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Introduction to mathematical arguments

Introduction to mathematical arguments (background handout for courses requiring proofs)by Michael HutchingsA mathematicalproofis an argument which convinces other people thatsomething is true. Math isn t a court of law, so a preponderance of theevidence or beyond any reasonable doubt isn t good enough. In principlewe try to prove things beyond any doubt at all although in real life peoplemake mistakes, and total rigor can be impractical for large projects. (Thereare also some subtleties in the foundations of mathematics, such as G odel stheorem, but never mind.)

tried to keep this introduction brief and I hope it will be a useful guide. In §1 we introduce the basic vocabulary for mathematical statements. In §2 and §3 we introduce the basic principles for proving statements. We provide a handy chart which summarizes the meaning and basic ways to prove any type of statement.

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