Problem on inequality about $x_1, x_2, x_3, . . ., x_n$ real numbers without using set theory.
93427
Show that $\sum_{i=1}^{n} \frac {a_i}{1+a-a_i} + \prod_{i=1}^{n} {(1-a_i)} \leq 1$
49783
A possible inequality related to binomial theorem (or, convex/concave functions)
5222
$\lfloor x\rfloor + \lfloor y\rfloor \leq \lfloor x+y\rfloor$ for every pair of numbers of $x$ and $y$
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
152342
$x_1+x_2+\cdots+x_n\leq M$: Cardinality of Solution Set is $C(M+n, n)$
109305
Non-existence of natural numbers such that $\sqrt{n} +\sqrt{n+1} <\sqrt{x} +\sqrt{y} <\sqrt{4n+2}$
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
93771
Prove that for any set $A$ there is some $x \notin A$
158882
Prove the existence of some weird family of sets
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
77286
Proving set theory question
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
77026
Proof with inequalities
46760
To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
126015
Elementary number theory in sets
64457
Prove:$|x-1|+|x-2|+|x-3|+\cdots+|x-n|\geq n-1$
143424
Sequence problem involving inequalities