Proof by Exhaustion | A-level Maths | OCR, AQA, Edexcel скачать в хорошем качестве

Proof by Exhaustion | A-level Maths | OCR, AQA, Edexcel

Proof by Exhaustion in a Snap! Unlock the full A-level Maths course at http://bit.ly/2m5inbq created by Lewis Croney, Maths expert at SnapRevise. SnapRevise is the UK’s leading A-level and GCSE revision & exam preparation resource offering comprehensive video courses created by A* tutors. Our courses are designed around the OCR, AQA, SNAB, Edexcel B, WJEC, CIE and IAL exam boards, concisely covering all the important concepts required by each specification. In addition to all the content videos, our courses include hundreds of exam question videos, where we show you how to tackle questions and walk you through step by step how to score full marks. Sign up today and together, let’s make A-level Maths a walk in the park! The key points covered in this video include: 1. Case Checking 2. Proof by Exhaustion 3. Examples Case Checking We have seen that we can use proof by deduction to turn a conjecture with appropriate axioms into a theorem. Sometimes a conjecture has to be split into a finite number of cases which have to be checked to be true in order to prove the conjecture. In these situations, a general direct proof may not be feasible. We can systematically check the cases to prove the result using a process called proof by exhaustion. Proof by Exhaustion The method of proving a conjecture using cases is called proof by exhaustion. To begin a proof by exhaustion, we must first separate the situation into cases. We can check each case against the conjecture. Once we have checked all of the cases that are possible - we are done. Checking cases has the advantage of providing extra information over the general situation. Summary Proof by exhaustion requires breaking up a situation into distinct cases Each case is checked against the conjecture Having distinct cases gives us extra information to use in the proof If even one single case is incorrect, the whole conjecture is false