Formally Ordered Number Sequence

A Formally Ordered Number Sequence is an ordered number sequence that is defined with an algebraic system (with arithmetic operations).

• AKA: Number Field, Explicit Numeric Sequence.
• Context:
  • It can be a Supersequence to a Number Sequence, such as a Numeric Interval.
  • It can range from being a Formally Ordered Continuous Number Sequence to being a Formally Ordered Discontinuous Number Sequence.
  • …
• Example(s):
  • an Arithmetic Sequence.
  • The Natural Number Sequence.
  • The Integer Number Sequence.
  • The Rational Number Sequence.
  • The Real Number Sequence.
  • …
• Counter-Example(s):
  • an Implicitly Ordered Number Sequence.
• See: Number Sequence, Algebraic Number Theory, Algebraic Extension, Field Extension, Field (Mathematics), Rational Number, Hamel Dimension, Vector Space.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Algebraic_number_field Retrieved:2015-4-22.
  • In mathematics, an algebraic number field (or simply number field) F is a finite degree (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q.

    The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.

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