# Definitions for completeness axiomcom·plete·ness ax·iom

### WiktionaryRate this definition:0.0 / 0 votes

1. completeness axiomnoun

The following axiom (applied to an ordered field): for any subset of the given ordered field, if there is any upper bound for this subset, then there is also a supremum for this subset, and this supremum is an element of the given ordered field (though not necessarily of the subset).

### WikipediaRate this definition:0.0 / 0 votes

1. completeness axiom

Completeness is a property of the real numbers that, intuitively, implies that there are no "gaps" (in Dedekind's terminology) or "missing points" in the real number line. This contrasts with the rational numbers, whose corresponding number line has a "gap" at each irrational value. In the decimal number system, completeness is equivalent to the statement that any infinite string of decimal digits is actually a decimal representation for some real number. Depending on the construction of the real numbers used, completeness may take the form of an axiom (the completeness axiom), or may be a theorem proven from the construction. There are many equivalent forms of completeness, the most prominent being Dedekind completeness and Cauchy completeness (completeness as a metric space).

### Numerology

1. Chaldean Numerology

The numerical value of completeness axiom in Chaldean Numerology is: 1

2. Pythagorean Numerology

The numerical value of completeness axiom in Pythagorean Numerology is: 1

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"completeness axiom." Definitions.net. STANDS4 LLC, 2024. Web. 7 Sep. 2024. <https://www.definitions.net/definition/completeness+axiom>.

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