Cantor's diagonalization argument and rational numbers
114650
In Cantor's Diagonalization Argument, why are you allowed to assume you have a bijection from naturals to rationals but not from naturals to reals?
83842
Alternate proofs (other than diagonalization and topological nested sets) for uncountability of the reals?
36546
For an irrational number $a$ the fractional part of $na$ for $n\in\mathbb N$ is dense in $[0,1]$
138446
Proving that there exists an irrational number in between any given real numbers
53399
Proof of the uncountability of reals using the diagonal argument—problem?
121831
Proving that rational numbers are dense
47653
Cantor diagonalization and fundamental theorem
141424
$\log_7 n$ is either an integer or an irrational number
77129
Density of irrationals
133206
Is the Cantor set made of interval endpoints?
5420
Why doesn't Cantor's diagonal argument also apply to natural numbers?
34998
How to prove that $\mathbb{Q}$ ( the rationals) is a countable set
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
34710
Cardinality of Irrational Numbers
147350
Homeomorphism between $\prod X_i$ and the Cantor set
86914
Cardinality of the set of hyperreal numbers
76635
Proof through combinatorial argument