Prove that an interval of rationals has the same cardinality as the rationals
1117
Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
156783
$\mathbb R$ has the same cardinality of any interval
152518
Proof that the set of all possible curves is of cardinality $\aleph_2$?
151544
Prove that if $B$ is the set of rationals in $[0,1]$ with a finite subcover, then: $1 \leq \sum_{k=1}^n m^*(I_k)$
109320
Why do the rationals, integers and naturals all have the same cardinality?
126212
Proving uniform continuity on an interval
87764
Prove that the difference between two rational numbers is rational
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
85099
How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
149382
Prove that $(0,1) \subseteq\mathbb R$ and $(4,10) \subseteq\mathbb R$ have the same cardinality.
15733
Show that the cardinality of $\mathbb N$ is the same as the cardinality of $\mathbb N \times \mathbb N$
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
98666
Continuity defined for rational and irrational numbers
139622
Generator of rational functions unchanged under $\sigma(X) = X + 1$
102583
Infinite number of rationals between any two reals.
83518
Proving Two sets have same cardinality
141227
How to show the integers have same cardinality as the natural numbers?