topic entry on rational numbers

PlanetMath articles concerning the rational numbers

Definition

• rational number

• fraction

Properties

• commensurable numbers

• rational algebraic integers

Forms

• partial fractions

• any rational number is a sum of unit fractions

• Egyptian fractions

• mixed fraction

• decimal fraction

• decimal expansion

• order valuation

• continued fraction

Where are rational numbers?

• rational points on one dimensional sphere

• rational sine and cosine

• rational Briggsian logarithms of integers

• irrational to an irrational power can be rational

• square roots of rationals

• Roth’s theorem

• rational root theorem

• canonical form of element of number field

• http://planetmath.org/node/12127solutions of the equation  $x^y=y^x$

Sets

• rings of rational numbers

• prime subfield

• proof that the rationals are countable

• another proof of cardinality of the rationals

• dense set

Polynomials and functions

• Bernoulli polynomials and numbers

• Euler polynomials

• Dirichlet’s function

• a pathological function of Riemann

Rational vs. irrational

• theory of rational and irrational numbers