If $x^y = y^x$ prove that $x<e<y $
5595
$x^y = y^x$ for integers $x$ and $y$
50273
How to prove $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$?
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
79024
the derivation of E(X|X)
7775
Show that $|x-y|\leq |x|+|y|$.
72081
$\forall x,y>0, x^x+y^y \geq x^y + y^x$
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
65319
For all $x,y∈\Bbb{R}$ define that $ x\equiv y$ if$ x^2=y^2$
33332
A classic exponential inequality: $x^y+y^x>1$
94319
Expected value of $|X - Y|$
38636
A basic question about exponentiation: when is $a^{xy}=(a^x)^y$?
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
45555
$(x+y)^c\le x^c+y^c$ for $0<c\le1$
96153
$ x^3<y^3 \iff x<y $ proof issue.
39270
Showing that $e^x > 1+x$
95022
Help understanding proof of the following statement $E(Y) = \sum_{i = 1}^{\infty} P(Y \geq k)$
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$