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An Introduction to Mathematical Reasoning by Peter J. Eccles

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6

The language of set theory

The students’ task in learning set theory is to steep themselves in unfamiliar and essentially shallow generalities till they become so familiar that they can be used with almost no conscious effort.

Paul R. Halmos, Naive set theory (adapted slightly).

The language of set theory is used throughout mathematics. Many general results involve ‘an integer n’ or ‘a real number a’ and, to start with, set theory notation provides a simple way of asserting for example that n is an integer. However, it turns out that this language is remarkably flexible and powerful and in much mathematics it is indispensable for a proper expression of the ideas involved.

In the second part of this book we introduce the basic vocabulary of ...

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