What’s on the Continuity Theorems poster
A 5-row table: Theorem · Hypotheses · Conclusion.
Every one of these needs a closed and bounded interval.
- Intermediate value — f continuous on [a, b] — Attains every value between
- Extreme value — f continuous on [a, b] — Attains a maximum and minimum
- Boundedness — f continuous on [a, b] — f is bounded on [a, b]
- Heine-Cantor — f continuous on [a, b] — f is uniformly continuous
- Brouwer in 1D — f maps [a, b] into itself — Some c satisfies f(c) = c
Drop closedness and all four fail at once: 1/x on (0, 1] is continuous, unbounded, attains no maximum and is not uniformly continuous.
Questions about the Continuity Theorems poster
- What’s on the Continuity Theorems poster?
- A 5-row table: Theorem · Hypotheses · Conclusion. Every one of these needs a closed and bounded interval. Intermediate value — f continuous on [a, b] — Attains every value between; Extreme value — f continuous on [a, b] — Attains a maximum and minimum; Boundedness — f continuous on [a, b] — f is bounded on [a, b]; Heine-Cantor — f continuous on [a, b] — f is uniformly continuous; Brouwer in 1D — f maps [a, b] into itself — Some c satisfies f(c) = c. Drop closedness and all four fail at once: 1/x on (0, 1] is continuous, unbounded, attains no maximum and is not uniformly continuous.
- Who is the Continuity Theorems poster for?
- Continuity Theorems 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 Continuity Theorems poster?
- Before invoking a maximum or a root, check the interval is closed and bounded. A wall chart earns its place by being glanceable from where the work is happening, so Continuity Theorems belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Continuity Theorems?
- Absolute vs Conditional, Bolzano-Weierstrass and Cauchy Sequences sit alongside Continuity Theorems 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 Continuity Theorems poster free to download and print?
- Yes. Continuity Theorems 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 Continuity Theorems poster print at?
- Continuity Theorems 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 Continuity Theorems loses nothing.Printing guide
Related posters
Charts that sit alongside Continuity Theorems on the same wall.
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