Rudin exercise 2.18: perfect set with only irrational numbers.
12701
Perfect set without rationals
117366
Is there a simple, constructive, 1-1 mapping between the reals and the irrationals?
10882
irrationality of $\sqrt{2}^{\sqrt{2}}$.
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
30411
The closure of the irrational numbers on $\mathbb{R}$
95947
Cantor set + Cantor set =$[0,2]$
53945
The square root of a prime number is irrational
142577
Algebraic proof that a set generated by irrational rotations is dense in $S^1$.
10008
Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers
102075
A function continuous on all irrational points
81150
Positive integer multiples of an irrational mod 1 are dense
72666
Prime Numbers And Perfect Squares
98666
Continuity defined for rational and irrational numbers
30796
Is the set of irrationals separable as a subspace of the real line?
31744
Proving that there is an irrational number between any two unequal rational numbers.
46323
Criteria for convergent sequence (Baby Rudin Theorem 3.22)
43268
How to prove that the set of rational numbers are countable?