Maths conundrum

[Skeptisk]

This video made my head hurt. Can anyone explain how both statements can be true ie that you can always find a rational number between any two real numbers yet the set of rational numbers are countable and the set of real numbers isn’t.

https://vm.tiktok.com/ZGeSrwDcV/

[ATG]

There's not just one rational number between two reals, there's an infinite number of rational numbers between any two reals.

But there are "even more" real numbers between those two reals. It's a different kind of infinite.

[Super Sonic]

Real numbers includes rational and irrational numbers.