Which numbers are real? / Michael Henle.

Format:

Book

Author/Creator:

Henle, Michael, author.

Series:

Classroom resource materials (Unnumbered)

Classroom resource materials

Language:

English

Subjects (All):

Numbers, Real.

Numbers, Complex.

Number theory.

Physical Description:

1 online resource (x, 219 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Washington : Mathematical Association of America, 2012.

Language Note:

English

Summary:

Which Numbers are Real? surveys alternative real number systems: systems that generalize and extend the real numbers while staying close to the properties that make the reals central to mathematics. These systems include, for example, multi-dimensional numbers (the complex numbers, the quaternions, and others), systems that include infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). All the systems presented have applications and several are the subject of current mathematical research. Which Numbers are Real? will be of interest to anyone who likes numbers, but particularly upper-level undergraduates, graduate students, and mathematics teachers at all levels.

Contents:

[Pt.] I. The reals. Axioms for the reals

Construction of the reals

[pt.] II. Multi-dimensional numbers. The complex numbers

The quaternions

[pt.] III. Alternative lines. The constructive reals

The hyperreals

The surreals.

Notes:

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Includes bibliographical references (p. 205-208) and index.

Description based on print version record.

ISBN:

1-61444-107-3

OCLC:

817966939