Set of irrationals between two reals is uncountable I know that between any two reals, there is an irrational number.
See: Proving that there exists an irrational number in between any given real numbers
Now let a, b $\in$ $R$ such that a < b. And let M be the set of irrationals between a and b. 
I want to show that M is uncountable. To do this, I think I need to show that there does not exist a bijection from M to the natural numbers.


*

*Can someone give me a hint about how to start to show this?

*What's the best way to approach "non-existence" proofs in general?
Thanks

Instead you could show that there is a bijection between this set and interval (0,1)
