[1] : WordNet (r) 2.0

real number
     n : any rational or irrational number syn: real
see also:
real 

[2] : The Free On-line Dictionary of Computing (27 SEP 03)

real number
     
         one of the infinitely divisible range of values
        between positive and negative infinity, used to represent
        continuous physical quantities such as distance, time and
        temperature.
     
        between any two real numbers there are infinitely many more
        real numbers.  the integers "counting numbers" are real
        numbers with no fractional part and real numbers "measuring
        numbers" are complex numbers with no imaginary part.  real
        numbers can be divided into rational numbers and irrational
        numbers.
     
        real numbers are usually represented approximately by
        computers as floating point numbers.
     
        strictly, real numbers are the equivalence classes of the
        cauchy sequences of rationals under the equivalence
        relation "~", where a ~ b if and only if a-b is cauchy with
        limit 0.
     
        the real numbers are the minimal topologically closed
        field containing the rational field.
     
        a sequence, r, of rationals i.e. a function, r, from the
        natural numbers to the rationals is said to be cauchy
        precisely if, for any tolerance delta there is a size, n,
        beyond which: for any n, m exceeding n,
     
         | rn - rm | < delta
     
        a cauchy sequence, r, has limit x precisely if, for any
        tolerance delta there is a size, n, beyond which: for any n
        exceeding n,
     
         | rn - x | < delta
     
        i.e. r would remain cauchy if any of its elements, no matter
        how late, were replaced by x.
     
        it is possible to perform addition on the reals, because the
        equivalence class of a sum of two sequences can be shown to be
        the equivalence class of the sum of any two sequences
        equivalent to the given originals: ie, a~b and c~d implies
        a+c~b+d; likewise a.c~b.d so we can perform multiplication.
        indeed, there is a natural embedding of the rationals in the
        reals via, for any rational, the sequence which takes no
        other value than that rational which suffices, when extended
        via continuity, to import most of the algebraic properties of
        the rationals to the reals.
     
        1997-03-12
     
     
see also:
infinity integers complex numbers rational numbers irrational numbers floating point 
equivalence classes cauchy sequences rationals equivalence relation cauchy 
topologically closed field natural numbers embedding 

Cardinal Number >> C Words
Cardinal Number, definition of term: Cardinal Number
cardinal+number_pag1.html

Complex Number >> C Words
Complex Number, definition of term: Complex Number
complex+number_pag1.html

Ip Number >> I Words
Ip Number, definition of term: Ip Number
ip+number_pag1.html

Abundant Number >> A Words
Abundant Number, definition of term: Abundant Number
abundant+number_pag1.html

Cardinal Number >> C Words
Cardinal Number, definition of term: Cardinal Number
cardinal+number_pag1.html

Amicable Number >> A Words
Amicable Number, definition of term: Amicable Number
amicable+number_pag1.html

Atomic Number >> A Words
Atomic Number, definition of term: Atomic Number
atomic+number_pag1.html

Call Number >> C Words
Call Number, definition of term: Call Number
call+number_pag1.html

I P Number >> I Words
I P Number, definition of term: I P Number
i+p+number_pag1.html