CALCULUS

CALCULUS

1. Direct Proof

   • givens or deductions from previous statements
   • Sample

2. Methods of Mathematical Proof

3. Contrapositive Proof

   • Sample
   • to prove conditional statements of the form “If P, then Q.”

4. Contradictive Proof

   • Sample
     • • • • From this last equation, we see that 1 is an even number, a contradiction
   • to assume that the statement we want to prove is false, and then show that this assumption leads to nonsense.

5. Mathematical Induction

   • Sample
     • • • • • Thus the result follows by mathematical induction
   • a means of proving a theorem by showing that if it is true of any particular case

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