High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Suppose X is a Tychonoff space, also called a T3.5 space, and C(X) is the algebra of continuous real-valued functions on X. Suppose P is a prime ideal in C(X). Then the factor algebra A = C(X)/P is by definition an integral domain which is a real algebra and which can be seen to be totally ordered. The field of fractions F of A is a superreal field if F strictly contains the real numbers Bbb{R}, so that F is not order isomorphic to Bbb{R}. If the prime ideal P is a maximal ideal, then F is a field of hyperreal numbers. The terminology is due to Dales and Woodin. Dales and Woodin's supperreals are different from super-real numbers of David O. Tall, which are lexicographically ordered fractions of formal power series over the reals.

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