Definition: Bounded Subsets of Real Numbers
- \(D\) is called bounded above, if there is a real number \(B\) with \(x \le B\) for all \(x\in D\). In this case, \(B\) is called an upper bound of \(D\).
- \(D\) is called bounded below, if there is a real number \(B\) with \(x \ge B\) for all \(x\in D\). In this case, \(B\) is called a lower bound of \(D\).
If \(D\) is bounded above and bounded below, or if \(|x|\le |B|\) for all \(x\in D\), then we say that \(D\) is bounded.
| | | | | created: 2014-04-26 22:23:37 | modified: 2018-01-02 20:34:01 | by: bookofproofs | references: 
1.Corollary: A Criterion for Subsets of Real Numbers to be Bounded
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Bibliography (further reading)
 Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983