## Book of ProofDepartment of Mathematics & Applied Mathematics, Virginia Commonwealth University, 2009 - Mathematics - 294 pages This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality. |

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answer bijective binomial theorem cardinality Cartesian product Chapter codomain column conditional statement contains continuum hypothesis contrapositive proof countably infinite counterexample defined as f(x definition DeMorgan's laws direct proof divisor elements equation equivalence classes equivalence relation example Exercises for Section exists expression F F F fact Figure following statements function f gcd(a gcd(a,b implies injective integer lists of length logically equivalent mathematical induction means multiple natural number need to show negation notation odd number open sentence ordered pair parity perfect number positive number prime number Prove or disprove Q is true quantified statement rational number real number reflexive Russell's paradox sake of contradiction set-builder notation Sk+1 statement is true subset surjective symbols symmetric and transitive true or false truth table uncountable Venn diagrams write