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MAT137 Lecture Notes

MAT137 Lecture NotesTyler Holden,c 2014-2015 Contents1 Logic and Sets and notation .. Fundamental Logic .. , Then .. and the Contrapositive .. Definitions and Theorems .. and Proofs .. Induction .. 162 A Quick Primer on Absolute Values .. Definition .. Measure of Distance .. Limited Intuition .. Waving Arguments .. Of epsilons and deltas .. of Limits .. Limits at Infinity .. Continuity .. The Squeeze Theorem .. The Value Theorems .. Value Theorem .. Value Theorem .. 5013 First Principles .. of Differentiability.

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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