Prove that $\sup(AB) = \sup(A)\cdot \sup(B)$
7112
Product of sets and supremum
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 $i$
35564
Prove that $u\cdot v = \frac{1}{4}||u+v||^2 - \frac{1}{4}||u-v||^2 \forall u,v \in \mathbb{R^n}$
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
144372
How to Prove that if $A$ is bounded, then $A \cdot A$ is bounded?
155999
How to prove the following properties of infimum and supremum involving the union and intersection of the sets $A_k$
61666
Proving $ [(\vec{a}+\vec{b})\times(\vec{b}+\vec{c})]\cdot(\vec{c}+\vec{a})=2\vec{c}\cdot(\vec{b}\times\vec{a})$
149287
Prove that $A,B>0$ and $A_{ij}0$
18528
Show that $a \star b=a \cdot b+a+b$ is binary operation for the group $\Bbb{ Q} \setminus \{-1\}$
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
81794
Prove that $(ab,cd)=(a,c)(b,d)\left(\frac{a}{(a,c)},\frac{d}{(b,d)}\right)\left(\frac{c}{(a,c)},\frac{b}{(b,d)}\right)$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
100565
Property of sup of a set of numbers
143130
Proving that the supremum of $(a,b)$ is $b$.
76267
Prove that: $x_1\cdot x_2\cdots x_n>y_1\cdot y_2\cdots y_m$.