Infinity isn't a number. It can only occur in a numerical theory in the form of a limit (either as Lim or implicitly in an integral). To say that something is infinite is the same as saying its size is unbounded, except that 'unbounded' can include objects whose size vary over time. And as the size of an unbounded object can tend to infinity over time, it doesn't help in construction.
Furthermore each language requiring an infinite store is equivalent in behaviour to a language requiring a store that can grow without limit but is finite at any particular time and initialised when needed (except if the initialisation function is non-computable, in which case the original language could never be implemented according to the Church-Turing Thesis).
Sorry to get a bit technical, but I think this entry needs rewording (keep the humour though :-).
--Safalra 16:44, 3 Aug 2005 (GMT)
- Your definition of 'number' is rather inflexible, then. :) Infinity is not a real number, of course, but I see nothing wrong with calling it a number. lament (a Math major in the making)
"A finite number is one that you can imagine; infinity is, therefore, unimaginable."
- This isn't entirely true, of course; really, a better definition of "imagine" is needed. --Ihope127 01:05, 16 Sep 2005 (GMT)
- That's an odd definition of a finite number. It is nearly impossible to imagine huge numbers (e.g. googol) and tiny numbers (e.g. 1/googol), but they're still finite. To some extent certain infinite numbers are more imaginable than some finite numbers. A better definition would be a number whose magnitude (to include complex numbers &ct.) is real (where real numbers can be defined formally in terms of set theory and Dedekind cuts), rather than something as vague as imagination.4D enthusiast (talk) 18:35, 12 July 2013 (BST)
Man, I got's me trouble imagining numbers bigger than nine... --(this comment by 188.8.131.52 at 17:08, 24 November 2009 UTC; please sign your comments with ~~~~)