MAT137Y1 Lecture Notes - Lecture 6: Monotonic Function
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MAT137Y1 Full Course Notes
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Pf: let f be a function with domain d i assume f is increasing on d wts: f is one-to-one on d wts: I need to nd one function that is one-to-one but not increasing. Introduce the variables don"t assume the conclusion use words. Pf: let x, y be two odd numbers wts: x + y is even by de nition of odd, we know s. t. x = 2a + 1, y. = 2b + 1 x + y = 2a + 1 + 2b + 1 = 2a + 2b + 2 = 2(a + b + 1) therefore x + y is divisible by 2 i"ve shown that x.