EECS 1019 Lecture Notes - Lecture 2: Opata Language, Pigeonhole Principle
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EECS 1019 Full Course Notes
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Notes: the assignment can be handwritten or typed. It must be legible: you must do this assignment individually, submit this assignment only if you have read and understood the policy on academic honesty on the course web page. Please do not send les by email: your answers should be precise and concise. Points may be deducted for long, rambling arguments: assume r to denote the real numbers, z to denote the set of integers (. , 2, 1, 0, 1, 2, . and n to denote the natural numbers (1, 2, 3, . [4 points] prove using mathematical induction that for all natural numbers n, [4 points] prove that n3 + (n + 1)3 + (n + 2)3 is divisible by 9. [4 points] recall that a number y is rational if it satis es y = p/q where p, q are integers and q (cid:54)= 0. Prove that any number of the form a + b.