Talk:Real number

"Real number" or "real numbers"?

I'd prefer, overall, this article to be at real numbers, rather than at the singular name. After all, unlike ordinal numbers, a single real number does not really have any property that can be expressed without referring to other real numbers, unless the (non-standard) choice of which construction to use is made.

(Note I accidentally started the other article before I noticed the singular article had already been copied over. I'm now not sure which one to turn into a redirect.)

Thoughts?

Philipp Rumpf 13:56, 3 February 2007 (CST)

I vote for 'real number'. The language of the article is not straightforward. I wish my memory was good enough to quote my second grade classmate Michael Cohen (Mike, are you out there?) ((whose father was a professor at the Institute for Advanced Study)) when he explained the term to our disapproving second grade teacher. Can you simplify the language? NancyNancy Sculerati MD 16:18, 3 February 2007 (CST)

Any reasons for preferring "real number"? It's possible to write an article about a "real number" (something along the lines of "a real number is a rational number, or a mathematically consistent description of how a new number would be larger than some rationals, and smaller than some other rationals, but not necessarily rational itself") - but that would make our choice for one preferred definition (Dedekind cuts, in this case), which might be controversial, but the current article is more about "the field of real numbers".

Hmm, I was just asked by someone physically present to define real number, and went for "it's an orderable number that's not infinitesimal and not infinitely large, i.e. smaller than some natural, and larger than the reciprocal of some natural". Admittedly, it only covers the positive case, but (while not very mathematical), I must say I kind of like the definition. Starting with the totality of all imaginable "numbers", you must delete those that are infinitely small, in the "close to zero" sense, or infinite, or not orderable on a line, and all those which would result in one of the first three by arithmetic operations, but you're still left with quite a few, and those are the real numbers.

Back to your comment, what do you think could be improved? It's really hard for some mathematicians, including myself, to still realise which bits of an introductory article on a subject I'm familiar with are inaccessible to other readers.

Philipp Rumpf 16:52, 3 February 2007 (CST)