Prove that $\sup{(A+B)} = \sup{A}+\sup{B}$
14162
How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
152817
Proving $\sup B=\inf A$
95852
Prove that $(a+b)(b+c)(c+a) \ge8$
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
149287
Prove that $A,B>0$ and $A_{ij}0$
100565
Property of sup of a set of numbers
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
136789
How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?
76863
How to show $ \sup \inf g(x,y) \leq \inf \sup g(x,y)$?
86378
Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
59396
Show that the rank of $A+B$ is no more than the sum of the ranks of $A$ and $B$
78463
Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
27482
How to show $-\sup(-A)=\inf(A)$?
137511
Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$