Uniform ContinuityOne delta for the whole domain, and why compactness gives it free.Mathematicsf is uniformly continuous when a single δ works atevery point at once, not a different δ for each point.∀ε ∃δ ∀x, y : |x − y| < δ ⇒ |f(x) − f(y)| < εf(x) = x on ℝUniformly continuousTake δ = ε.f(x) = x² on ℝNot uniformlySlope grows without end.f(x) = x² on [0, 1]Uniformly continuousA compact domain.THE COMMON MISTAKEAssuming continuous means uniformly continuousIt does on a compact set, not in general1/x is continuous on (0, 1) and not uniformly so. Compactness of the domain iswhat upgrades the one to the other.Every Lipschitz function is uniformly continuous. The converse fails: √xon [0, 1] is uniformly continuous and not Lipschitz.Uniform Continuitylearnposters.com
Uniform Continuity — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Uniform Continuity poster

The rule, 3 worked examples, and the mistake everyone makes.

Every Lipschitz function is uniformly continuous. The converse fails: √x on [0, 1] is uniformly continuous and not Lipschitz.

Questions about the Uniform Continuity poster

What’s on the Uniform Continuity poster?
The rule, 3 worked examples, and the mistake everyone makes. f is uniformly continuous when a single δ works at every point at once, not a differe…; ∀ε ∃δ ∀x, y : |x − y| < δ ⇒ |f(x) − f(y)| < ε; f(x) = x on ℝ = Uniformly continuous; f(x) = x² on ℝ = Not uniformly; f(x) = x² on [0, 1] = Uniformly continuous; Common mistake: Assuming continuous means uniformly continuous → It does on a compact…. Every Lipschitz function is uniformly continuous. The converse fails: √x on [0, 1] is uniformly continuous and not Lipschitz.
Who is the Uniform Continuity poster for?
Uniform Continuity belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning analysis can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Uniform Continuity poster?
In any proof about integrability or the interchange of limits. A wall chart earns its place by being glanceable from where the work is happening, so Uniform Continuity belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Uniform Continuity?
Absolute vs Conditional, Bolzano-Weierstrass and Cauchy Sequences sit alongside Uniform Continuity in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Absolute vs ConditionalBolzano-WeierstrassCauchy Sequences
Is the Uniform Continuity poster free to download and print?
Yes. Uniform Continuity downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Uniform Continuity poster print at?
Uniform Continuity is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Uniform Continuity loses nothing.Printing guide

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