Rigorous proof of the closure of irrational numbers are reals
30411
The closure of the irrational numbers on $\mathbb{R}$
50555
Approximation of real number to the power of irrational
119858
Proof: Every convergent sequence of real numbers is bounded
10008
Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers
102583
Infinite number of rationals between any two reals.
96204
Irrational number $\sqrt2$ proof
136851
Proof that the set of subsequential limits is closed
30523
A binary irrational with bits defined by primes
22232
Proving that cardinality of the reals = cardinality of $[0,1]$
114043
Prove the existence of a real number satisfying a property
154406
Real analysis - proof approach help
83842
Alternate proofs (other than diagonalization and topological nested sets) for uncountability of the reals?
32848
Prove that the product of a non-zero rational and irrational number is irrational.
63804
Proof that every repeating decimal is rational
15110
About irrational logarithms
77129
Density of irrationals
34710
Cardinality of Irrational Numbers