Definition: Infimum, Greatest Lower Bound

Let \(D\) be a non-empty subset of real numbers. The real number \(\inf(D)\) is called the infimum (or the greatest lower bound) of \(D\), if

  1. \(\inf(D)\) is a lower bound of \(D\) and
  2. it is greater than or equal to every lower bound of \(D\), i.e. if $B$ is any lower bound of $D$ then \(\inf(D) \ge B\).

Equivalently, for every \(\epsilon > 0\) there exists an \(y\in D\) with \(\inf(D) + \epsilon > y\).


Definitions: 1 2
Proofs: 3 4 5 6 7
Propositions: 8 9

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  1. Heuser Harro: "Lehrbuch der Analysis, Teil 1", B.G. Teubner Stuttgart, 1994, 11th Edition