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applicability: $\mathbb {R}$

Definition: Real Intervals

Let \(a,b\in\mathbb R\) be real numbers. Using the order relation for real numbers, we call a subset \(I\subseteq\mathbb R\) of real numbers a real interval, if it satisfies the following properties:

By allowing either \(a\), or \(b\) to be unbounded, i.e. \(a,b\in\{\mathbb R,+ \infty, -\infty\}\) we define

| | | | | created: 2015-02-28 15:34:30 | modified: 2020-07-06 11:47:16 | by: bookofproofs | references: [581]

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Bibliography (further reading)

[581] Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983