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

True ELI5: there’s a lot of sand dust in a sandbox but also on a beach or in the dessert. so you could say each it’s an infinite amount. But we can still say, that the sandbox has less sand than the beach, which has less sand than the dessert. By knowing more about the beach or dessert, like the length and width of each, we can also aestimate how much larger the dessert is in comparism to the beach.

ELI20:
you probably remember f(x)=x from school. It’s a straigt line.
you probably also remember g(x)=x^2.

Both graphs go to infinity, but g(x) still has an much higher value.