Completeness of the real numbers

Nonexistence of gaps in the number line
Abstract

Completeness is a property of the real numbers that, intuitively, implies that there are no "gaps" 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.

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