real number

In mathematics, a real number is a value that represents a quantity? along a continuum, such as -5 (an integer), 4/3 (a rational number that is not an integer?), 8.6 (a rational number given by a finite decimal representation), √2 (the square root of two, an irrational number) and π (3.1415926535..., a transcendental number). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation (such as that of π above), where the consecutive digits indicate into which tenth of an interval given by the previous digits the real number belongs to. The real line can be thought of as a part of the complex plane, and correspondingly, complex numbers include real numbers as a special case.

These descriptions of the real numbers are not sufficiently rigorous by the modern standards of pure mathematics. The discovery of a suitably rigorous definition of the real numbers — indeed, the realization that a better definition was needed — was one of the most important developments of 19th century mathematics. The currently standard axiomatic definition is that real numbers form the unique complete totally ordered field (R,+,·,<), up to isomorphism, whereas popular constructive definitions of real numbers include declaring them as equivalence classes of Cauchy sequences of rational numbers, Dedekind cuts, or certain infinite "decimal representations", together with precise interpretations for the arithmetic operations and the order relation. These definitions are equivalent in the realm of classical mathematics. Wikipedia - Real Numbers (external link)

See Also

1.21 - It Really Is a Musical Universe
8.16 - Law of Corporeal Vibration
8.19 - Law of Corporeal Oscillations
10.02 - Reality vs Actuality
12.21 - Fibonacci Whole Numbers v Irrational Decimal near Equivalents
13.05 - Seven Levels Subdivisions Planes or Realms of Mind Matter and Energy
atomic number
cardinal number
Figure 2.16 - Alchemical Graphics showing Celestial and Terrestrial Realms
Figure 3.00 - Infinite Number of Atomoles or Alphanon filling all Space
Figure 10.02 - Illusion labeled and accepted as Reality
imaginary number
Indig Numbers
Law of Corporeal Oscillations
Law of Corporeal Vibrations
mass number
Oxidation Number
proton number
quantum number
Sympsionics Numbers
wave number

Page last modified on Wednesday 24 of August, 2011 03:39:32 MDT

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