– 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

Let’s say you and I are driving rockets that never run out of fuel into space and have no friction applied to us. My ship accelerates 2m/s more every second, where yours adds 1m/s to it’s speed every second. Both of our speeds are *approaching* infinity, but we know my speed will always be bigger than yours.