logic2

logic2 - Some Useful Logic: Part 2 Math 8 2009, Chris Lyons...

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Some Useful Logic: Part 2 Math 8 2009, Chris Lyons Very often in Math 1a, we’ll consider true-or-false statements about the elements in some set. We may want to consider whether all elements in the set have some property, or whether at least one element has that property. This is where “quantifiers” come in. We’re going to discuss quantifiers in just enough detail so that we can use them for Math 1a purposes. Don’t forget: If x is an element of the set T , we write x T . The following are abbreviations for sets: the natural numbers N = { 1 , 2 , 3 , 4 ,... } , the integers Z , the rational numbers Q , and the real numbers R . Quantifiers Consider a true-or-false statement such as P : Every x R satisfies x 2 0 . We can write it differently, but without changing the meaning, as P : For every x R we have x 2 0 . Typically in math, phrases like “for every” or “for all” or “for each” get replaced by the symbol . So the above statement would be written
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This note was uploaded on 07/19/2010 for the course MA 8 taught by Professor Vuletic,m during the Fall '08 term at Caltech.

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logic2 - Some Useful Logic: Part 2 Math 8 2009, Chris Lyons...

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