Strategy for Mathematical Proof

CONTRAPOSITIVE
3. Used when: contraposotive proof is easier, simple direct proof would be problematic.
4. To prove proposition "If p, then q."
  1. contrapositive form ∼ Q ⇒∼ P
    1. assume ∼ Q is true use this to deduce that ∼ P is true
DIRECT
1. Proposition : True statement but not as significant Lemma :prove other theorem Collary:immediateconsequence of a theorem or proposition
2. If p, then q
3. 1. Assume that P is true. 2. Use P to show that Q must be true.
5. Accept these facts without justification or proof.
6. Using Cases
7. Definition : Odd number : 2a + 1, a E
INDUCTION
1. use recursion to demonstrate an infinite number of facts in a finite amount of space.
2. condition : when a set of statements is given ex. Fibonacci numbers
3. Step 1: Proof S1 is true
  1. Step 2 : Proof Sk →Sk+1 is true
4. examples
CONTRADICTION
1. used when direct and contrapositive methods do not seem to work.
2. assume that the statement we want to prove is false, and then show that this assumption leads to nonsense.
  1. 1. Assume that P is true.
    1. 2. Assume that ~Q is true.
      1. 3. Use P and ~Q to demonstrate a contradiction.

Resource summary

	Created by Jia Wen Sew over 9 years ago