MATH1151 Chapter Notes - Chapter 1: Malcolm Turnbull, Sequence, Bounded Function
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Reals, sets and notation (purple notes ch 1) (q29-q32) Consider the sequence of rational numbers xn = 1 + n = 1, 2, 3, . The reason that i know that the sequence xn converges to something is that the sequence is: increasing (ie x1 < x2 < x3 . ), and: bounded above (eg xn < 3 for every n). Every increasing sequence of real numbers which is bounded above converges to a real limit. Notation for standard sets: n = {0, 1, 2, 3, , z = {. , 3, 2, 1, 0, 1, 2, 3, : z+ = {1, 2, 3, , q = { p, r (set of all real numbers), c (set of all complex numbers) (the empty set). Suppose that a and b are two sets. If every element of a is also an element of b then a is called a subset of b.
