Show that if $a,b \in \Bbb R$ then
58629
Show that the $\max{ \{ x,y \} }= \frac{x+y+|x-y|}{2}$.
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
151607
Show that  $A\Delta B = C$ if and only if $A = B\Delta C$
96217
If a and b are non-negative real numbers then demonstrate inequality
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
14162
How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
143130
Proving that the supremum of $(a,b)$ is $b$.
3301
If $AB = I$ then $BA = I$
67483
Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
138283
$|(a,b)| = |\Bbb R|$ ? Cardinality of any open interval
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
60707
Show that if $ \ A \cup B = A$ and $ \ A\cap B = A$ then $ \ A = B$
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
80789
Prove that $\forall a,b,c,d\in \mathbb{R}\,$, $(a^2-b^2)(c^2-d^2)\leq(ac-bd)^2$ and equalities hold if and only if $ad=bc$.