what is infinity divided by infinity?

From elementary school, our math teacher tells us that anything divided by itself is equal to one. But why is infinity divided by infinity undefined?

To answer this question, we must know that infinity is a concept, not a variable like x y or z. And there can be “bigger” infinity and “smaller” infinity, that why when x = infinity and y = infinity, and x/y is undefined because we don’t really know their value.

Let’s take an example here:

How many numbers are there between 0 and 1? The answer is infinity, there is 0.1,0.11,0.111 …………

How many numbers are there between 0 and 2? The answer is also infinity.

However, we know there must be more numbers between 0 to 2 compared to 0 to 1, so there is a difference between the infinities.

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