real numbers

The number line

Real numbers include all numbers that can be placed on a continuous number line—integers, fractions, and irrational numbers like π and √2.

The term distinguishes them from imaginary numbers, which involve the square root of negative one.

In everyday math, nearly every number you encounter is real: The solution must be a real number, not imaginary.

constants

pi

Circle's fundamental ratio

  • eFifth alphabetic character
  • phiTwenty-first Greek letter
  • zeroNumerical absence of quantity

one · infinity · golden ratio · Avogadro · Planck

structure

integers

Numbers without fractional components

natural numbers · whole numbers · decimals · fractions · interval · subset · countable · uncountable · density · completeness

analysis

continuity

Uninterrupted progression or coherence

sequence · series · calculus · derivative · integral · function · domain · range · bound · monotonic

notation

decimal

Tenths-based notation

rounding · approximation · precision · floating-point · mantissa · exponent · radical · square root · logarithm

Categories
Opposites
mathematical number classification

real numbersimaginary numbers

Multiples of i

complex numbers · complex plane · transfinite numbers · infinitesimals · cardinal numbers

mathematical abstraction vs. discrete countability

real numbersintegers

Numbers without fractional components

natural numbers · whole numbers · rational numbers · counting numbers

Family

real, number, realize, reality, unreal, realistic, realization, surreal, realistically

Familiarity
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Used worldwide · Timeless · Abstract · Rated G