Proof of absolute value identities $|x+y| = |x| + |y|$ and $|x-y| = |x | - |y|$
56954
Equality holds in triangle inequality iff both numbers are positive, both are negative or one is zero
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
149354
Proof of continuity $f(x+y) = f(x) + f(y)$
127183
Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
157268
Proving a bijection with absolute value
41300
Show $(x+y)^a > x^a + y^a$ for $x,y>0$ and $a>1$
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
116223
Show that the angles satisfy $x+y=z$
57418
How to prove this statement: $\binom{r}{r}+\binom{r+1}{r}+\cdots+\binom{n}{r}=\binom{n+1}{r+1}$
5595
$x^y = y^x$ for integers $x$ and $y$
64457
Prove:$|x-1|+|x-2|+|x-3|+\cdots+|x-n|\geq n-1$
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
1932
How to show this equality of $\rho(X,Y)$
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
138575
Proof that $\cos^2(x)\cosh^2(y) + \sin^2(x)\sinh^2(y) = -1 + \sin^2(x) - \sinh^2(y)$
121853
$X$,$Y$,$Z$ mutually independent implies $X+Y$ independent of $Z$