Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

Real number

In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356... the square root of two, an irrational algebraic number) and π (3.14159265..., a transcendental number). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one. The real line can be thought of as a part of the complex plane, and correspondingly, complex numbers include real numbers as a special case.

These descriptions of the real numbers are not sufficiently rigorous by the modern standards of pure mathematics. The discovery of a suitably rigorous definition of the real numbers — indeed, the realization that a better definition was needed — was one of the most important developments of 19th century mathematics. The currently standard axiomatic definition is that real numbers form the unique complete totally ordered field (R,+,·,<), up to isomorphism,[1] Whereas popular constructive definitions of real numbers include declaring them as equivalence classes of Cauchy sequences of rational numbers, Dedekind cuts, or certain infinite "decimal representations", together with precise interpretations for the arithmetic operations and the order relation. These definitions are equivalent in the realm of classical mathematics.

Office Hours

Monday 10 -2

Tuesday 10-12

Thursday 11-1

My Timetable


Contacts


email: [email protected]

[email protected]

Phone: 2570

Welcome

Welcome To Faculty of Engineering

Almajmaah University


IEEE


http://www.ieee.org/

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Links of Interest


http://www.utk.edu/research/

http://science.doe.gov/grants/index.asp

http://www1.eere.energy.gov/vehiclesandfuels/

http://www.eere.energy.gov/


Travel Web Sites

http://www.hotels.com/

http://www.orbitz.com/

http://www.hotwire.com/us/index.jsp

http://www.kayak.com/

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