◀ ▲ ▶Branches / Analysis / Proposition: Compact Subset of Real Numbers Contains its Maximum and its Minimum

Proposition: Compact Subset of Real Numbers Contains its Maximum and its Minimum

Let $A$ be a non-empty compact subset of a the real numbers $\mathbb R$. Then $$\max(A)\in A,~\min(A)\in A,$$ where $\max(A)$ and $\min(A)$ denote the maximum and minimum of $A$, respectively.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1

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

Github:

References

Bibliography

1. Forster Otto: "Analysis 2, Differentialrechnung im $\mathbb R^n$, Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984