Infinity * Zero = Any Number ARGUE HERE

[EI_Tizzy]

Well, I don't know if anyone in here is in Calculus, but you can have infinity x 0 = any number... it just depends how you arrive at infinity and zero. Also, you have to assume you CAN go out to infinity.

For instance, take the limit of x sin(1/x) as x goes to infinity. The "x" term will approach infinity (obviously), and the "sin(1/x)" term approaches 0. Yet, as we can see on a graphing calculator, the ends of this equation clearly go to 1. So in this case, infinity x 0 = 1.

In another example, take the limit of x ln(x) as x goes to 0. The "x" term reaches 0 and the "ln(x) term reaches -infinity. Using l'Hopital's Rule with (ln(x))/(1/x), the limit is now (1/x)/-(1/x^2). Multiply top and bottom by x^2 and now the answer is the limit of -x as x goes to 0, which is 0. Here, infinity (or rather, -infinity) x 0 = 0.

It all depends how the numbers are reached...

[vengefullangel]

Zero is not equal to 1/inf.

1/inf APPROACHES zero.

Even I with my limited knowledge of math know this much. Your entire beginning premise is false. Therefore I don't even have to read on to know that your proof is wrong.

Don't hurt yourself yelling. And before completely displaying your stubbornness, first consider this:

Imagine you are running down a road and you are trying to catch up to a turtle. You approach the turtle and get to half the distance to the turtle from where you started. You then get to half that distance. This continues.

When does it stop? Your distance to the turtle, as its being halved an infinite number of times, approaches 0. If it never reaches 0, you can never pass the turtle.

This is one of Zeno's paradoxes. It's also a gigantic headache. The thing is. Since you can actually pass the turtle, something has to happen to your distance as it gets closer to zero. What happens? Leave that to physicists. What we do know is that basically the distance at some point becomes non-existent. And so why can't the distance between two numbers have the same effect?

In other words if X approaches infinitely close to infinity why can't X be infinity?

Besides, X was approaching infinity, not 1/inf approaching 0.

Originally Posted by EI_Tizzy

Well, I don't know if anyone in here is in Calculus, but you can have infinity x 0 = any number... it just depends how you arrive at infinity and zero. Also, you have to assume you CAN go out to infinity.

Well, I am in calculus. It's nice to meet someone who knows what they're talking about.

Originally Posted by EI_Tizzy

For instance, take the limit of x sin(1/x) as x goes to infinity. The "x" term will approach infinity (obviously), and the "sin(1/x)" term approaches 0. Yet, as we can see on a graphing calculator, the ends of this equation clearly go to 1. So in this case, infinity x 0 = 1.

Sorry to be an ogre (especially if I turn out to be wrong) but....

The limit as x approaches infinity of sin 1/x does not equal 1. The sin of 0 does not equal 1. Sin (0) = 0. The limit as x approaches infinity of cos 1/x does equal 1 however.

Originally Posted by EI_Tizzy

In another example, take the limit of x ln(x) as x goes to 0. The "x" term reaches 0 and the "ln(x) term reaches -infinity. Using l'Hopital's Rule with (ln(x))/(1/x), the limit is now (1/x)/-(1/x^2). Multiply top and bottom by x^2 and now the answer is the limit of -x as x goes to 0, which is 0. Here, infinity (or rather, -infinity) x 0 = 0.

It all depends how the numbers are reached...

I actually thought this had a mistake until a minute ago:

{all numbers except inf}

I was sure that zero did not belong in the set for a second. But you've saved the day with your limit. My class actually had to rush through the limit as x approaches infinity and negative infinity section. No worries, I still understood it. We just never got to the limits of natural logarithms.

[lord_carbo]

Originally Posted by Chrissi

Zero is not equal to 1/inf.

1/inf APPROACHES zero.

Even I with my limited knowledge of math know this much. Your entire beginning premise is false. Therefore I don't even have to read on to know that your proof is wrong.

Actually, with limits you can prove that infinitesimals = 0.

[xinpig]

but still isnt anything * 0 still 0????
its basic mathematics
say infinity = 99999999999999999999999 in this case
99999999999999999999999 * 0 = 0
no matter how you look at it anything * 0 = 0

[xinpig]

this is just like pi

btw x/inf gets you a very small # provided x does not = 0
it just tiny .00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
still aint 0 no matter how many 0 you add

[GuidoHunter]

Read the thread before you post in it. Also, don't double post and get some decent grammar.

--Guido

http://andy.mikee385.com

[Reach]

Originally Posted by xinpig

this is just like pi

btw x/inf gets you a very small # provided x does not = 0
it just tiny .00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
still aint 0 no matter how many 0 you add

The reason this isn't true is hard for most people to understand because of the concept of infinity itself.

Infinity does not have a quantifiable 'rate'...that is, you cannot imagine a number that is constantly getting smaller and smaller like you have shown here. It is false to do so.

Infinity exists without any bounds, and therefore its rate has no bounds. Instead of imagining what you have just shown, take a minute to try and imagine what would happen if you let those zeros extend such that they exist everywhere that can exist at any given point in time.

Difficult, isn't it? But what happens to that one? It's gone! You'll never find it. The unbounded set of zeros infront of it exist everywhere that can exist, unbounded annihilating the 1.


If anything, just remember that you cannot quantify the value of infinity in this case.

[EI_Tizzy]

Originally Posted by vengefullangel

Sorry to be an ogre (especially if I turn out to be wrong) but....

The limit as x approaches infinity of sin 1/x does not equal 1. The sin of 0 does not equal 1.

Sorry to be an ogre, as well, but:

Originally Posted by EI_Tizzy

For instance, take the limit of x sin(1/x) as x goes to infinity. The "x" term will approach infinity (obviously), and the "sin(1/x)" term approaches 0. Yet, as we can see on a graphing calculator, the ends of this equation clearly go to 1. So in this case, infinity x 0 = 1.

I said it was 0, but the limit of xsin(1/x) is 1.

Like it's been said many times before, we ALL know X can never reach infinity... but if we couldn't ASSUME it does, Calculus couldn't ever work, and most of the technology you use today wouldn't be able to function, just because things can't be quantized into infinitely small/large parts.


Calculus is SOOO awesome too. You can prove that 1^infinity is exactly e... or any power of e for that matter. I guess some people won't learn until it's presented in front of them, which obviously can't happen as infinity isn't a concrete idea. Oh well XD

[lord_carbo]

Originally Posted by EI_Tizzy

Calculus is SOOO awesome too. You can prove that 1^infinity is exactly e... or any power of e for that matter. I guess some people won't learn until it's presented in front of them, which obviously can't happen as infinity isn't a concrete idea. Oh well XD

Maybe my informal education is limited, but I'm fairly certain you can't "prove" 1^inf is equal to any power of e because, well, 1^inf isn't even really equal to anything and e is a mathematical constant.

[rel89]

I can't agree that -infinite exists.

[Raveren]

Heh, this great, I can't wait till I take Calculus AP next year....

[RandomPscho]

Which Ap course? AB or BC? Just A?

[bluguerrilla]

Originally Posted by lord_carbo

Maybe my informal education is limited, but I'm fairly certain you can't "prove" 1^inf is equal to any power of e because, well, 1^inf isn't even really equal to anything and e is a mathematical constant.

The reason that you can say that "1^infinity" can be anything is because it is an indeterminate form -- you have to get there somehow. Usually you start with an expression like (1-1/x)^x and you consider what this is equal to as x goes to infinity. If you just put in infinity you get "1^infinity" but if you do it carefully you get 1/e. It's the "doing it carefully" and not naively part that gets people in trouble.

So, you really can say that "1^infinity" can be anything, especially if you change that expression above to be (1-y/x)^x. Then you get e^-y as the limit, which can be any real number (yes even zero).

[lord_carbo]

Originally Posted by rel89

I can't agree that -infinite exists.

It does, and if you take/learn calculus you'll use it.

Originally Posted by bluguerrilla

The reason that you can say that "1^infinity" can be anything is because it is an indeterminate form

1^infinity isn't indeterminate--it's undefined. There's a difference. And AFAIK, expressions can't be indeterminate because you're not solving for anything in an expression, but that's irrelevant either way.

[Kilgamayan]

Why do people keep posting in this thread? x(

[Linkisdoomed]

Here's my two cents:

Infinity = any number
x = variable (any real, nonreal, imaginary number)
0 = nothing.

Infinity * X = Any real, nonreal, imaginary number.
" * 0= Nothing. Anything * 0 = absolutely nothing.

[lord_carbo]

Originally Posted by Kilgamayan

Why do people keep posting in this thread? x(

Because people feel like they can put their "two cents" on fact, e.g. the post above me.

[RandomPscho]

STOP POSTING IN THIS THREAD. Please.

Infinity * 0 = Undefined.

[bluguerrilla]

Originally Posted by lord_carbo

It does, and if you take/learn calculus you'll use it.


1^infinity isn't indeterminate--it's undefined. There's a difference. And AFAIK, expressions can't be indeterminate because you're not solving for anything in an expression, but that's irrelevant either way.

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

Uhh... yes it is /\ and no it isn't \/

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

Edit: Even better: http://mathworld.wolfram.com/Indeterminate.html

[lord_carbo]

Originally Posted by bluguerrilla

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

Uhh... yes it is /\ and no it isn't \/

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

Edit: Even better: http://mathworld.wolfram.com/Indeterminate.html

Oh.

Edit: OH.