$ \forall \epsilon \in \mathbb{R}^{*}_{+} , | x -y | < \epsilon \iff x = y $
105316
Prove : $|x - y| \leqslant \epsilon$ $\forall \epsilon > 0$ iff $x = y$
132971
Prove that $|a| < b \iff -b<a<b$
83873
Find $E(|X-Y|^a)$ where $X$ and $Y$ are independent uniform on $(0,1)$
6238
How to find delta, for a given epsilon?
147978
Limits using epsilon delta definition $f(x,y)=xy$ for functions of two variables
73074
$f \text{ convex }\Rightarrow \forall (x_0,f(x_0))\in \Gamma(f) \exists a : \forall x\in \mathbb{R}, f(x) \ge a(x-x_0)+f(x_0)$
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
135694
Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
157733
Are positive real numbers $x,y$ allowed to be taken out during this proof?
50833
Find all $f:\mathbb R\to\mathbb R$ such that $\forall x,y\in\mathbb R$ the given equality holds: $xf(y)+yf(x)=(x+y)f(x)f(y)$.
33543
is "y1 < x < y2" an inequality or inequalities?
7876
If $f(x+y)=f(x)+f(y) ,\forall\;x,y\in\Bbb{R}$, then if $f$ is continuous at $0$, then it is continuous on $\Bbb{R}.$
62118
Prove $\epsilon$-$\delta$ definition of continuity implies the open set definition for real function
132873
Understanding Epsilon-Delta Proof
7775
Show that $|x-y|\leq |x|+|y|$.
52880
Intuition: If $a\leq b+\epsilon$ for all $\epsilon>0$ then $a\leq b$?