Infinity * Zero = Any Number ARGUE HERE

[Tokzic]

Re: Infinity * Zero = Any Number ARGUE HERE

o = o thats it infinety is an undetermined number it is larger than any other number its infinety

thank you for your insightful contribution to the topic

[skyrunner06]

Re: Infinity * Zero = Any Number ARGUE HERE

heres what wikipedia says :In mathematics, infinity is relevant to, or the subject matter of, limits, aleph numbers, classes in set theory, Dedekind-infinite sets, large cardinals, Russell's paradox, hyperreal numbers, projective geometry, extended real numbers and the absolute Infinite.

[Doug31]

Re: Infinity * Zero = Any Number ARGUE HERE

Here's how I think things work, even though most of it is based off of the limit as x approaches infinity. I'll base this off of one of shash's posts.
Inf * inf = inf
True.

0 * 0 = 0 (lol, obviously)
True.

Inf * -inf = -inf
true.

Inf - Inf = undef
In finding the limits as x approaches infinity, this can be anything, depending on the rate at which each piece of the equation is approaching infinity. lim(x->infinity) e^x - lim(x->infinity) x^2=infinity, lim(x->infinity) e^x - lim(x->infinity) e^x = 0, and lim(x->infinity) x^2 - lim(x->infinity) e^x = -infinity.

also

0^inf = undef
This most certainly always equals 0. It doesn't matter what rate the number is approaching 0 at, since even .5^infinity would still equal 0.

1^inf = undef
True, in terms of limits. Again, if the equation of the base is approaching 1 really slowly, like 1+1/x*2, and the exponent is approaching infinity really fast, like e^x, then it would equal infinity, and the other way around would equal one, and approaching one from the between 0 and 1 side could make it equal 0.

inf/0 = inf
I disagree. If it were approaching 0 from the negative side, it could equal negative infinity, also.

0/inf = 0
True.

[banditcom]

Re: Infinity * Zero = Any Number ARGUE HERE

I know my calculus it says u + me = us


But yeah what Reach said.

[Doug31]

Re: Infinity * Zero = Any Number ARGUE HERE

Also, in responce to the title, "Infinity * Zero = Any Number ARGUE HERE," it really can equal any number. If the infinity = lim(x->infinity) e^x, and the zero = lim(x->infinity) 1/x, then it equals infinity, and if the infinity equals lim(x->infinity) ln x, and the zero = lim(x->infinity) 1/x, then it equals zero.

To make it so that it can equal any number, make it lim(x->infinity) ax and lim(x->infinity) 1/x, which would equal 1, if a=1, then just change a to make it any number you want.

[ToshX]

Re: Infinity * Zero = Any Number ARGUE HERE

I can't think of anything times zero where it is not zero.

Therefore I see it as zero.

[Shashakiro]

Re: Infinity * Zero = Any Number ARGUE HERE

Doug: we aren't talking about limits at all, so basically everything you said contradicting me is wrong.

lim x -> inf (.5^x) is not the same thing as .5^inf. The former is 0, the latter is undefined.

[Doug31]

Re: Infinity * Zero = Any Number ARGUE HERE

How does lim(x->infinity) e^x = infinity not satisfy wikipedia's definition of infinity? Also, 0^infinity does equal 0, and so does (1/2)^infinity, which equals (1/2)*(1/2)*(1/2)*...=0, which is a horrible way of me explaining it, which doesn't prove anything, but I know 0^infinity=0 is true.

Edit: ignore that first sentence.

[Shashakiro]

Re: Infinity * Zero = Any Number ARGUE HERE

Ah, I think you're right about 0 and .5...I was probably getting 0^inf confused with inf^0 (which is definitely undefined).

shutup it's been a while lol

[JKPolk]

Re: Infinity * Zero = Any Number ARGUE HERE

How does lim(x->infinity) e^x = infinity not satisfy wikipedia's definition of infinity? Also, 0^infinity does equal 0, and so does (1/2)^infinity, which equals (1/2)*(1/2)*(1/2)*...=0, which is a horrible way of me explaining it, which doesn't prove anything, but I know 0^infinity=0 is true.

Edit: ignore that first sentence.

Technically, (.5)^infinity =/= 0, but the limit as the power approaches infinity = 0. But that's just a minor technicality. Most of the issues in this thread have just been confusing the usage of the symbol infinity with a limit as x->infinity.

[itmorr]

Re: Infinity * Zero = Any Number ARGUE HERE

Why is infinite - infinite undefined?

[_A2P]

Re: Infinity * Zero = Any Number ARGUE HERE

ANYTHING WITH INFINITY IS UNDEFINED

THE END

[Reach]

Re: Infinity * Zero = Any Number ARGUE HERE

Why is infinite - infinite undefined?

Because the solution can be infinity, 0, or negative infinity.

Actually, there might be other ridiculously complicated solutions, but nothing I am aware of.

Think of it this way. It's like a teeter totter. If the two weights on the teeter are equal, you have 0 movement. If one side is more than the other the teeter tips all the way over.

x-> infinity

e^x - e^x = 0
e^x - x = infinity
x - e^x = -infinity

pretty basic stuff. The only difference between this and the teeter totter is we arn't dealing with actual values, but RATES. For example, e^x - x is infinity because e^x beats x to infinity.

Actually, e^x beats any polynomial to infinity. If you want some quick fun with calculus show lim x-> infinity (x^10000000000000)/e^x = 0

[JKPolk]

Re: Infinity * Zero = Any Number ARGUE HERE

lim x-->infinity e^x - x^1000000000 = infinity

Using L'Hospital's Rule:

1billionth derivative of e^x
-----
1billionth derivative of x^1000000000

=

e^x
--
1000000000

= infinity
baddabing badda boom

[Reach]

Re: Infinity * Zero = Any Number ARGUE HERE

lim x-->infinity e^x - x^1000000000 = infinity

Using L'Hospital's Rule:

1billionth derivative of e^x
-----
1billionth derivative of x^1000000000

=

e^x
--
1000000000

= infinity
baddabing badda boom

e^x / -x^-1000000000, since l'hopital only applies to quotients.

And even if you could do that, it would be 1000000000! on bottom.


I changed the question anyway. Not like you were supposed to post the answer here though. >.>