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"