– 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

I think it has to do with countability. If you are able to define a set within two arbitrary points, it is considered countable. Uncountable sets are, by definition, larger than countable sets. Therefore, an infinite Uncountable set is larger than an infinite countable set.