# real number system

## real number system

[¦rēl ′nəm·bər ‚sis·təm]
(mathematics)
The unique (to within isomorphism) complete ordered field; the field of real numbers. Also known as real continuum.
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The text assumes that readers know that the real number system satisfies the ordered field axioms.
He offers tips on passing the exam and reviews its various topics, with examples, questions, and answers: sets, the real number system, algebra, functions and their graphs, geometry, probability and statistics, and logic.
The dictionary provides an example of usage: "zillions of mosquitoes." It isn't a part of the real number system. It is equal to JILLION, which also means "an indeterminately large number." In fact it is equal to other members of the indeterminate number system, such as BAJILLION, BAZILLION, GAZILLION and UMPTILLION.
Elementary real analysis deserves its place as a core subject in the undergraduate mathematics curriculum because of the way it provides a rigorous foundation for the theory of calculus through logical deduction from the properties of the real number system, yet most textbooks on the subject treat it with the writing style of professional mathematics, unsuited to students at the undergraduate level, according to Denlinger (Millersville U.), who here addresses that situation by presenting a text with conversational exposition, emphasis on the underlying ideas and unity of the subject, proofs written in a style appropriate for undergraduate homework, and adoption of logical symbolism intended to aid the student in recognizing formal patterns of thinking, among other pedagogical features.
* our real number system is too small, but a solution of [x.sup.2] + 1 = 0 may be found in a larger number system.
In contrast with Einstein's theory of relativity, in which time is modeled using the real number system, state theory defines a state as a moment in time, a point of time, an instant, and as such has no duration.
Bridges, an eminent disciple of Errett Bishop, and provides a wide-ranging constructivist (primarily Bishopian) view of the real number system. This paper, whose concerns are very different from those of all the others, detracts from the collection's unity; but as it has considerable intrinsic merit, it would be churlish to complain about its inclusion.
Then he moves to a fairly conventional discussion of various aspects of the completeness of the real number system. Final chapters look at sequential continuity, differentiability, and the validity of Newton's and Euler's methods and results.
They systematically treat important properties of the real number system and such concepts as mapping, sequences, limits, and continuity.
Goodfriend (George Washington U.) describes the development of the real number system as it relates to subjects in higher mathematics such as abstract algebra, number theory, and analysis.

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