– How can some infinites be bigger than others?

Question

I have just come across the concept that there are different types of infinite numbers (whole integers, irrational numbers etc.) and the concept that for example, the amount of irrational numbers between 0 and 1 is higher than the amount of whole numbers from 1 to infinity.

I guess I just don’t understand how an infinite amount of something can be bigger/smaller than an infinite amount of something else…

Please un-f**k my brain 😀

In: 4

Answer 1

The way I try to explain it to younger learners is that “infinity” is really a placeholder for when we want to say “a lot, so much that it might as well be too much to think about”.

However, there are situations that we want to compare two or more different kinds of “too much to think about”, and that’s why some infinities are “bigger” than others.

Oversimplified, but not sure how advanced the five year old is.