Enrichment Chapters 1-4 Form an Idealized Undergraduate Course

Book Id: WPLBN0000673395
Format Type: PDF eBook:
File Size: 0.3 MB
Reproduction Date: 2005

Title:	Enrichment Chapters 1-4 Form an Idealized Undergraduate Course
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Language:	English
Subject:	Science., Mathematics, Logic
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Citation APA MLA Chicago Enrichment Chapters 1-4 Form an Idealized Undergraduate Course. (n.d.). Enrichment Chapters 1-4 Form an Idealized Undergraduate Course. Retrieved from http://gutenberg.us/

Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: When we say that the rational numbers form a group under addition, we mean that rational numbers can be added and subtracted, and the result will inevitably be rational. Similarly for the integers, the real numbers, and the complex numbers. But the integers (even the nonzero integers) do not form a group under multiplication. If a is an integer other than+/-1, there is no integer b such that ab = 1. The nonzero rational numbers form a group under multiplication, as do the nonzero reals and the nonzero complex numbers. Not only can we add and subtract rationals, we can multiply and divide them (if the divisor is nonzero). The rational, reals and complex numbers are examples of fields, which will be studied systematically in Chapter 3.