◀ ▲ ▶Branches / Analysis / Corollary: Continuous Real Functions on Closed Intervals are Bounded

Corollary: Continuous Real Functions on Closed Intervals are Bounded

(related to Proposition: Continuous Real Functions on Closed Intervals Take Maximum and Minimum Values within these Intervals)

Let \([a,b]\) be a closed real interval and let \(f:[a,b]\to\mathbb R\) be an arbitrary continuous real function. Then $f$ is bounded.

Table of Contents

Proofs: 1

Mentioned in:

Chapters: 1
Proofs: 2

Thank you to the contributors under CC BY-SA 4.0!

Github:

References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983