### What does **completeness of the real numbers** mean?

# Definitions for completeness of the real numbers

com·plete·ness of the real num·bers

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **completeness of the real numbers**.

### Wikipedia

Completeness of the real numbers

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

Chaldean Numerology

The numerical value of completeness of the real numbers in Chaldean Numerology is:

**5**Pythagorean Numerology

The numerical value of completeness of the real numbers in Pythagorean Numerology is:

**4**

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"completeness of the real numbers." *Definitions.net.* STANDS4 LLC, 2024. Web. 20 Apr. 2024. <https://www.definitions.net/definition/completeness+of+the+real+numbers>.

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