Veeky Forums, Is 1 infinitely larger than 0?

Veeky Forums, Is 1 infinitely larger than 0?
I'm in an argument with a friend and he says it is not, I say it is because 0 is basically nothing and might as well not exist, so any-number (except 0) is infinitely larger than 0,, so 1 is is infinitely bigger than 0.

Am I right or is he?

>Is 1 infinitely larger than 0?
Proportionally, yes. In absolute terms, no, it's only larger by 1.

A number x is z times larger than y means that x/y=z. 1/0 is undefined, so your question has no answer.
>inb4 wheel theory

a is infinitely larger than b if for any integer n, a > bn. so yeah.

>hurrrrrrrrr

zero times infinity is still zero. this proves that nothing can be infinitely larger than zero.

however, one is infinitely larger than an infinitesimal, which is distinctly different than zero.

Yeah, I mean in proportional terms.

Obviously depends on your definition of the word "larger." Additively, it is "one unit" larger than zero. Multiplicatively, it is infinitely larger than zero.

Put it into some real-world context. If I have one dollar and you have zero dollars, I don't have infinitely more money than you. I have one unit more, which is enough to buy a pack of gum or something. That's an "additive" comparison, no infinities involved.

I guess a "multiplicative" comparison would be something like -- my odds of winning some wager against you are 1:0... I win no matter what, you lose no matter what. So I am infinitely more likely to win than you.

>zero times infinity
Literally stopped reading there. Undergrads are fucking retarded.

1 is proportional to 0 at the ratio of 1/0, which is undefined. Now you have a nice way to end the argument without losing or winning.

define "infinitely larger"

high school boy doesn't know what a limit is yet?
you must be at least 18 to post on this board

In binary terms, yes.

There are an uncountably infinite amount of numbers in between 0 and 1, so in that sense yes. But if by larger you mean distance, then no

Just didn't want to use bigger 2 times

>high school boy doesn't know what a limit is yet?
Saying "infinity times 0" does not imply you're taking a limit. Even if it did, consider:
[math] \lim_{x \to \infty} (x^2 \cdot \frac{1}{x}) =
"\infty" [/math] or undefined, whichever floats your boat.
Here we have an "infinity" (the x^2 as x goes to infinity) times a "zero" (1/x as x goes to infinity) which does not have a defined limit of zero.

But an infinitesimal is bigger than zero, aka one is more than infinitely bigger than zero.

yet the limit as x goes to infinity of x^2 * 0 is still equal to zero.

the dealio is that x^2 approaches infinity much faster than 1/x approaches zero. you can always flip it on its head and and take the limit as x goes to infinity of x * 1/x^2 , which is equal to zero.

the point is that you're fucking retarded if you don't understand that zero multiplied by itself is still zero, not even at any arbitrarily large number, but at infinity as well.

nothing is infinitely larger than zero.

*eats popcorn*

you don´t have an infinity times a zero since
x^2*1/x = x
therefore it is infinity

No. If you say a is x-times larger than b, you mean that a * x = b.

Try 0 * "infinity". You still get 0.