Introduction to Mathematical Thinking by Devlin Keith

Author:Devlin, Keith [Devlin, Keith]
Language: eng
Format: mobi, epub
ISBN: 9780615653631
Publisher: Keith Devlin
Published: 2012-07-18T03:00:00+00:00

We would read this as “For all real numbers x, the square of x is greater than or equal to 0.”

Most statements in mathematics involve combinations of both kinds of quantifier. For instance, the assertion that there is no largest natural number requires two quantifiers, thus:

This reads: for all natural numbers m it is the case that there exists a natural number n such that n is greater than m.

Notice that the order in which quantifiers appear can be of paramount importance. For example, if we switch the order in the above we get

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