Why do some infinities seem bigger than others, and how do mathematicians compare their sizes?

Question

Why do some infinities seem bigger than others, and how do mathematicians compare their sizes?

In: Mathematics

Answer 1

Because they are!

There is an infinite number of numbers between 1 and 2.

1.1, 1.2, 1.3, 1.4, 1.5. 1.6 1.7, 1.8, 1.9, 1.91 and so on

And there is an infinity twice as large between 1 and 3.

How do we compare them? Smart people do smart math that I can’t hope to know lol