Talk:Superreal number

Context
Yes, I agree that this article lacks sufficient context, and I've made the barest, feeblest attempt to rectify this but I'm not really an expert.

Also I did have one specific question: "The quotient field F of A is a superreal field "

Quotient of A by what? We started with a Tychonoff space X, got the algebra of continuous real-valued functions, C(X) identified P, a prime ideal in this algebra and formed A, the factor algebra of C(X)/P

What are we modding out by in the next step? F = A/

Zero sharp 00:09, 27 July 2007 (UTC)


 * Nothing; we're taking the field of fractions of A.Ben Standeven (talk) 06:51, 11 March 2009 (UTC)

Algebraically isomorphic to R but not order isomorphic to R?
The text says: The quotient field F of A is a superreal field if F strictly contains the real numbers, so that F is not order isomorphic to , though they may be isomorphic as fields.. Duh? I don't think this is possible: if F is algebraically isomorphic to R, then we can define positive or negative numbers of F using the existence or non-existence of the square root, etc. Albmont (talk) 14:31, 16 January 2008 (UTC)


 * Yeah, good point.Ben Standeven (talk) 06:49, 11 March 2009 (UTC)

Hewitt
The relation to Edwin Hewitt's paper should be clarified: Hewitt, Edwin (1948) Rings of real-valued continuous functions. I. Trans. Amer. Math. Soc. 64, 45--99. On page 74, Hewitt defined the hyper-real field. His construction is very similar to what is described here. Tkuvho (talk) 12:40, 19 April 2010 (UTC)

Title change?
The title is somewhat confusing.

First, the article of Dales and Woodin talks about "super-real fields" with a dash. Second, though one could say that a super-real number is an element of a super-real field, this is bad phrasing (just like saying that a ring-number is an element of a ring would be bad phrasing), and it would make more sense to directly talk about super-real fields. This avoids a further confusion in the introduction when "The field of superreal numbers" is mentioned as though it were one specific super-real field. Vincent Bagayoko (talk) 23:14, 13 December 2017 (UTC)

Expand upon "the algebra of continuous real-valued functions"
The term algebra here seems ambiguous. At least, ambiguous enough to warrant further clarification. — Preceding unsigned comment added by 2601:281:8000:FE0:B85E:C6F5:68A0:25EC (talk) 23:29, 23 June 2018 (UTC)