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Definition: Supremum of Extended Real Numbers

Let \(D\) be a non-empty subset of the extended real numbers $\overline{\mathbb R}.$ The supremum $\sup(D)$ is the element of $\overline{\mathbb R},$ which

• Case 1: is equal to the supremum of $D$ defined for the set of real numbers $\mathbb R$, if $D$ is bounded above,
• Case 2: equals $+\infty$, if $D$ is not bounded above.

Mentioned in:

Definitions: 1 2 3
Lemmas: 4 5
Proofs: 6 7

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References

Bibliography

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