Sets, functions, and logic: an introduction to abstract mathematics
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Content: PREFACESTUDENTS START HEREWHAT IS MATHEMATICS AND WHAT DOES IT DO FOR US?It's Not Just NumbersMathematical NotationMaking the Invisible Visible This is Where You Come InThe Study of Modern Mathematics MATH SPEAKThe Language of Mathematics: Part 1Properties of the LanguageThe Language of Mathematics: Part 2Properties of Quantification Proofs in Mathematics The IntegersMathematical TruthSET THEORYSetsOperations on SetsReal Intervals Absolute ValuesInequalitiesArbitrary Unions and IntersectionsCartesian Products The Historical Development of Set TheoryFUNCTIONSThe Function ConceptExamples of FunctionsHistory of the Modern Function ConceptOne-One and onto FunctionsComposition and Inverse FunctionsDenumerability UncountabilityRELATIONSBinary Relations Properties of Relations Relations as Sets of Ordered Pairs Relations as GraphsEquivalence Relations Functions as Relations An Example: the Reals Upper Bounds. Completeness SequencesNo Answers to the ExercisesList of SymbolsIndex
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