Norm (abelian group)

In mathematics, specifically abstract algebra, if is an (abelian) group with identity element then is said to be a norm on if:

  1. Positive definiteness: ,
  2. Subadditivity: ,
  3. Inversion (Symmetry): .

An alternative, stronger definition of a norm on requires

  1. ,
  2. ,
  3. .

The norm is discrete if there is some real number such that whenever .

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