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Unformatted text preview: 1. AUGUST 30TH: BASIC NOTATION, QUANTIFIERS 1 1. August 30th: Basic notation, quantifiers 1.1. Homework. 1.1 . Assume that P ( x ) is some statement whose truth depends on x . Which of the following is grammatically correct? P ( x ) , x, P ( x ) x P ( x ) Answer: To fix ideas, assume that P ( x ) is the statement x is a rational number. The first sentence would read x is a rational number, for all and it sounds pleasantly zen, but I dont know what it could possibly mean. The dangling for all, by itself, means nothing. The third one says For all x in x is a rational number, and again I dont know what this means: x is a rational number is a statement, not a set. The second one, For all x , x is a rational number, makes sense. It may be true or false, depending on the context (we dont know what x denotes here), but its meaning is clear. 1.2 . Let S be an indexed set of real numbers: S = { s n  n N } ....
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 Fall '11
 Aluffi

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