# Formally Ordered Number Sequence

(Redirected from algebraic number field)

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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.
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**Example(s):****Counter-Example(s):****See:**Number Sequence, Algebraic Number Theory, Algebraic Extension, Field Extension, Field (Mathematics), Rational Number, Hamel Dimension, Vector Space.

## 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.

- In mathematics, an