Assertion: real number's value | /r/HasProperty | norm
Facets:
Source sentences:
text: When the real numbers R are considered as the one-dimensional vector space R1, the absolute value is a norm, and is the p-norm (see Lp space) for any p.
text: This picture of an order, absolute value, and complete field derived from them can be generalized to algebraic number fields and their valuations (certain mappings from the multiplicative group of the field to a totally ordered additive group, also called orders), absolute values (certain multiplicative mappings from the field to the real numbers, also called norms), and places (extensions to complete fields in which the given field is a dense set, also called completions).