Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

1: Numbers - Real (ℝ) and Rational (ℚ)

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    • 1.1: Real and Rational Numbers
      The set of real numbers (denoted, ℝ) is badly named. The real numbers are no more or less real – in the non-mathematical sense that they exist – than any other set of numbers, just like the set of rational numbers (ℚ), the set of integers (ℤ), or the set of natural numbers (ℕ). The name “real numbers” is (almost) an historical anomaly not unlike the name “Pythagorean Theorem” which was actually known and understood long before Pythagoras lived.
    • 1.E: Numbers - Real (ℝ) and Rational (ℚ) (Exercises)

    Thumbnail: Bust of Pythagoras of Samos in the Capitoline Museums, Rome. Image used with permission (CC BY-SA 3.0; Galilea).


    • Eugene Boman (Pennsylvania State University) and Robert Rogers (SUNY Fredonia)