MATH1151 Chapter Notes - Chapter 1: Sydney Trains S Set, Empty Set, Upper And Lower Bounds
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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. Sets and elements: definition, a set is a collection of distinct objects, the objects in a set are called the elements (or members) of the set. Notation for standard sets: n = {0, 1, 2, 3, . (set of all natural numbers, z = {. 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.
