How many maps $\phi \colon \Bbb N \to \Bbb N \cup \{0\}$ are there?
3775
How many maps $\phi:\Bbb{N}\to\Bbb{N}$ are there with $\phi(ab) = \phi(a)+\phi(b)$?
49833
Simple bijection $\mathbb N_0 \times \mathbb N_0 \to \mathbb N_0$
44065
If $B$ is finitely generated as a $k$-algebra, and $\phi:A\to B$ is a $k$-algebra map, is $\phi^{-1}(M)$ maximal for any maximal $M\subset B$?
50159
How to prove if $\Bbb R^n=W_1\cup W_2\cup \cdots\cup $ where each $W_k$ is a subspace, then $\Bbb R^n=W_i$ holds for some $i$
146436
Cardinality of the set of bijective functions on $\mathbb{N}$?
46065
How do you find all $n$ such that $\phi(n)|n$
15000
Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
157597
Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
64140
Find a bijection from $\mathbb R$ to $\mathbb R-\mathbb N$
124333
A bijection between $\mathbb{N}$ and $\mathbb{P}(\mathbb{N})$?
38946
Show that $\{\cup_{n\in K} (n, n+1]: K \subset \mathbb{Z}\}$ is a $\sigma$-algebra on $\mathbb{R}$
1799
How many k-dimensional subspaces there are in n-dimensional vector space over $\mathbb F_p$?
52629
Example 1, Sec. 22 in Munkres' TOPOLOGY, 2nd edition: How to verify that this map is closed?
4530
For which natural numbers are $\phi(n)=2$?
142174
Nonexistence of an injective $C^1$ map between $\mathbb R^2$ and $\mathbb R$
83116
Uncountability of basis of $\mathbb R^{\mathbb N}$
124847
Is the set of surjective functions from $\mathbb{N}$ to $\mathbb{N}$ uncountable?