catflap.org Online Dictionary Query

  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,
       
           | r[n] - r[m] | < 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,
       
           | r[n] - 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)
       
       

  real number
       n : any rational or irrational number [syn: real]

  real number
     n.
     1 (lb en mathematics) The limit of a convergent sequence of rational
  numbers, whether the limit is a rational number such as 2, -5, or 2/7 or
  whether the limit is an irrational number such as the square root of two
  or the circumference of the circle whose radius is one.
     2 (lb en computing) A floating-point number.

  real number
     n.
     1 (lb en mathematics) The limit of a convergent sequence of rational
  numbers, whether the limit is a rational number such as 2, -5, or 2/7 or
  whether the limit is an irrational number such as the square root of two
  or the circumference of the circle whose radius is one.
     2 (lb en computing) A floating-point number.

  real number
     n.
     1 (lb en mathematics) The limit of a convergent sequence of rational
  numbers, whether the limit is a rational number such as 2, -5, or 2/7 or
  whether the limit is an irrational number such as the square root of two
  or the circumference of the circle whose radius is one.
     2 (lb en computing) A floating-point number.

  real number
     n.
     1 (lb en mathematics) The limit of a convergent sequence of rational
  numbers, whether the limit is a rational number such as 2, -5, or 2/7 or
  whether the limit is an irrational number such as the square root of two
  or the circumference of the circle whose radius is one.
     2 (lb en computing) A floating-point number.

  real number
     Englanti n.
     (yhteys matematiikka k=en) reaaliluku

  real number
     Engelska n.
     (tagg språk=en matematik) reellt tal

  real number /ɹˈiəl nˈʌmbə/ 
   [poč] číslo s desetinnou čárkou

  real number /ɹˈiəl nˈʌmbə/
  reelle Zahl  [math.]

  real number /ɹˈiəl nˈʌmbə/ 
  reaaliluku
  limit of a convergent sequence of rational numbers

  real number /ɹˈiəl nˈʌmbə/ 
  実数
  limit of a convergent sequence of rational numbers

  real number /ɹˈiəl nˈʌmbə/ 
  reelt tall
  limit of a convergent sequence of rational numbers

  real number /ɹˈiəl nˈʌmbə/ 
  reellt tal, reella tal
  limit of a convergent sequence of rational numbers