What Makes Irrational Numbers So Intriguing Between Rational Ones?

[icystrike]

They can fit into number lines but not marked on a sewing thread ?

I love to think of between 2 infinity small rational numbers there is a infinity deep hole that you can always pick a different irrational number out of it. (Is it a safe idea? )

 

[LeonhardEuler]

I'm not sure what you mean by a sewing thread, but yes, it is true that between any two distinct rational numbers there are always an infinite number of irrational numbers, no matter how close together you pick the rational numbers. It's also true that there are an infinite number of rational numbers between any two different rational numbers.