If $0<p<q<1$ Prove that $q<p+q-pq<1$
64108
how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
14221
How can we prove it? ${a}{b}≤\frac{a^p}{p}+\frac{b^q}{q}$
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
109778
Proving $(x-c)|(p(x)-p(c))$
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
140599
Inequality Proof in Real Numbers: If $p+q=1$ then $pq\le\frac14$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
6119
If both $P$ and $Q$ are true , how can I tell that $P$ implies $Q$?
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
96327
Show that $a^x+b^x+c^x>(a+b+c)^x$ for all $a,b,c>0$ and $0<x<1$
108704
Help with proof of $|x+y| \geq |x|-|y|$
100375
Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$.
65534
Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
120309
Number Theory Inequality Proof