Proving that in a finite set $S$, there is an element $a \in S$ such that $a*a=a$
7536
Is there an idempotent element in a finite semigroup?
32929
Questions about proving $\lnot \lnot a = a$
33030
Proof that $\inf A = -\sup(-A)$
1409
Proving that the given set has at most $2^{n-1}$ elements
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
87830
Relating the union of the power set of a set to the set itself
136710
Prove that for every $a\in A$ $\exists$ $q\in M,s\in A$ s.t. $a=sba+qa$ where $M$ is maximal ideal in $A$.
110464
Let $A=\{1,...,n\}.$ Show that there is a bijection of $P(A)$ with the cartesian product $X^n$ where $X$ is the two element set $X=\{0,1\}$
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
70278
$A\subseteq B\to C\setminus B\subseteq C\setminus A\,$ -- how to prove this?
72256
Prove there exists two sub-sets of indices $I,J\subseteq [2n]$ such that $\sum_{i\in I}a_i=\sum_{j\in J}b_j$
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
145397
How to prove that for every $i$, $a_i = i$
59813
Prove that for all sets A and B, A ∩ B = ∅ implies ( A ∪ B ) - B = A
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
19856
Prove that a subset of a separable set is itself separable
118595
Proving that a set is countable by finding a bijection