PROOF

Amirul Omar
Mind Map by Amirul Omar, updated more than 1 year ago
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Mind Map on PROOF, created by Amirul Omar on 07/13/2016.

Resource summary

PROOF
1 Methods
1.1 Indirect Method
1.1.1 Contrapositive
1.1.1.1
1.1.2 Contradiction
1.2 Direct Method
1.2.1 Conditional Statement
1.2.1.1 If p, then q (p --> q)
1.2.2 Outline
1.2.2.1 If p, then q
1.2.2.1.1 Suppose p
1.2.2.1.1.1 ...
1.2.2.1.1.1.1 Therefore q
1.2.3 Example
1.2.3.1 Prove that if x is odd, then x2 is odd
1.2.3.1.1 Suppose x is odd
1.2.3.1.1.1 x = 2k + 1
1.2.3.1.1.1.1 x2 = (2k+1)2
1.2.3.1.1.1.1.1 4k2 + 4k + 1
1.2.3.1.1.1.1.1.1 2(2k2+1)+1
1.2.3.1.1.1.1.1.1.1 m=2k2+2k
1.2.3.1.1.1.1.1.1.1.1 x2=2m+1
1.2.3.1.1.1.1.1.1.1.1.1 Therefore, x2 is odd
1.3 Mathematical Induction
1.3.1 Conditional statement
1.3.1.1 AxeN, P(x)
1.3.2 Outline
1.3.2.1 Basis step
1.3.2.1.1 Prove P(1) is true
1.3.2.1.1.1 Inductive step
1.3.2.1.1.1.1 Prove P(k) --> P(k+1) is true
1.3.3 Example
2 Definition
2.1 Theorem
2.1.1 A mathematical statement that is true and proved to be true
2.2 Proof of a Theorem
2.2.1 A written verification
2.3 Definition
2.3.1 An exact an unambiguous (no double imterpretations) explanation of a meaning of a mathematical word or phrase
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