what is infinity divided by infinity?

You can't say. It could be infinity, 0 or any other value. What I'm saying is about function's limits.

In another terms, it depends on how the first infinite is infinite compared to the second one.

how can one infinity be bigger than another?

Let's take the case of the function f(x)=x^3/x^2

lim x^3 when x go infinity = infinity and lim x^2 when x go infinity = infinity

We have an infinity/infinity case... but

x^3 go infinity quicker than x^2 so when x go infinity x^2 become negligeable in front of x^2 and limit of the function f is infinity.

Also lim g(x)=x^2/x^3 when x goes infinity is 0

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