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chapterI - The introductory chapter to Apostols Calculus 1...

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The introductory chapter to Apostol’s Calculus 1 is kind of a mish-mash of different topics, but it includes the introduction of several vital topics for the study of Calculus. 1. Section I.1: Historical Introduction This is a really introductory section, read it at least once, but it does not contain any facts/methods that you really need to know. 2. Section I.2: Some basic concepts in the theory of sets We will be working a lot with sets so it is vital you have a rough idea what a set is, and can work with the notations introduced here. A set can be viewed as a big bag, which can hold arbitrarily many items, but holds each item at most once. It gets particularly complicated when the elements of a set are themselves sets. The most important notations you should be familiar are x A : Element of A = { 1 , 4 , 5 } : Defining a set by listing its elements; A B (and derived notations as A B , A B , A B ): Being contained in; A = { x | Some condition on x } : Definition by defining property; A B , and S n A n : Union; A B , and T n A n : Intersection; A - B = A \ B : Complement; • ∅ : Empty set.

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