? I'm pretty sure it is not a number.
By this logic, wouldn't negative numbers also not be numbers?

[wickedbob]

If i have six classes with zero zero's how many zero's do i have?

Zorro! I mean zero.

[MuniAddict]

If i have six classes with zero zero's how many zero's do i have?The question is moot and irrelevent.:cool: Yes, we have no bananas!:p If I have no money, how much money do I have? Lol! 1 or more is the question. Forget zero haha.

[wickedbob]

By this logic, wouldn't negative numbers also not be numbers?

I was told they are technically not, my school is dumb ass sh*t though. I just go by what I have been told.

[peleschramm]

haha they are called negative NUMBERS

yeah, by saying there are zero bananas, that means that there are no bananas. i would say that would make it qualify as a number.

[catinabag1]

A number means there is something there, like say 1 book. If there are 0 books there is no books at all. So how can the lack of something be represented by something? I'm pretty sure it is not a number.
0 is a limit and can therefore be represented by a number.

[MuniAddict]

neg 1 or negative whatever is not a quantity, but rather a *lack" of quantity. If my checkbook is overdrawn $10, then that is a negative amount, and not an actual quanity. It only represents what is missing, not what is tangibly there.

[catinabag1]

technically all numbers don't exist, they are just abstract ideas used to quantify.

[Tyler_N]

Zorro! I mean zero.
what I'm wondering is if the zero describing the zero's counts as zero.

[nimblelight]

technically all numbers don't exist, they are just abstract ideas used to quantify.
by the arguments everyone else is using, yes,
but then you could argue that they exist as fluctuations of sound able to be interpreted by the human brain or encoded through writing/input into any kind of computer which may then use them to solve problems.

[wickedbob]

what I'm wondering is if the zero describing the zero's counts as zero.


Yes.

[peleschramm]

this thread reminded me of this (http://www.unicyclist.com/forums/showthread.php?t=70265)

[dudewithasock]

0 is a limit and can therefore be represented by a number.

I don't think that's a valid argument...infinite can be a limit as well (constant increase of a function) and that's obviously not a concrete number.

[catinabag1]

I don't think that's a valid argument...infinite can be a limit as well (constant increase of a function) and that's obviously not a concrete number.
infinity is a number because it has value.

[uni57]

I figured someone might mention *zero*, but to clarify, it's 1 and over, lol.

That's the old argument that "nothing" is something. Forget zero! 1 or more please.:D :p :cool:

The question is moot and irrelevent. [...] 1 or more is the question. Forget zero haha.

LOL, threads don't always go the way you want, do they? :)

[uni57]

I just checked. Zero is a number. It's on the numeric keypad on my keyboard.


Edit: and before someone says that Num Lock must therefore also be a number... I don't want to hear your crappy logic

[dudewithasock]

infinity is a number because it has value.

Then show me infinity of something, please.

[dudewithasock]

I just checked. Zero is a number. It's on the numeric keypad on my keyboard.

In programming, the first three numbers are 0, 1, and 2. That should be proof enough. :D

[catinabag1]

Then show me infinity of something, please.
a black hole has infinie density. it has a defined mass but infinite density because everything is pulled to a single point in space-time.

[dudewithasock]

a black hole has infinie density. it has a defined mass but infinite density because everything is pulled to a single point in space-time.

Pft, that's your argument? Who's to say the density isn't just constantly increasing past a measurable point? Sounds pretty theoretical to me, bud.

[mornish]

I just checked. Zero is a number. It's on the numeric keypad on my keyboard.


Edit: and before someone says that Num Lock must therefore also be a number... I don't want to hear your crappy logic

I can use my recently learned my transitive property skills for this!

If 4 is on the numeric keypad and 4 is a number, and if num lock is on the numeric keypad, then num lock is a number.

go me!

I am so amazing.

[catinabag1]

Pft, that's your argument? Who's to say the density isn't just constantly increasing past a measurable point? Sounds pretty theoretical to me, bud.
here is my source: http://en.wikipedia.org/wiki/Black_hole

here is my quote: According to general relativity, a black hole's mass is entirely compressed into a region with zero volume, which means its density and gravitational pull are infinite, and so is the curvature of space-time that it causes.

want me to show you the math behind it?

[MuniAddict]

this thread reminded me of this (http://www.unicyclist.com/forums/showthread.php?t=70265)Yesh, but mine came first!:D To really be accurate, it is the other thread that would "remind" you of this thread, since this one came first.:)

[catinabag1]

ok so i decided to show the math because i want to delay my homework as long as possible.

the equation for density is: Density=mass/volume. well if volume equals 0 which it does at the singularity of a black hole, then the density is infinite.

[uni57]

How did we get...

2+2=4 from here ^^^

Who's to say the density [of a black hole] isn't just constantly increasing past a measurable point?to here? ^^^

:)

[catinabag1]

How did we get...

from here ^^^

to here? ^^^

:)
sorry. lol :D . i had to bring physics in to prove a point.

[MuniAddict]

LOL, threads don't always go the way you want, do they? :)Haha idc. It's fun to get people thinking!:cool:

[MuniAddict]

How did we get...

from here ^^^

to here? ^^^

:)Trying to change the subject because they don't have an answer? Lol!:o

[Seager]

None of you freaking paid attention in highschool algebra, did you?

Zero is a "whole number."

Don't believe me? (http://www.purplemath.com/modules/numtypes.htm)

[wickedbob]

None of you freaking paid attention in highschool algebra, did you?

Zero is a "whole number."

Don't believe me? (http://www.purplemath.com/modules/numtypes.htm)

These days we take it in middle school. Well, I did.

[Seager]

Well, yea... I just taught it at the beginning of this year to freshman, but it was a remedial class.

[JayS]

there are imaginary numbers that equal the same if you add them or multiply them.


I suspect you may be wrong here: Care to quote an example?

[monkeyman]

ok so i decided to show the math because i want to delay my homework as long as possible.

the equation for density is: Density=mass/volume. well if volume equals 0 which it does at the singularity of a black hole, then the density is infinite.

Yes, we know. We've taken two years of physics with a unit in astrophysics. What you're saying is totally right...except for you saying that infinity is a number. If you have enough of them, you can accumulate 999,999,999,999,999,999,999 grains of sand. No matter how many 9s you add, you can get them. But infinity, by definition, is a concept that cannot be reached. It's not an actual number.

[catinabag1]

Yes, we know. We've taken two years of physics with a unit in astrophysics. What you're saying is totally right...except for you saying that infinity is a number. If you have enough of them, you can accumulate 999,999,999,999,999,999,999 grains of sand. No matter how many 9s you add, you can get them. But infinity, by definition, is a concept that cannot be reached. It's not an actual number.
here's what wikipedia has to say on the issue

"In mathematics, "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is a different type of "number" from the real numbers. Infinity is related to limits, aleph numbers, classes in set theory, Dedekind-infinite sets, large cardinals,[1] Russell's paradox, non-standard arithmetic, hyperreal numbers, projective geometry, extended real numbers and the absolute Infinite."

[kington99]

a simple proof that 2 is the only solution:

x^2 = 2x

div x

x=2

'nuff said.

[catinabag1]

a simple proof that 2 is the only solution:

x^2 = 2x

div x

x=2

'nuff said.
2 is the only solution for real numbers. if we get into complex and imaginary numbers the solutions i believe are infinite.

it's been so long since i've used those numbers so it will take me a bit to prove this.

[JayS]

a simple proof that 2 is the only solution:

x^2 = 2x

div x

x=2

'nuff said.


NO:
x^2 = 2x

x^2 - 2x =0

x(x-2)=0

x= 0 OR x =2

[JayS]

2 is the only solution for real numbers. if we get into complex and imaginary numbers the solutions i believe are infinite.

it's been so long since i've used those numbers so it will take me a bit to prove this.


...waiting for your proof: The situation gives us a quadratic equation: therefore two solutions: 0 and 2. So no room left for a complex or imaginary answer.

But I would be happy if you can prove that to be wrong.

[catinabag1]

...waiting for your proof: The situation gives us a quadratic equation: therefore two solutions: 0 and 2. So no room left for a complex or imaginary answer.

But I would be happy if you can prove that to be wrong.
ok i figured it out. here is what needs to be true to satisfy the requirements:


2a+2bi=(a^2-b^2)+(b^2+a^2)i

if you substitute any same number for a and b you will find that they are equal. so there is an infinite number of solutions to this problem.

edit: plus the quadratic equation only gives real numbers.

[catinabag1]

ok i figured it out. here is what needs to be true to satisfy the requirements:


2a+2bi=(a^2-b^2)+(b^2+a^2)i

if you substitute any same number for a and b you will find that they are equal. so there is an infinite number of solutions to this problem.

edit: plus the quadratic equation only gives real numbers.
i just caught myself there. if you substitute 2 for both a and b you get the same sum as product. you can use a different equation to give you a infinite amount of answers. and 2+2i does not equal 2 so it is another answer

[JayS]

ok i figured it out. here is what needs to be true to satisfy the requirements:


2a+2bi=(a^2-b^2)+(b^2+a^2)i

if you substitute any same number for a and b you will find that they are equal. so there is an infinite number of solutions to this problem.

edit: plus the quadratic equation only gives real numbers.

Sorry: I don't understand where you get this equation from

2a+2bi=(a^2-b^2)+(b^2+a^2)i

If you are saying that a+bi fits the bill then the equation is surely


2(a+bi) = (a+bi)^2

now choose "any" value: say a=1 b=0
this would work out as 2 =1 so that choice of value fails

let a=0 b=1 hmmm that also failed


a=2 b=0 works as does a=0 b=0

How did you work out your equation: looks wrong to me

[catinabag1]

Sorry: I don't understand where you get this equation from

2a+2bi=(a^2-b^2)+(b^2+a^2)i

If you are saying that a+bi fits the bill then the equation is surely


2(a+bi) = (a+bi)^2

now choose "any" value: say a=1 b=0
this would work out as 2 =1 so that choice of value fails

let a=0 b=1 hmmm that also failed

How did you work out your equation: looks wrong to me
i said make a=b=2

i got my equation from the rule of sums and products for complex numbers and i simplified it. if i didn't simplify it would have shown an infinite number of solutions but that's beyond my math.

also your simplification doesn't work when you simplified to (a+bi)^2

[JayS]

i just caught myself there. if you substitute 2 for both a and b you get the same sum as product. you can use a different equation to give you a infinite amount of answers. and 2+2i does not equal 2 so it is another answer


That is an interesting statement "you can use a different equation to give an infinite number of answers"

C'mon Cat lets see some proper maths from you. That is utter drivel. You can't just drag another equation out of thin air to give you another answer.

[catinabag1]

That is an interesting statement "you can use a different equation to give an infinite number of answers"

C'mon Cat lets see some proper maths from you. That is utter drivel. You can't just drag another equation out of thin air to give you another answer.
it's the same equation just not simplified. to get the one i did i made assumptions about the numbers but no rules were violated, it just narrows the number of answers i get to one. if i don't simplify the equation you can get an infinite amount of answers but to do so you have to take an integral of complex numbers which i don't know how to do.


here is the unsimplified version: (a+bi)+(c+di)=(a+bi)(c+di) so (a+c)+(b+d)i=(ac-bd)+(bc+ad)i
the left of the = sign is the addition equation and the right side is the multiplication

i assumed that a=b=c=d to make the simplification easier. this breaks no rules but it does limit my solutions to one. if i didn't make this assumption there would be an infinite amount of solutions. my calculus teacher showed the infinite way but it is beyond my math level.

[JayS]

i said make a=b=2

i got my equation from the rule of sums and products for complex numbers and i simplified it. if i didn't simplify it would have shown an infinite number of solutions but that's beyond my math.

also your simplification doesn't work when you simplified to (a+bi)^2




My "simplification", as you call it, does not work with a=b=2, because 2+2i is NOT a solution to the problem

in that case 2(a+bi) = 4 + 4i and (a+bi) squared is a^2 -b^2 +2abi
=4 -4 +8i =8i


and 4+4i is certainly not equal to 8i

[catinabag1]

My "simplification", as you call it, does not work with a=b=2, because 2+2i is NOT a solution to the problem

in that case 2(a+bi) = 4 + 4i and (a+bi) squared is a^2 -b^2 +2abi
=4 -4 +8i =8i


and 4+4i is certainly not equal to 8i
no if you substitute a=b=2 into the equation you get (4+4i)=(4+4i). check your math.

[JayS]

no if you substitute a=b=2 into the equation you get (4+4i)=(4+4i). check your math.



Using YOUR equation a=b=c=d=2

(a+c)+(b+d)i=(ac-bd)+(bc+ad)i

(2+2)+(2+2)i = ( 4 -4 ) + (4+4)i

4+4i = 8i

So tell me: where exactly did my maths go wrong?
Nothing wrong with my maths I fear:

Use my equation and you get exactly the same.

[catinabag1]

Using YOUR equation a=b=c=d=2

(a+c)+(b+d)i=(ac-bd)+(bc+ad)i

(2+2)+(2+2)i = ( 4 -4 ) + (4+4)i

4+4i = 8i

So tell me: where exactly did my maths go wrong?
Nothing wrong with my maths I fear:

Use my equation and you get exactly the same.
don't substitute the 2 until you simplify. in order for that situation to work you have to wait until you simplify because i created a special situation. you aren't following me at all. what math did you get to?

[JayS]

don't substitute the 2 until you simplify. in order for that situation to work you have to wait until you simplify because i created a special situation. you aren't following me at all. what math did you get to?

I reached a very high level of university maths.

Simplification of an equation does not change that equation: it merely makes it easier to deal with: the time at which the 2 is substituted has no effect on the solution. You are making simple schoolboy errors in your maths

write out your steps in simple form in your next post

[catinabag1]

I reached a very high level of university maths.

Simplification of an equation does not change that equation: it merely makes it easier to deal with: the time at which the 2 is substituted has no effect on the solution. You are making simple schoolboy errors in your maths

write out your steps in simple form in your next post
actually the way i simplified it does change the equation. as i've said several times before, during my simplification i created a special situation to make it easier to simplify. without doing so you need to be able to take an integral of a complex number which i can not do. so to get around this i made a few assumptions, but this only makes the equation work for one value but my equation is right. you haven't been following me on this so i will no longer debate because it is a lost cause. also your simplifications have been wrong. my math checks out and is correct. check your own math before you insult mine.

[unidunc]

Mathletes! lol just playing. you guys have me lost...

[Niko]

Lol, this thread made me laugh hard. I am willing to hand out free "Math Loser" T-shirts. You can wear those and save yourself the work of adding more posts in this thread. catinabag1 gets one in gold, as a special price for his achievement of knowing complex numbers while at the same time remaining completely ignorant of mathematics. :D

And yes, I know I'm mean and arrogant. But it is hard to be not when reading a thread like this. :)

[JayS]

actually the way i simplified it does change the equation. as i've said several times before, during my simplification i created a special situation to make it easier to simplify. without doing so you need to be able to take an integral of a complex number which i can not do. so to get around this i made a few assumptions, but this only makes the equation work for one value but my equation is right. you haven't been following me on this so i will no longer debate because it is a lost cause. also your simplifications have been wrong. my math checks out and is correct. check your own math before you insult mine.

I am not insulting your maths, just not giving you very many marks out of ten. I am sorry cat, but I have already checked mine: I put it into a post in very simplistic terms so you could follow it, and asked you to point out the errors. You were unable to do so. Your equation, which was a correct enough equation, did not work even for the values you chose: You miscalculated. It only works for the two real simple solutions of 2 and 0. I substituted your chosen value of 2+2i into the equation so as to demonstrate that fact for you, but you didn't bother to check it through, and declined to tell me where you think I went wrong.
I have no objections to your choosing a special situation, but when you put the values you chose into your equation they do not give a valid result.

[GILD]

Lol, this thread made me laugh hard. I am willing to hand out free "Math Loser" T-shirts.
Can I buy some advertising space on those shirts?

This has got to be one of the more entertaining ePenii out-whippage threads we've had for a while.
Catinabag, zip it lad.

[kington99]

This has got to be one of the more entertaining ePenii out-whippage threads we've had for a while.
Catinabag, zip it lad.


or to continue the metaphor, tuck it away

[Fooby]

This thread makes my head hurt, and by the way, about the very start of this thread someone said 1 and more are the only real numbers, zero point zero recuring then 1 on the end is the smallest number in my books, which is next to nothing, but still more than nothing.

[yoopers]

Zero point zero recuring then 1 on the end is the smallest number in my books, which is next to nothing, but still more than nothing.
What if you put a ½ on the end instead of a 1. ½ is smaller than one, isn't it?

[Niko]

about the very start of this thread someone said 1 and more are the only real numbers, zero point zero recuring then 1 on the end is the smallest number in my books, which is next to nothing, but still more than nothing.

Here, take a free T-shirt. And thank you for this intimate and disturbing view into the state of the educational system.

[MuniAddict]

Lol, this thread made me laugh hard. I am willing to hand out free "Math Loser" T-shirts. You can wear those and save yourself the work of adding more posts in this thread. catinabag1 gets one in gold, as a special price for his achievement of knowing complex numbers while at the same time remaining completely ignorant of mathematics. :D

And yes, I know I'm mean and arrogant. But it is hard to be not when reading a thread like this. :)Ok Niko, please go back to my *initial* post in this thread, and try to answer the original question. I just thought it was kinda cool that 2+2 *and* 2x2 equal the same number. I couldn't think of any other instance where two of the same numbers (other than zero, which I didn't consider) whether added or mulitplied, resulted in the same total. :)

[dudewithasock]

here's what wikipedia has to say on the issue

"In mathematics, "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is a different type of "number" from the real numbers. Infinity is related to limits, aleph numbers, classes in set theory, Dedekind-infinite sets, large cardinals,[1] Russell's paradox, non-standard arithmetic, hyperreal numbers, projective geometry, extended real numbers and the absolute Infinite."

Oh come on, don't run to wikipedia for that. Seriously, just think about it. You can use any known formula you want, infinite does not represent an absolute number, it represents the idea of a never-ending increasing function, a limit to never be reached. No human has ever 'achieved' infinite or 'observed' infinite, thereby making an abstract concept.

[nimblelight]

a black hole has infinie density. it has a defined mass but infinite density because everything is pulled to a single point in space-time.
no, as you approach the center of a black hole it approaches infinite density.
Infinity remains a limit.
unless i'm wrong.

[Seager]

As I read this thread I'm imagining this:

My math-fu is better than your math fu!
Oh yea! Crouching Alegbra!
I counter with Flying Multiplication!
Have a taste of my Taunting Calculus Technique!
Aha ha! I see an error in your technique! I counter with the Smug Nerd Counter-attack!
Ahh! I see your Math-fu is a match for mine!
Bow before me!
Oh ho! I sneak attack with the Infinite Number Conundrum!
Ahhh! You've trapped me in a quagmire of douchyness for all eternity! Nooooooooooooo
Oh nooo! I've fallen in myself! Aaarrg!

[hobo_chuck]

no, as you approach the center of a black hole it approaches infinite density.
Infinity remains a limit.
unless i'm wrong.
You're not.
YOU CAN"T DIVIDE BY ZERO VOLUME!!!!

[Naomi]

no, as you approach the center of a black hole it approaches infinite density.
Infinity remains a limit.
unless i'm wrong.


Well, astrophysics is not my speciality, but as you pointed out to Catinbag, a black hole does have a non zero physical size, and therefore a non infinite density. I think I read somewhere that if the sun were to collapse sufficiently it would become a black hole about 3 km in diameter. Nothing to worry about though as it is thought to be too small to collapse in this way. I understand the size of a black hole is considered to be the volume or diameter of its event horizon.
As for the density at its centre: theory may well suggest that the matter has condensed into a singularity, but as the internals of a black hole are hardly observable, the theory is likely to remain just a theory. So infinite density? Your guess is as good as mine. And I would not be so bold as to make that guess.

Nao

PS It did worry me some time ago when I read that some scientists were actually likely to make a black hole. Before reading the article my immediate response was to want to lock up these idiots. After reading the article my worries were watered down. see:

http://www.livescience.com/environment/060919_black_holes.html

I'd go out for a drink now if I were you: the earth may not be here when you come back ...didn't someone already do that line? ;-)

[harper]

It recently occured to me that only the number *2*, either added to itself or multiplied by itself, yields the exact same number. So in this case, there is ZERO difference between adding or multiplying. Does this happen with any other number?

In integer modulo number systems in which the modulus is evenly divisible by four it will work for the number 2 and for half of the modulus. For example, in a modulo 8 number system

0-1-2-3-4-5-6-7-0-1...

the sum 4+4=0 and the product 4*4=0. It may work for some other numbers as well in higher order modulo systems (12, 16, 20, 24...) but I can't think of any. This is perhaps outside the region of interest for you. Just pick your number system.

[Brian O.]

I don't know if its been settled yet, but it hadn't been within the first two pages. So, Wikipedia to the rescue! http://en.wikipedia.org/wiki/0_(number)

[Jerrick]

=768

[dudewithasock]

I don't know if its been settled yet, but it hadn't been within the first two pages. So, Wikipedia to the rescue! http://en.wikipedia.org/wiki/0_(number)

I still say it's debatable. Numbers are just ways of communicating universal concepts that our senses can't perceive, anyway.

[maestro8]

Numbers are just ways of communicating universal concepts that our senses can't perceive, anyway.
So that's why people call our one-wheeled contraptions "bikes"? 'Cause they can't perceive the number of wheels?

[maestro8]

Haha idc.
http://www.lurid.org/wordpress/wp-content/uploads/2007/06/idk_my_bff_jill.jpg

[Niko]

Ok Niko, please go back to my *initial* post in this thread, and try to answer the original question. I just thought it was kinda cool that 2+2 *and* 2x2 equal the same number.

The answer was posted in this thread long ago:

x*x = x + x <=> x * (x-2) = 0

This equation has exactly two solutions: x = 0 and x = 2

Even without this very basic algebra this is easy to see: obviously 3*3 = 3+3+3, which is larger than 3+3. For 4 we get 4*4=4+4+4+4 and so on. This is so obvious that I find it hard to get excited about this.

On the complex number bs:
In the complex numbers every polynomial of degree n has exactly n zero crossings. In the real numbers there can be fewer zero crossings (e.g. x^2 = -1). This is by the way one reason why complex numbers were "invented", because they are algebraically complete, as opposed to the real numbers.

Is 0 a number?
The term "number" alone is not properly defined. You have to specify which number system you mean. 0 is not part of the "natural numbers", but is a member of the "rational numbers" for example.

On the volume of black holes:
Again this is first of all a matter of definition. The naive definition would be the volume inside the event horizon. But since the space-time (on which the term "volume" is generally based) inside the event horizon is somewhat "problematic" this probably will not work. Since we do not have a verified theory of quantum-gravity yet we lack the basic knowledge to describe black holes properly. We do not even have a non-verified but at least working theory of quantum theory. So this question has to be postponed, unless one of the geniuses in this thread can come up with one.
Note that the area of a black hole (i.e. the area of the event horizon) is a somewhat better understood term.

Any open questions left?
(but can we please skip the mandatory meaning-of-life-42 reference...)

P.S.: MuniAddict, your vidoes are great. You give me hope that I will be still unicycling when I am an "old geezer". I just hope my math skills will be not as bad as yours by then. :D :)

[Rubix]

Zero is a lack of number/quantity, much like black is an absence of color.

Technically, black is a shade, not a color.

[maestro8]

The answer to life, the universe and everything
http://kikidesign.hautetfort.com/files/Applause.gif

[maestro8]

Technically, black is a shade, not a color.
Technically, you didn't read Dude's post.

[catinabag1]

no, as you approach the center of a black hole it approaches infinite density.

that's what i just said. lol:D

[MuniAddict]

Nope. That's not what I meant. Yes, three 3's are 9, and 3 times three is 9.

This is what I meant:
3+3=6
3x3=9

Only works with the number 2. Nice try though.:p

The answer was posted in this thread long ago:

x*x = x + x <=> x * (x-2) = 0

This equation has exactly two solutions: x = 0 and x = 2

Even without this very basic algebra this is easy to see: obviously 3*3 = 3+3+3, which is larger than 3+3. For 4 we get 4*4=4+4+4+4 and so on. This is so obvious that I find it hard to get excited about this.

On the complex number bs:
In the complex numbers every polynomial of degree n has exactly n zero crossings. In the real numbers there can be fewer zero crossings (e.g. x^2 = -1). This is by the way one reason why complex numbers were "invented", because they are algebraically complete, as opposed to the real numbers.

Is 0 a number?
The term "number" alone is not properly defined. You have to specify which number system you mean. 0 is not part of the "natural numbers", but is a member of the "rational numbers" for example.

On the volume of black holes:
Again this is first of all a matter of definition. The naive definition would be the volume inside the event horizon. But since the space-time (on which the term "volume" is generally based) inside the event horizon is somewhat "problematic" this probably will not work. Since we do not have a verified theory of quantum-gravity yet we lack the basic knowledge to describe black holes properly. We do not even have a non-verified but at least working theory of quantum theory. So this question has to be postponed, unless one of the geniuses in this thread can come up with one.
Note that the area of a black hole (i.e. the area of the event horizon) is a somewhat better understood term.

Any open questions left?
(but can we please skip the mandatory meaning-of-life-42 reference...)

P.S.: MuniAddict, your vidoes are great. You give me hope that I will be still unicycling when I am an "old geezer". I just hope my math skills will be not as bad as yours by then. :D :)

[unibikeling]

Nope. That's not what I meant. Yes, three 3's are 9, and 3 times three is 9.

This is what I meant:
3+3=6
3x3=9

Only works with the number 2. Nice try though.:p

am i the only one that understands, or cares to listen to what terry is saying?

[maestro8]

Nope. That's not what I meant.
Actually, that is what you're implying. You just don't realize it.

[catinabag1]

am i the only one that understands, or cares to listen to what terry is saying?
of course not. terry rocks. :D

[harper]

am i the only one that understands, or cares to listen to what terry is saying?

Yes. You're very special.

[unibikeling]

Yes. You're very special.

and i thank you for recognizing that.



lol..

[Seager]

Man, Harper is one smug bastard.

[catinabag1]

You're not.
YOU CAN"T DIVIDE BY ZERO VOLUME!!!!
you can if you take a limit.

[Niko]

Nope. That's not what I meant. Yes, three 3's are 9, and 3 times three is 9.

I am deeply moved by this thread, it changes my whole perspective on humanity.

I just realized that you are probably the dumbest person I will ever know. :(

[catinabag1]

I am deeply moved by this thread, it changes my whole perspective on humanity.

I just realized that you are probably the dumbest person I will ever know. :(
hey terry is sweet. how about we all stop with the insults.

[GILD]

As I read this thread I'm imagining this:

My math-fu is better than your math fu!
Oh yea! Crouching Alegbra!
I counter with Flying Multiplication!
Have a taste of my Taunting Calculus Technique!
Aha ha! I see an error in your technique! I counter with the Smug Nerd Counter-attack!
Ahh! I see your Math-fu is a match for mine!
Bow before me!
Oh ho! I sneak attack with the Infinite Number Conundrum!
Ahhh! You've trapped me in a quagmire of douchyness for all eternity! Nooooooooooooo
Oh nooo! I've fallen in myself! Aaarrg!
Sigged.

[Tyler_N]

0+0=0
0*0=0
2+2=4
2*2=4

[MuniAddict]

I am deeply moved by this thread, it changes my whole perspective on humanity.

I just realized that you are probably the dumbest person I will ever know. :(Well, you know what they say, "ignorance is bliss.":p

[dudewithasock]

I am deeply moved by this thread, it changes my whole perspective on humanity.

I just realized that you are probably the dumbest person I will ever know. :(

Dude, come on. Uncalled for.

[Brian O.]

I am deeply moved by this thread, it changes my whole perspective on humanity.

I just realized that you are probably the dumbest person I will ever know. :(
I respected you for your knowledge on the discussed subjects but you ruined it when you resorted to personal insults.

[Niko]

I respected you for your knowledge on the discussed subjects but you ruined it when you resorted to personal insults.

O.K., it was unnecessary. And I don't care if anyone here respects me for any knowledge. I just wanted to give the explanations to settle this (after being asked by MuniAddict to do so) and to demonstrate that all these questions actually do have straight forward answers. But obviously that was the naive think to do...

So come on: His question was answered repeatedly in this thread. I even included a more lengthy explanation instead of just repeating the mathematical proof.
Still he does not understand a single word I wrote. But instead of thinking "Hm, I don't understand this, probably because I suck at math." he thinks "Hm, I don't understand this, so it must be wrong.". This is really the most annoying form of arrogance that I know.

It is also the root of most of the problems in the world. Instead of thinking "this is a new aspect I didn't think of, maybe I was wrong..." people often go "this aspect doesn't really fit my opinion, so it must be wrong or irrelevant".

Unicyclists like to think that they are more open minded than the majority, but I find little evidence for that.

[MuniAddict]

(Referring to Nicko's post) I respected you for your knowledge on the discussed subjects but you ruined it when you resorted to personal insults.Thanks Brian and others for your support. But I simply can't take what he [nicko] said seriously; but he's ceratinly entiltled to his opinion(s). I even had a good chuckle, lol! :) Besides, I'm just happy this thread got some replies; some very interesting. Well, time to go riding! No wait...gonna go see the new Indiana movie first!:D

[Niko]

But I simply can't take what he [nicko] said seriously, since his comments about me are so patently absurd, lol. :)

Well, my "insult" actually wasn't meant that serious or personal. Otherwise I would have come up with something far more devastating :D

And I definitely agree on the "let's go riding part". As things stand I am already satisfied if you don't want to become the next president of the US :p

P.S. Who is this "Nicko" guy? He must be a real jerk!

[harper]

Unicyclists like to think that they are more open minded than the majority, but I find little evidence for that.

Nor do you provide any.

[Seager]

Nor do you provide any.

Do you contribute anything to these forums anymore besides posting one liners that pass judgment on other people?

[nimblelight]

you can if you take a limit.
Yes, and that was exactly MY point.....infinity is a limit that cannot be defined, as there are several different levels of infinity
Infinity plus one equals a slightly different infinity-in fact, there are infinite levels of infinity, say your black hole has an atomic mass of 1--a single proton. It has a much smaller event horizon than the theoretical black holes at the center of some galaxies, yet some theorists would place its density at infinity much the same-infinity.

to basics--
how do you take 0 parts out of a pie?
you can't

you may have some luck if they pie is 0

[harper]

Do you contribute anything to these forums anymore besides posting one liners that pass judgment on other people?

Never.

[tobbogonist]

Never.
you still have time.

[maestro8]

Do you contribute anything to these forums anymore besides posting one liners that pass judgment on other people?
Obviously his contributions are going over your head.

Perhaps you should stop surfing the fora whilst lying down.

[MuniAddict]

Well, my "insult" actually wasn't meant that serious or personal. Otherwise I would have come up with something far more devastating :D

And I definitely agree on the "let's go riding part". As things stand I am already satisfied if you don't want to become the next president of the US :p

P.S. Who is this "Nicko" guy? He must be a real jerk!Why thank you kind sir for sparing me from your full, devastating wrath!, rotfl!:p

So anyway peoples, I enjoyed in new Indie movie! Now it's time to practice some sif highjumps..on my lighter KH MUni! :cool:

[unibikeling]

O.K., it was unnecessary. And I don't care if anyone here respects me for any knowledge. I just wanted to give the explanations to settle this (after being asked by MuniAddict to do so) and to demonstrate that all these questions actually do have straight forward answers. But obviously that was the naive think to do...

So come on: His question was answered repeatedly in this thread. I even included a more lengthy explanation instead of just repeating the mathematical proof.
Still he does not understand a single word I wrote. But instead of thinking "Hm, I don't understand this, probably because I suck at math." he thinks "Hm, I don't understand this, so it must be wrong.". This is really the most annoying form of arrogance that I know.

It is also the root of most of the problems in the world. Instead of thinking "this is a new aspect I didn't think of, maybe I was wrong..." people often go "this aspect doesn't really fit my opinion, so it must be wrong or irrelevant".

Unicyclists like to think that they are more open minded than the majority, but I find little evidence for that.

Dude, shut up. Seriously. You misunderstood most everything that Terry, or anyone else, had been saying.

You, Niko, are insulting a very large group of people. Many many of these people are very smart people, that are bound to change the world someday. They see things in ways that other do not, they are interested in things that most others are not. You, sir, are interested in ego bashing everyone on this forum, to make yourself feel bigger. I, after years of bullying, know how people like you act. You decide to take someone down off their 'high horse', and attempt to make them feel like dirt. I can feel for you if the person would have been some extreme arrogant, narssasistic person. But, this is different. This is a very well respected person, that is on the verge of his sport, asking a simple question. You are sick, attacking the ones who don't deserve it.

Graham

[catinabag1]

Dude, shut up. Seriously. You misunderstood most everything that Terry, or anyone else, had been saying.

You, Niko, are insulting a very large group of people. Many many of these people are very smart people, that are bound to change the world someday. They see things in ways that other do not, they are interested in things that most others are not. You, sir, are interested in ego bashing everyone on this forum, to make yourself feel bigger. I, after years of bullying, know how people like you act. You decide to take someone down off their 'high horse', and attempt to make them feel like dirt. I can feel for you if the person would have been some extreme arrogant, narssasistic person. But, this is different. This is a very well respected person, that is on the verge of his sport, asking a simple question. You are sick, attacking the ones who don't deserve it.

Graham

couldn't have said it better myself. lol:D

[yoopers]

Do you contribute anything to these forums anymore besides posting one liners that pass judgment on other people?
Seems your passing a little judgement yourself, there.

Maestro, perhaps lying down is the right thing for Mr. Seager to be doing right now.

[monkeyman]

Oh my dear lordy. All of you, knock it off. The majority of you are supposed to be the people who moderate and who the rest of us look up up on these fora. Quit bickering.

[Into the blue]

So anyway peoples, I enjoyed in new Indie movie!

I was going to say leave the theatre when he gets to South America, but I was too late.

I am truly sorry.

[yoopers]

Oh my dear lordy. All of you, knock it off. The majority of you are supposed to be the people who moderate and who the rest of us look up up on these fora. Quit bickering.
Sorry, sir. I'll try to behave more appropriately. :)

[nimblelight]

you can if you can take a limit

Yes, and that was exactly MY point.....infinity is a limit that cannot be defined, as there are several different levels of infinity
Infinity plus one equals a slightly different infinity-in fact, there are infinite levels of infinity, say your black hole has an atomic mass of 1--a single proton. It has a much smaller event horizon than the theoretical black holes at the center of some galaxies, yet some theorists would place its density at infinity much the same-infinity.

to basics--
how do you take 0 parts out of a pie?
you can't

you may have some luck if the pie is 0
And this is where your so-called "limits" come in.
lim as x approaches 3 of (x^2+x-12)/(x-3) is 1, for example.
however, as you approach dividing by zero volume to find mass you reach an asymptote.....from the negative side it approaches negative infinity, though I must wish you good luck with finding a negative volume.
I continue to disagree with you

[Seager]

Seems your passing a little judgement yourself, there.

Maestro, perhaps lying down is the right thing for Mr. Seager to be doing right now.

Tu Quoque (http://en.wikipedia.org/wiki/Tu_quoque) (Fallacy)

[yoopers]

Tu Quoque (http://en.wikipedia.org/wiki/Tu_quoque) (Fallacy)
Black kettles, my good man.

Beware the monkeyman!

[Seager]

Black kettles, my good man.

Beware the monkeyman!

You didn't understand that fallacy explanation at all, did you?

Father: Smoking is bad for you, Son!
Son: But you smoke, DAD!
<-- This is not proof that smoking isn't bad for you.

Bah. I had a long response but it's just not worth it. There are enough good role models on these forums to offset the few dicks who just make snide remarks while wearing "role model" clothing.

[skrobo]

zero and infinity can be definite in real world cases only, but in the real world you can only truly approach either, therefore, everything in between is false as well and can only be defined with limits.

then comes calculus.

[catinabag1]

zero and infinity can be definite in real world cases only, but in the real world you can only truly approach either, therefore, everything in between is false as well and can only be defined with limits.

then comes calculus.
how can you only approach zero. if i have 1 apple and i take one away, i have zero apples. lol.

[Muniacal]

2 is the only solution for real numbers. if we get into complex and imaginary numbers the solutions i believe are infinite.

it's been so long since i've used those numbers so it will take me a bit to prove this.



OK, so remembering what I have left of my school math, let's get into the possibility of complex solutions to the problem:


A general expression that would be a solution under these conditions would be

a + bi where a and b are both real numbers

AND where b is non zero. ( if b were zero then the answer would have no imaginary component , and would not be complex)

so the original problem gives us this equation:

2 ( a + bi ) = ( a + bi )( a + bi )

expanding

2a + 2bi = a*a - b*b + 2abi

separating out the imaginary terms:

2bi = 2abi

dividing both sides by 2bi , which we can do, for b is non zero.

a=1 , meaning any complex solution has to have a=1

Now taking the real terms

2a = a*a - b*b

substitute our calculated value for a

2 = 1 -b*b

or b*b =-1

therefore b = i

But we have already specified that b is a real number. Hence there can be no complex solutions.

I think this type of proof is called reductio ad absurdum


Catinabag: with so many of the forum's known big scientific guns ranged against you, I would have suspected that I might be wrong a long time ago.

[Muniacal]

addendum to that:

I should have actually concluded with

therefore b= +i or b= -i

this doesn't affect the proof, but it is worthy of note that if we substitute these two values for b into a+bi, then with a=1 we end up back with the two real solutions of 0 and 2.

[GILD]

Can gays do maths?

[Muniacal]

Can gays do maths?

I think so, they always get an answer of 2 to the question 1+1=?

[Fooby]

I think so, they always get an answer of 2 to the question 1+1=?
Yes, but in our logic 1 pie + 1 pie = a great lunch!

[yoopers]

how can you only approach zero. if i have 1 apple and i take one away, i have zero apples. lol.
Maybe you don't take it very far away.

[Fooby]

Sorry, but in my post I missread the post above, I thought it read can guys do maths, but it said can gays do math, my post is about guys math

how can you only approach zero. if i have 1 apple and i take one away, i have zero apples. lol.
there is still 1 apple, it is just moved to a different place, and if it is eaten it is just a change in matter, it still exists, just as poop:D

[Tyler_N]

how can you only approach zero. if i have 1 apple and i take one away, i have zero apples. lol.
I have 3 cookies and i eat 2, now I have 4 cookies because I stole 3 from my friend.

[dudewithasock]

I have 3 cookies and i eat 2, now I have 4 cookies because I stole 3 from my friend.

I like that kind of math!

[dirk]

Not considering imaginary numbers, the reason 2 is the only number you can multiply and add and get the same number is because by definition you are doing the same thing. What I mean is, saying "adding a number to itself" is the same thing as saying multiply by 2.

So you could say, what number can you added to itself three times and get the same number as mulitplying by itself? That would be 3. I think you get the picture...

I can't beleive I'm doing this, I should be looking at unip.

-Dirk

[GILD]

Whatever 'unip' is?

Welcome to the forum Dirk.
An interetsing choice for a first post.

Have you been riding long?

[AlanChambers]

So you could say, what number can you added to itself three times and get the same number as mulitplying by itself? That would be 3. I think you get the picture...

I think the generalisation of this is the argument that every number is interesting in some way. The lowest number regarded as not interesting would of course be interesting for that reason. :-) A problem is that
the argument does not define 'interesting'.

http://en.wikipedia.org/wiki/Interesting_number_paradox

I'm 41, so I'll randomly select that as an exemplar. Starting with 41, add 2, then 4, then 6, then 8, .... This gives a sequence of 40 numbers which are all primes. The 41st number in the sequence is 41 squared. Interesting? Next up is 42, for which Douglas Adams has much to answer.


Al

[yoopers]

Not considering imaginary numbers, the reason 2 is the only number you can multiply and add and get the same number is because by definition you are doing the same thing. What I mean is, saying "adding a number to itself" is the same thing as saying multiply by 2.

So you could say, what number can you added to itself three times and get the same number as mulitplying by itself? That would be 3. I think you get the picture...

I can't beleive I'm doing this, I should be looking at unip.

-Dirk
Yep. I tell my students that multiplication is simply a lazy way of doing addition.

[MuniAddict]

Not considering imaginary numbers, the reason 2 is the only number you can multiply and add and get the same number is because by definition you are doing the same thing. What I mean is, saying "adding a number to itself" is the same thing as saying multiply by 2.

So you could say, what number can you added to itself three times and get the same number as mulitplying by itself? That would be 3. I think you get the picture...

I can't beleive I'm doing this, I should be looking at unip.

-DirkNot counting the non-substantive "number" zero, the number TWO, when doubled (added to itself) *or* muliplied by itself, yields the same total of four. If you double (not TRIPLE lol!) the number three you get six, if multiplied you get nine. That's all I was saying. I'm not referring at all to taking a number like, 7, and saying 7+7+7+7+7+7+oubled7=49, and 7x7=49...wow! How amazing! haha no. :rolleyes::rolleyes::rolleyes:

My original post was quite clear. 2+2=4 and 2x2=4. Following that exact formula, I could not find any other number-past one-where you get the same total when adding TWO of the same numbers, or multiplying TWO of the same numbers. Just found it interesting that's all, lol.:cool:

Once again, as an example: 3+3=6 and 3x3=9. 4+4=8 and 4x4=16, and so on.

[Niko]

This thread gets better and better. :)

And people actually dissed me for calling MuniAddict stupid... :p

I guess after the above post the case can be closed. :D

[MuniAddict]

This thread gets better and better. :)

And people actually dissed me

And for good cause. But if you think you were dissed here-and you most assuredly were-you should read all the PM's I received, lol! This is a family forum, so I can't, and wouldn't post them here! :) :) :)

PS: "Stupid is, as Nicko does":p:cool::D

[harper]

Not counting the non-substantive "number" zero...

I think this might be Niko's main concern in this post. Zero is actually considered one of the most important numbers and its discovery, late among the numbers, is quite remarkable. It's not that intuitive. It still doesn't justify mud-slinging, it's something that you probably just didn't know.

[MuniAddict]

I think this might be Niko's main concern in this post. Zero is actually considered one of the most important numbers and its discovery, late among the numbers, is quite remarkable. It's not that intuitive. It still doesn't justify mud-slinging, it's something that you probably just didn't know.Haha, yeah, I think I may have heard of it. And it's hard to get any mud on you when the "slinger" has no, or should I say, "ZERO" ammunition, lol! ZING! As I indicated just a few posts earlier, and *should* have made clear from the outset, I was referring to the number one or greater.

[Niko]

Zero is actually considered one of the most important numbers and its discovery, late among the numbers, is quite remarkable. It's not that intuitive.

Come on, now you are pulling my leg by writing bs. ;)

It's really funny how people with no mathematical education think that there is actually something mysterious about the number "0". Like it was discovered by Indiana Jones and stolen from the temple of the dead numbers.
It is about as mysterious as Zeno's paradox of Achilles and the tortoise - which has a mysteriousness of exactly zero. ;)

P.S. Damn, MuniAddict beat me to the zero-joke.

[someunicyclist]

how can you only approach zero. if i have 1 apple and i take one away, i have zero apples. lol.

actually, you're wrong.
if you have one apple and you take one away then you still have one apple.

now if you have one apple and someone else takes it away, then you have zero apples.

just my $ 2/100

[dirk]

Whatever 'unip' is?

Welcome to the forum Dirk.
An interetsing choice for a first post.

Have you been riding long?


unip = unicyle pornograghy. Looking at naked pictures of other peoples uni's.

Thanks for the welcome GILD. I'm an engineer, so math piques my curiousity.

I hung out with about 6 guys in high school that all rode schwins. We used to muni a little back then. (We were pretty good, but nothing like the stuff I can do now, which is nothing like the stuff others can do.) Then I sheared the crank in college and stopped riding. About 2 years ago I hooked up with the guy who's unicyle I orignally learn on back in high school and he had a real muni. Last year I finally broke down and bought a KH24 and got hooked. And just this week I built a 36" commuter from parts given or sold cheap from the local uni hardcores. I commuted on it to/from work today...16 miles round trip. There you go...more information than you bargained for.

What does JCTK stand for? I googled it, are you into Celtic Triangle Knots?

[GILD]

unip = unicyle pornograghy. Looking at naked pictures of other peoples uni's.
Ah.



What does JCTK stand for? I googled it, are you into Celtic Triangle Knots?
Just Conversation Thread Killer - it all started in this thread.
(http://www.unicyclist.com/forums/showthread.php?t=39610&highlight=thread+killer)
I don't know if you noticed, but occasionally we get kinda silly around here.
That was one of those occasions.
We were wondering about who 'killed' the most threads.
Gilby ran some searchy thingy and it ended up that, at the time, I had themost last posts on threads in Just Conversation.
I immediately proclaimed myself as Just Conversation Thread Killer, added it to my CV and promptly shortened it to JCTK.

For the waffle tosser bit you'll have to check out the TV series ED.

[ivan]

Zero and infinite both do the same thing, though they aren't really numbers.
Infinity x infinity > infinity + infinity.

Get your abstract concept manipulations straight.

[GILD]

Infinity x infinity > Brittney Spears



Fixed it for ya.

[glen]

2 things....

1) In my digital logic class 1+1=1 and 1*1=1

2) For those who keep saying zero isn't a number...quit it:mad:
I don't want to have to deal with a discontinuity every time I integrate across an axis:D

[dudewithasock]

Infinity x infinity > infinity + infinity.

Get your abstract concept manipulations straight.
I've been taught that infinite is equal to any operation performed on infinite. Blame my teachers if you have to, but it makes sense to me.

Well ok, with a few exceptions, like infinite/infinite.

[Niko]

I've been taught that infinite is equal to any operation performed on infinite. Blame my teachers if you have to, but it makes sense to me.

Well ok, with a few exceptions, like infinite/infinite.

I think both your teachers failed to educate you. :D

Since factual knowledge seems to be of little interest in this thread I don't want to provide the correct answer (didn't work out too well last time). :rolleyes:

[harper]

I think both your teachers failed to educate you.

He only had 2 teachers? Two seems to be a recurring theme in this thread.

[dudewithasock]

I think both your teachers failed to educate you. :D

I take personal offense to that statement. My teachers have all been incredibly adept at teaching both an open mind and the foundations of my current knowledge. I do pity you for thinking that someone has "failed" if their theories don't match up to yours. The theory of infinite that I mentioned does make logical sense to me, and is valid. I'm sure whatever you call the "correct" theory is just as valid. :)

[mscalisi]

I think we can agree that the set of positive integers is infinitely large.
I think we can also agree that the set of positive even integers is infinitely large.

One set is a subset 1/2 the size of the other set, but they are both infinite. Does one equal the other?


I've been taught that infinite is equal to any operation performed on infinite. Blame my teachers if you have to, but it makes sense to me.

Well ok, with a few exceptions, like infinite/infinite.

[glen]

Infinity x infinity > infinity + infinity.

Get your abstract concept manipulations straight.

I don't buy that either.

[glen]

I think we can agree that the set of positive integers is infinitely large.
I think we can also agree that the set of positive even integers is infinitely large.

One set is a subset 1/2 the size of the other set, but they are both infinite. Does one equal the other?

Two people line up 5m from a wall.
Every second, person A moves forward 0m.
Every 2 seconds, person B moves forward 0m.

Does person A reach the wall twice as fast?

[dudewithasock]

One set is a subset 1/2 the size of the other set, but they are both infinite. Does one equal the other?

Yes, they both equal each other. They're both infinite. :)

[mscalisi]

No. However infinity is not equal to zero, and your example only works with zero.

However, as I demonsrated with my previous example, not all sets of infinity are equal.

Two people line up 5m from a wall.
Every second, person A moves forward 0m.
Every 2 seconds, person B moves forward 0m.

Does person A reach the wall twice as fast?

[glen]

No. However infinity is not equal to zero, and your example only works with zero.

However, as I demonsrated with my previous example, not all sets of infinity are equal.

The analogy is that when it takes an infinite number of seconds to go anywhere, it doesn't matter who's going 'twice as fast'.

In your example, the sets both have the same number of elements even though the 'n' set appears to have twice as many as the '2n' set. They both have an equal, infinite number of elements.

[mscalisi]

Why are they equal when one contains twice as many non-zero elements?
Splain so that us slow folk can understand.


In your example, the sets both have the same number of elements even though the 'n' set appears to have twice as many as the '2n' set. They both have an equal, infinite number of elements.

[adjuggler]

He only had 2 teachers? Two seems to be a recurring theme in this thread.
Well, I believe the it can be said "and" his two teachers or his two teacher "together".

[glen]

Why are they equal when one contains twice as many non-zero elements?
Splain so that us slow folk can understand.

I don't claim to be an expert, and this stuff isn't intuitive for me either by any means...

The trick is that the one set *doesn't* contain twice as many non-zero elements...that would only work if the sets were finite. It doesn't make sense for infinite sets.

That paradox you mentioned is explained here (http://www.suitcaseofdreams.net/Even_and_natural_numbers.htm) and here (http://descmath.com/diag/gal.html)

[MuniAddict]

2 things....

1) In my digital logic class 1+1=1 and 1*1=1

I'd quit that class lol! 1+1=1:confused::confused::confused: (Thanks, I needed to LOL! :) )

[Niko]

I take personal offense to that statement. My teachers have all been incredibly adept at teaching both an open mind and the foundations of my current knowledge. I do pity you for thinking that someone has "failed" if their theories don't match up to yours. The theory of infinite that I mentioned does make logical sense to me, and is valid. I'm sure whatever you call the "correct" theory is just as valid. :)

Your statement just didn't make much sense on its own. Yes, there is generally only one "infinity".
But obviously ivan's statement was ment in the sense that

lim_{x -> infinity} (x + x) / (x*x) = 0

So you can "interpret" this as infinity + infinity < infinity * infinity, but this statement doesn't have a sensible meaning on its own.

And I wouldn't take such matters of math personal. Fortunately there is objective truth in math, so if you are wrong then crying won't help. Nobody cares what makes sense to you, unless you can prove it or give a solid background.

[maestro8]

I don't claim to be an expert, and this stuff isn't intuitive for me either by any means...
Then what are you doing making arguments against theories posited by mathematical experts?

The trick is that the one set *doesn't* contain twice as many non-zero elements...that would only work if the sets were finite. It doesn't make sense for infinite sets.
There is no trick here. You're not expected to make sense of the explanation without a proper introduction to set theory... but to summarize:

Think of a set of integers... from zero to whatever you like. There is a one-to-one correspondence between the series "n, n+1, n+2..." and the integers in our set... every number in our series has a representative number in our set.

Now consider the series "2n, 2(n+1), 2(n+2)...". For every number in our set that appears in the series "2n", there is a number in our set that does not appear in the series. Make this set larger, and you'll have a larger "population" of integers that are not represented.

No matter how you slice the problem, the number of represented integers in the "n" series and the "2n" series will never be equal... in fact, this disparity grows as you extend the series (and corresponding set) towards infinity.

If you cannot see this, then you need to go back to school and relearn basic arithmetic.

That paradox you mentioned is explained
The links you provide go to an interpretation of the paradox that comes from the 1600s. Unless you know something I don't, we're in the 21st century now. A lot has been discovered since then. You've got some catching up to do!

Until set theory was created in the late 1800s, the concept of infinity wasn't given much regard by mathematicians. Since its creation, however, set theory has become ubiquitous within mathematics, and can be used to express even the simplest of proofs.

Here is another example that is in the same vein of the n vs. 2n "paradox" posed by Mr. Scalisi.:

Consider a number line of real numbers that extends from zero to infinity. It shouldn't be hard to see there are an infinite number of points on that line.

Now consider the portion of the number line between 1 and 2. Theoretically, there are also an infinite number of points in this section of the number line.

But, wait, if there are infinite points between 1 and 2, and the line extends on into infinity, does that imply there are even more points on the line then we first supposed?

No. The number of points on that line all exist within the set of real numbers R. This is a well-defined set; we should easily be able to distinguish numbers within this set.

There are, however, sets that exist in which the set R is but a subset of the entire "population". There must be, then, "larger infinities" than what we've been talking about, and indeed, set theory explains how such sets can exist, how to describe them, and how they are significant.

Set theory is not without it's own paradoxes, but at it illuminates the simple n / 2n problem that has left you completely flummoxed, as well as many other problems in modern mathematics.

[Niko]

Small addition to my last post:
In terms of cardinality of sets there are indeed two types of "infinity": countable and uncountable.
But infinity as some kind of number is more associated with taking limits.

[glen]

Then what are you doing making arguments against theories posited by mathematical experts?

Until about an hour ago, I had never heard of Georg Cantor. My apologies.

Thanks for the post.

[dudewithasock]

But obviously ivan's statement was ment in the sense that

lim_{x -> infinity} (x + x) / (x*x) = 0

It wasn't obvious to me, so I'm sorry. This is still confusing to me, though...based on what I've been taught, I would approach this using L'Hospital's Rule (since you have infinite over infinite), giving you

lim {x -> infinite} 2 / (2x), which would be zero...I'm not entirely sure what that proves, though that's mostly due to my not having taken any college math yet.

[catinabag1]

ok so going back to my theory that there is an infinite amount of complex numbers with the properties that were discussed at the beginning of this thread. there are an infinite number of ways to describe any number using complex numbers. for example to describe the number 2 the complex number can be 3+i^2=2 or even 4+2(i)^2=2. so the number two can be expressed with this formula a+bi where b=(a-2)i. so take this formula and plug in any number, for instance 10. we get 10+8(i)^2=2. i rest my case.

[glen]

ok so going back to my theory that there is an infinite amount of complex numbers with the properties that were discussed at the beginning of this thread. there are an infinite number of ways to describe any number using complex numbers. for example to describe the number 2 the complex number can be 3+i^2=2 or even 4+2(i)^2=2. so the number two can be expressed with this formula a+bi where b=(a-2)i. so take this formula and plug in any number, for instance 10. we get 10+8(i)^2=2. i rest my case.

Sub b=(a-2)i into a+bi

=a+(a-2)i^2
=a-(a-2)
=2

which is hardly impressive because we knew 2 was a solution.

If we wanted to play by those rules, we could say there are infinite solutions without needing to invoke imaginary numbers.

4+2i^2 is just 4-2 which isn't a number. 2 is a number.

[glen]

It wasn't obvious to me, so I'm sorry. This is still confusing to me, though...based on what I've been taught, I would approach this using L'Hospital's Rule (since you have infinite over infinite), giving you

lim {x -> infinite} 2 / (2x), which would be zero...I'm not entirely sure what that proves, though that's mostly due to my not having taken any college math yet.

lim(x->∞) (x+x)/(x*x)
=lim(x->∞) 2x/(x*x) <-factor out an x
=lim(x->∞) 2/x
=0

[Seager]

there are an infinite number of ways to describe any number using complex numbers.

You aren't playing by the rules. I can describe you many different ways, but there is still only one you. It doesn't matter how many crazy ways you represent 2, you are still only representing 2.

[dudewithasock]

lim(x->∞) (x+x)/(x*x)
=lim(x->∞) 2x/(x*x) <-factor out an x
=lim(x->∞) 2/x
=0

...thanks for restating what I said. I got zero with what I did also. But what exactly does that prove?

[Niko]

...thanks for restating what I said. I got zero with what I did also. But what exactly does that prove?

When some people see this for the first time they are puzzled, because both numerator and denominator alone are infinite in the limit. So they think infinity / infinity = 1.
Of course this does not make sense, one has to be more careful when taking limits. But as a rule of thumb one can argue that infinity * infinity > infinity + infinity, therefore the result is zero.

When terms like "infinite" are used in math they are always defined in a precise way. Confusion only arises if one does not follow the definitions but starts to argue in a superficial way (like in the nonsensical question "Is zero a number?").

[Niko]

ok so going back to my theory that there is an infinite amount of complex numbers with the properties that were discussed at the beginning of this thread. there are an infinite number of ways to describe any number using complex numbers. for example to describe the number 2 the complex number can be 3+i^2=2 or even 4+2(i)^2=2. so the number two can be expressed with this formula a+bi where b=(a-2)i. so take this formula and plug in any number, for instance 10. we get 10+8(i)^2=2. i rest my case.

The complex numbers just called, they want you to stop talking about them. They are offended by your ignorant misunderstanding. They say you have obviously no idea what they are about.

I am just relaying this message, but I absolutely agree with them by the way.

[dudewithasock]

When some people see this for the first time they are puzzled, because both numerator and denominator alone are infinite in the limit. So they think infinity / infinity = 1.
Of course this does not make sense, one has to be more careful when taking limits. But as a rule of thumb one can argue that infinity * infinity > infinity + infinity, therefore the result is zero.

When terms like "infinite" are used in math they are always defined in a precise way. Confusion only arises if one does not follow the definitions but starts to argue in a superficial way (like in the nonsensical question "Is zero a number?").

So was I right in using L'Hospital's Rule, or no? It seemed logical to me.

Ok ok, I see what you're saying. Because zero is the limit, the denominator approached infinite at a faster rate than the numerator, which supports the idea of infinite^2 being greater than 2*infinite. That makes sense.

Yay! Math is fun!

[Niko]

So was I right in using L'Hospital's Rule, or no? It seemed logical to me.

Ok ok, I see what you're saying. Because zero is the limit, the denominator approached infinite at a faster rate than the numerator, which supports the idea of infinite^2 being greater than 2*infinite. That makes sense.

Yay! Math is fun!

Yes, you can use L'Hospital's Rule (the conditions of the theorem are met I believe). In this case it is not really necessary, because you can simplify the expression.

The important point is that you can't just switch the order of dividing and taking the limit. It doesn't even make sense in this case, because infinity here is not some kind of number but a short form for saying that the expression diverges in the limit.

And I agree that math is extremely cool. It is also difficult by most standards and demands a high level of discipline.

[catinabag1]

The complex numbers just called, they want you to stop talking about them. They are offended by your ignorant misunderstanding. They say you have obviously no idea what they are about.

I am just relaying this message, but I absolutely agree with them by the way.
mmmm. i fi have no idea what i'm talkin about i dare you to find fault in my last post.

[glen]

mmmm. i fi have no idea what i'm talkin about i dare you to find fault in my last post.

Seager and I explained in very, very simple terms why you're wrong. If you can't understand the explanations, the wise thing to do would be to ask for clarification. That's how people get smarter. Plugging your ears and saying the same thing over and over again accomplishes nothing.

Alas, I shall try to make this explanation simpler.

You say a+bi with b=(a-2)i equals 2. Correct. Let's set that up and simplify it.

a+(a-2)i^2 = 2
a-(a-2) = 2
2 = 2

So, 2 = 2. Good. Now, what you are arguing is that the number on the left hand side is DIFFERENT from the number on the right hand side. It's not. It's a 2.

The two numbers are the same, ie. they are equal. We can tell that because there is an equal sign. That means equal, as in, they are the same number.

It's not a different "way" of expressing a 2...it's a freaking 2.


Consider it this way...

Suppose I have 5 animals, and they are all different. They are a jackel, a jackel, a jackel, a jackel, and a jackel.

The appropriate response to this claim would be, "The animals called, they want you to stop talking about them".

[catinabag1]

Seager and I explained in very, very simple terms why you're wrong. If you can't understand the explanations, the wise thing to do would be to ask for clarification. That's how people get smarter. Plugging your ears and saying the same thing over and over again accomplishes nothing.

Alas, I shall try to make this explanation simpler.

You say a+bi with b=(a-2)i equals 2. Correct. Let's set that up and simplify it.

a+(a-2)i^2 = 2
a-(a-2) = 2
2 = 2

So, 2 = 2. Good. Now, what you are arguing is that the number on the left hand side is DIFFERENT from the number on the right hand side. It's not. It's a 2.

The two numbers are the same, ie. they are equal. We can tell that because there is an equal sign. That means equal, as in, they are the same number.

It's not a different "way" of expressing a 2...it's a freaking 2.


Consider it this way...

Suppose I have 5 animals, and they are all different. They are a jackel, a jackel, a jackel, a jackel, and a jackel.

The appropriate response to this claim would be, "The animals called, they want you to stop talking about them".

i get that. but what i'm saying is there is still an infinite number of complex numbers to that solution even if they stll all equal 2.

[Seager]

i get that. but what i'm saying is there is still an infinite number of complex numbers to that solution even if they stll all equal 2.

What you mean to say is "There is only one answer, 2, which can be represented in an infinite number of ways using complex numbers."

Here is a word problem for you.

Who made the post that I just replied to?
Answer: Cantinabag1

But lets say that whenever I say Jack I really mean Catinabag1. And whenever I say:
John=Catinabag1
Mike=Catinabag1
Jose=Catinabag1
Mark=Catinabag1
Paul=Catinabag1
George=Catinabag1
Ringo=Catinabag1
YourMom=Catinabag1

Now, are there nine solutions to my above word problem, or just one?

[catinabag1]

What you mean to say is "There is only one answer, 2, which can be represented in an infinite number of ways using complex numbers."

Here is a word problem for you.

Who made the post that I just replied to?
Answer: Cantinabag1

But lets say that whenever I say Jack I really mean Catinabag1. And whenever I say:
John=Catinabag1
Mike=Catinabag1
Jose=Catinabag1
Mark=Catinabag1
Paul=Catinabag1
George=Catinabag1
Ringo=Catinabag1
YourMom=Catinabag1

Now, are there nine solutions to my above word problem, or just one?

there are an infinite number of non 2 answers to that problem, i just dont know the math to show the proof. and about it all equaling 2, i guess it depends on how you look at it. even though 3+i^2 and 4+2i^2 both equal two, they are expressed differently. some may say they are different numbers because they appear different and some may say they are the same since they both equal two. it all depends on how you look at it. in my book i agree with you completely. they all equal two. but what i initially said, and what got taken the wrong way, is there are an infinite number of ways to express the number 2 and there are an infinite number of ways to express any number.

[Seager]

is there are an infinite number of ways to express the number 2 and there are an infinite number of ways to express any number.

I can agree with that, and you don't need complex numbers. 3-1, 4-2, 5-3,...

It does seem like a silly point to make, though. :)

[catinabag1]

I can agree with that, and you don't need complex numbers. 3-1, 4-2, 5-3,...

It does seem like a silly point to make, though. :)
yes but you are subtracting to get your number, therefore it is unsimplified and therefore not an answer. when you use complex numbers the form a+bi is simplified and therefore an answer.

[glen]

yes but you are subtracting to get your number, therefore it is unsimplified and therefore not an answer. when you use complex numbers the form a+bi is simplified and therefore an answer.

...and therein lies your mistake. You answer is NOT of the form a+bi, since you are squaring the i and removing the imaginary component.

Your answer is not simplified, and I have shown you repeatedly how to simplify it. Your answer simplifies to 2. It does not have an imaginary component. If it did, I wouldn't be able to simplify it to a 2. But I can simplify it to a 2, because it IS a 2.

It's a 2, a whole 2, and nothing but a 2, so help me God.

[Seager]

"First shalt thou take out the Holy Pin. Then, shalt thou count to three, no more, no less. Three shalt be the number thou shalt count, and the number of the counting shalt be three. Four shalt thou not count, nor either count thou two, excepting that thou then proceed to three. Five is right out. Once the number three, being the third number, be reached, then lobbest thou thy Holy Hand Grenade of Antioch towards thou foe, who being naughty in my sight, shall snuff it."

King Arthur: One, two, five!
Sir Galahad: Three sir!
King Arthur: THREE!

Damnit, I'm quoting Monty Python on the internet. Kill me now.

[GILD]

Isn't there a derivation of Godwin's Law that applies to Monty Python?

[AlanChambers]

there are an infinite number of non 2 answers to that problem, i just dont know the math to show the proof.

There are not. There are precisely two solutions to x^2 = 2x: 0 and 2. Since you state that you can't prove your claim, it seems to me that you are on something of a hiding to nothing. You are wrong: just accept the fact and move on.

Well, to be fair, this thread has only considered complex numbers (which of course entail reals, rationals and integers): there are many other solutions in finite rings, such as integers modulo some prime or something like that. For example, (8 x 8) mod 3 = 1, and (8 + 8) mod 3 = 1. Yay!

I'm no expert on abstract algebra, so I leave it as an exercise for you to find some genuine complex solutions in some ring or other. Do Gaussian integers modulo some prime satisfy the requirements for an integral domain?


Al

[Seager]

Isn't there a derivation of Godwin's Law that applies to Monty Python?

Did you just call Terry Gilliam a Nazi?

[Naomi]

...and therein lies your mistake. You answer is NOT of the form a+bi, since you are squaring the i and removing the imaginary component.

Your answer is not simplified, and I have shown you repeatedly how to simplify it. Your answer simplifies to 2. It does not have an imaginary component. If it did, I wouldn't be able to simplify it to a 2. But I can simplify it to a 2, because it IS a 2.

It's a 2, a whole 2, and nothing but a 2, so help me God.


My God, I thought Catinabag had long given up on this one. Is he still wittering on?

Wasting your time Glen: others have said more or less the same as you but Catinabag appears unable to see out of his bag. Back in post 125/126 Muniacal actually proved that there is no solution of the form a+bi, but Cat appeared to be unwilling to read it or unable to understand it.
For Cat to now start saying that a solution is 10+(8 times (i squared)) is just further ineffective wriggling in his bag. Sooner or later that wriggling will become so annoying that somebody will surely drown him...and soon please!
Two solutions to the original problem, and only two, for no matter what pretty clothes Catinabag tries to dress the numbers up in, they remain the same two answers.

Thank God I won't have to teach him next year.

Nao

[GILD]

Did you just call Terry Gilliam a Nazi?
Yes, and a green one at that.

Do you want to make something of it - (johncleesedividedbysillywalks??!?) x 2?

[beeper]

Zero is a lack of number/quantity, much like black is an absence of color.

I like to think of white as an absence of color.

[MuniAddict]

I like to think of white as an absence of color.White is comprised of all colors of the spectrum.

[dudewithasock]

White is comprised of all colors of the spectrum.

The visible spectrum, anyway.

[beeper]

White is comprised of all colors of the spectrum.


That, I do know, but it seems more empty to me than black does. Thats all i'm getting at, although it is very thread irrelavant.

[Seager]

That, I do know, but it seems more empty to me than black does. Thats all i'm getting at, although it is very thread irrelavant.

It depends if you are talking about additive or subtractive color. In light, projection, etc, white is all colors. In paint black is all colors.