Set of Real Numbers

  • set theory
    the set of all rational and irrational numbers; the entire continuum of possible number values from negative infinity to positive infinity.
All terms


The set of real numbers, often denoted as , includes all the rational and irrational numbers. It represents all possible number values, extending from negative infinity to positive infinity.

The set of real numbers extends the set of rational numbers to include irrational numbers. Where rational numbers are numbers that can be expressed as a fraction, where both the numerator and the denominator are integers and the denominator is non-zero.

Irrational numbers are numbers that cannot be expressed as a fraction. This means that they can’t be written as a ratio of two integers. Examples include the square root of 2 and the number .

Related Terms

Set of Rational Numbers

The set of rational numbers, denoted as ℚ, can be defined by the quotient of two numbers belonging to the set of integers, where the divisor is non-zero.