I know that between any two reals, there is an irrational number.
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?