bijective function over $\mathbb{N}$ that isn't $f(X) = (X)$
5375
Is there a bijective function mapping Natural numbers to Natural numbers, other than $f(n) = n$?
97878
Are there uncountably many surjections from $\mathbb N$ to $\mathbb N$?
127921
Does there exist a function such that $\lim_{x \to a} f(x) = L$ for all $a \in \mathbb R$ but $f(x)$ is never $L$?
67644
How does one get the formula for this bijection from $\mathbb{N}\times\mathbb{N}$ onto $\mathbb{N}$?
99726
Proving that a function is not a contraction
21269
Bijective continuous function between $(0 ,\infty)$ and $\mathbb{R}$.
109710
Bijection between $\mathbb N \times \mathbb N$ and $\mathbb N$
69876
For every $n \in \mathbb{N}$, find a function $f$ which is differentiable $n$ times at $0$, but not $n+1$ times.
124333
A bijection between $\mathbb{N}$ and $\mathbb{P}(\mathbb{N})$?
52798
Finding counterexamples: bijective continuous functions that are not homeomorphisms
124374
A bijective function between a square and its side
110569
Does anyone know a closed-form expression for a bijection between $\mathbb{N}^k$ and $\mathbb{N}$?
21431
The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
87027
There is no continuous injective function $f:\mathbb{R}^n\longrightarrow\mathbb{R}^m$
138026
To show that $n!f(x) \in \mathbb{Z}[x]$
81799
Examples of functions where $f(ab)=f(a)+f(b)$
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$