Flashcards
Proof
Cards in this deck (6)
- 1What is proof?Mathematical proof involves the indisputable demonstration that a conjecture (mathematical theory) is true for all numbers in a set e.g. real or complex numbers
- 2How can proof be carried out?1. Proof by direct argument
2. Proof by exhaustion
3. Proof by contradiction
4. Disproof by counter-example - 3Proof by direct argumentIn a simplified form:
1. Take a fact that is indisputably true
2. Do indisputably true stuff to it
3. If the previous two steps were performed correctly, the result will also be indisputably true - 4Proof by exhaustionExtension of proof by direct argument - proof is split into two or more cases e.g. odd and even integers then each is proved in turn
- 5Proof by contradiction1. Assume that the conjecture is false
2. Set up an example in this false-conjecture system
3. Do indisputably true stuff to the example
4. End up with nonsense, implying that the initial conjecture was true - 6Disproof by counter-exampleIf, in order to become a theorem, a conjecture must be proven true for every member of its set.
Therefore, by finding an example within the set where the conjecture is false, it can be disproven.
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- A level OCR A level Maths (Problem Solving) Flashcards on Proof, created by James Norman on 28/05/2019.
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- James Norman
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