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

Title	topic entry on rational numbers
Canonical name	TopicEntryOnRationalNumbers
Date of creation	2013-03-22 19:08:15
Last modified on	2013-03-22 19:08:15
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	12
Author	pahio (2872)
Entry type	Topic
Classification	msc 13B30
Classification	msc 11A99
Classification	msc 03E99
Synonym	entries on rational numbers
Related topic	TopicEntryOnRealNumbers