Welcome guest
You're not logged in.
270 users online, thereof 0 logged in

Definition: Bounded Subsets of Real Numbers

Let \(D\) be a non-empty subset of real numbers. Using the definition of the order relation for real numbers “\(\ge\)”:

  1. \(D\) 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 \(D\).
  2. \(D\) 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: [581]

1.Corollary: A Criterion for Subsets of Real Numbers to be Bounded


This work was contributed under CC BY-SA 3.0 by:

This work is a derivative of:

(none)

Bibliography (further reading)

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

FeedsAcknowledgmentsTerms of UsePrivacy PolicyImprint
© 2018 Powered by BooOfProofs, All rights reserved.