Prove that there is an one-to-one function from $\mathbb R × \mathbb R$ to $\mathbb R$
34260
Injective function from $\mathbb{R}^2$ to $\mathbb{R}$?
100134
Proving existence of a surjection $2^{\aleph_0} \to \aleph_1$ without AC
134720
Show that there is no increasing function $f: \aleph_1 \to \mathbb{R}$
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
49953
Proving that a function from $N\times N$ to $N$ is bijective.
29403
Finding functions $f: \Bbb R_*^+ \to \Bbb R_*^+$ with certain properties
141114
Question about a bijection between $\mathbb R$ and $\mathbb R \cup \{\infty\}$
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
15491
Prove that $f:\mathbb R^n\to\mathbb R$ is affine if and only if it is convex and concave
152841
I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
48765
Let $S$ and $T$ be finite non-empty sets such that $|S| = |T|$. Show that the function $f : S\to T$ is onto if and only if it is one-to-one.
102299
Bijection between $\mathbb{R}^n$ and $\mathbb{R}^m$
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
118154
$f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ twice
89125
Prove that $r \in R$ such that $0 \lt r \lt 1$ then $\frac{1}{r (1 - r)} \ge 4$