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Definition: Infimum of Extended Real Numbers

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

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

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Definitions: 1
Proofs: 2

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References

Bibliography

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