Let E be a non empty 􏰁finite set, and let ∗ be an associative law on E. Show that there exists an element s ∈ E such that s ∗ s = s.
7536
Is there an idempotent element in a finite semigroup?
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
75966
Prove that if $A$ is a set with $m$ elements, $B$ is a set with $n$ elements, and $A \cap B = \emptyset$, then $A \cup B$ has $m+n$ elements.
145406
Prove every element of $G$ has finite order.
49709
Suppose $X$ is infinite and $A$ is a finite subset of $X$. Then $X$ and $X \setminus A$ are equinumerous
1707
How does one prove that addition on $\mathbb{R}$ is associative?
118195
How does one prove that $e$ exists?
127656
How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
147013
Subset of a finite set is finite
39293
Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $
95935
Prove A = $(A \cap B) \cup (A \cap B^c)$ using the distributive and associative law.
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
3599
show that if ${a_n} \to a$, and $a>0$, then $\exists N$ such that $a_n>0$ for $n \ge N$.
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
12436
The cardinality of the set of all finite subsets of an infinite set
51134
If $E \in \sigma(\mathcal{C})$ then there exists a countable subset $\mathcal{C}_0 \subseteq \mathcal{C}$ with $E \in \sigma(\mathcal{C}_0)$
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists