Re: Integers

William M. Klein wrote:
It seems to me that the term "integer" probably has standard/normal definitions within mathmatics (possibly slightly different - depending upon the branch of mathmatics)

There are sevaral ways to formulate axioms that characterize the integers, but they are all equivalent. As Kronecker put it, "God made integers, all else is made by man." Presumably he didn't mean that to be taken literally, as God managed to keep the universe ticking over for billions of years before Einstein and Schroedinger (and others) came along to explain to Him how it works. What he no doubt meant is that the integers or natural numbers have an inevitability about them that leaves no room for creative variations. Actually, the same can be said for the rationals, the reals, and the complex numbers. No matter how you formulate them, the integera and rationals are countable while the reals and complex aren't, SQRT(2), e, and pi are always irrational, sqrt(2) is algebraic while e and pi are transcendental, only the complex are algebraically closed, ...



BUT that within programming languages, it may (or may not) become
"language-specific jargon".

The only scope that machine and language desingners have is choice of representation and what to do when things are pushed too far and go off the rails.

....
.

Relevant Pages

  • Re: Review: Religulous (2008)
    ... it always seems to start fights on the Internet. ... but not between the Rationals and ... small to be put in one-to-one correspondence with the Reals. ... know if there is a God or not. ...
    (rec.arts.movies.current-films)
  • Re: Review: Religulous (2008)
    ... it always seems to start fights on the Internet. ... but not between the Rationals and ... small to be put in one-to-one correspondence with the Reals. ... know if there is a God or not. ...
    (rec.arts.movies.current-films)
  • Re: Integers
    ... As Kronecker put it, "God made integers, all else is made by man." ... Presumably he didn't mean that to be taken literally, as God managed to keep the universe ticking over for billions of years before Einstein and Schroedinger came along to explain to Him how it works. ... Actually, the same can be said for the rationals, the reals, and the complex numbers. ...
    (comp.lang.pl1)
  • Re: Review: Religulous (2008)
    ... One of the problems with reviewing a controversial documentary is that ... it always seems to start fights on the Internet. ... but not between the Rationals and ... know if there is a God or not. ...
    (rec.arts.movies.current-films)
  • Re: Review: Religulous (2008)
    ... One of the problems with reviewing a controversial documentary is ... that it always seems to start fights on the Internet. ... There are too few Rationals numbers and too many ... Any comprehensible argument that God ...
    (rec.arts.movies.current-films)