New posts in continuity

If $f$ is continuous, then there exists $x+\frac{1}{n}\in[0,1]$ and $f\left(x+\frac{1}{n}\right)=f(x)$

metric-spaces continuity

How do I use the Intermediate Value Theorem in this question?

real-analysis continuity

Let $f: \mathbb{R} \to \mathbb{R}$ be continuous periodic function with period $T>0$

real-analysis continuity periodic-functions

Continuity of the function $f(x,y)=\frac{\cos(x+y)+\cos(x-y) -2}{x^2 +y^2 }$

real-analysis multivariable-calculus continuity

If $f : [a,b]\to\Bbb R$ is continuous, are there $x_1,x_2\in (a,b)$ such that $\tfrac{f(b)-f(a)}{b-a} = \tfrac{f(x_1)-f(x_2)}{x_1-x_2}$?

real-analysis continuity

Continuity proof for compact domain

continuity compactness maxima-minima

Proving continuity using gluing lemma

continuity metric-spaces

proof of that a continuous function has a fixed point

calculus continuity

Lipschitz and uniform continuity

$f(16x)=16f(x) $ and $ f$ is continuous

functions continuity functional-equations

How do you enter numbers on a Mac when making a cellular voice call with iPhone?

macos call continuity

Why does the Mean Value Theorem require a closed interval for continuity and an open interval for differentiability?

calculus continuity

Send webpage from Mac to iOS using Handoff

macos ios safari google-chrome continuity

Is $f(x)=x+\frac{x}{x+1}$ uniformly continuous on $(0,\infty)$

calculus continuity

Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.

The derivative of $x!$ and its continuity

derivatives continuity factorial gamma-function

Discontinuity of Thomae Function on $\mathbb{Q}$

real-analysis continuity

Example of a continuous function with a discontinuous inverse

real-analysis continuity examples-counterexamples inverse

Is a continuous function on a bounded set bounded itself?

real-analysis continuity

Identify where $ f(x)= \sqrt{\frac{1-x}{|x|}}$ is continuous

calculus limits continuity limits-without-lhopital piecewise-continuity