STRATEGY FOR MATHEMATICAL PROOF

STRATEGY FOR MATHEMATICAL PROOF

1. DIRECT PROOF

   • 1) Determine the proposition
     • simple proposition
     • using cases
   • 2) Write the outline
   • 3) Determine the definition related
     • even number = 2a
     • odd number = 2a + 1
   • 4) Proof!!
     • example

2. CONTRAPOSITIVE

   • • 2) negate the statement
     • 3) converse the negate statement
     • 5) Proof !
       • example
     • 4) Write the outline
     • 1) Determine the proposition
       • not equal (≠) statement
       • to prove injuctive
   • Alternative to Direct Proof

3. CONTRADICTION

   • • 5) Proof
       • example
     • 3) Deduce new statement
     • 2) Assume that the statement is false
     • 4) Write the outline
     • 1) Determine the proposition
       • not equal (≠) statement
       • prove irrational number

4. MATHEMATICAL INDUCTION

   • • 5)Proof
       • example
     • 1) determined the proposition
       • suitable for progression proposition
       • Fibonacci sequences statement
     • 2) Show S(1) is true
     • 3) Assume S(k) is true
     • 4) Show that S(k+1) is true
       • Left-hand side equal to right-hand side

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