$|a\alpha-b\beta|\leq|a-b|+|\alpha-\beta|$
120390
An inequality involving 4 real or complex numbers
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
68986
Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
51347
Prove that $|a|\leq \max\{|b|,|c|\}$ if $b\leq a \leq c$
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
1914
General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$
7974
lim sup inequality $\limsup ( a_n b_n ) \leq \limsup a_n \limsup b_n $
7775
Show that $|x-y|\leq |x|+|y|$.
56391
Is this inequality true? $ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $, for positive $x$ & $y$, and for $0 < \alpha < 1$
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 $ad=bc$.
134535
Inequality $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \geq a + b+ c$ when $abc = 1$
137864
Prove that $ \left(1+\frac a b \right) \left(1+\frac b c \right)\left(1+\frac c a \right) \geq 2\left(1+ \frac{a+b+c}{\sqrt[3]{abc}}\right)$.
155884
What are the conditions on $\text{tr}(AB) \leq \text{tr(A)} \text{tr(B)}$ to be true?
38448
Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
29679
Prove: $|x-y|\leq |x|+|y|$
57096
Show that $\max{\{|a|+|b|,|c|+|d|\}} \leq \max{\{|a|,|c|\}}+\max{\{|b|,|d|\}}.$