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1.1: Sets
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We start off by providing a “definition” of a basic mathematical structure to which we will soon add bells and whistles. We use quotes here because what follows doesn't have the precision we usually require when defining a mathematical object.
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1.2: Functions
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You have probably encountered functions before. In introductory calculus, for instance, you typically deal with functions from real numbers to real numbers (e.g., the function f(x) = x^2). More generally, functions “send” elements of one set to elements of another set; these sets may or may not be sets of real numbers. We provide below a “good enough for government work” definition of a function.
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1.3: Cardinality
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One of the set traits that will be useful to us in distinguishing between algebraic structures is cardinality.
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1.4: Exercises
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This page contains the exercises for Chapter 1.