1_STRATEGY FOR MATHEMATICAL PROOF - created from Mind Map

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DIRECT PROOF

CONTRAPOSITIVE

CONTRADICTION

MATHEMATICAL INDUCTION

1) Determine the proposition

2) Write the outline

3) Determine the definition related

4) Proof!!

simple proposition

using cases

even number = 2a

odd number = 2a + 1

example

Alternative to Direct Proof

2) negate the statement

3) converse the negate statement

5) Proof !

4) Write the outline

1) Determine the proposition

example

not equal (≠) statement

to prove injuctive

5) Proof

3) Deduce new statement

2) Assume that the statement is false

4) Write the outline

1) Determine the proposition

example

not equal (≠) statement

prove irrational number

5)Proof

1) determined the proposition

2) Show S(1) is true

3) Assume S(k) is true

4) Show that S(k+1) is true

example

suitable for progression proposition

Fibonacci sequences statement

Left-hand side equal to right-hand side