Published 2019
Table of Contents:
“…and ⁶</P><P>Ordered Pairs; Product Sets</P><P>General Unions and Intersections</P><P>Axiomatic Set Theory (Optional)</P><P></P><B><P>Integers</P></B><P>Recursive Definitions; Proofs by Induction</P><P>Induction Starting Anywhere: Backwards Induction</P><P>Strong Induction</P><P>
Prime Numbers; Division with Remainder</P><P>Greatest Common Divisors; Euclid's GCD Algorithm</P><P>More on GCDs; Uniqueness of Prime Factorizations</P><P>Consequences of Prime Factorization (Optional)</P><P></P><B><P>Relations and Functions</P></B><P>Relations; Images of Sets under Relations</P><P>Inverses, Identity, and Composition of Relations</P><P>Properties of Relations</P><P>Definition of Functions</P><P>Examples of Functions; Proving Equality of Functions</P><P>Composition, Restriction, and Gluing</P><P>Direct Images and Preimages</P><P>Injective, Surjective, and Bijective Functions</P><P>Inverse Functions</P><P></P><B><P>Equivalence Relations and Partial Orders</P></B><P>Reflexive, Symmetric, and Transitive Relations</P><P>Equivalence Relations</P><P>Equivalence Classes</P><P>Set Partitions</P><P>Partially Ordered Sets</P><P>Equivalence Relations and Algebraic Structures (Optional)</P><P></P><B><P>Cardinality</P></B><P>Finite Sets</P><P>Countably Infinite Sets</P><P>Countable Sets</P><P>Uncountable Sets</P><P></P><B><P>Real Numbers (Optional)</P></B><P>Axioms for R; Properties of Addition</P><P>Algebraic Properties of Real Numbers</P><P>Natural Numbers, Integers, and Rational Numbers</P><P>Ordering, Absolute Value, and Distance</P><P>Greatest Elements, Least Upper Bounds, and Completeness</P><P></P><B><P>Suggestions for Further Reading</P></B>…”
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Taylor & Francis
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Electronic
eBook