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MAT137 Lecture Notes

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MAT137 Lecture NotesTyler Holden,c 2014-2015Contents1 Logic and Sets and notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamental Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , Then . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . and the Contrapositive.

choose to let our sets be unbounded by writing in nities: (1 ;a) = fx2R : x<ag (a;1) = fx2R : x>ag 2Some mathematicians do not believe that 0 is a natural number. 3Strange things can happen if we are not careful with de ning the real numbers. For example, consider the number

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