What is exhaustive proof?

An exhaustive proof is a special type of proof by cases where each case involves checking a single example. An example of an exhaustive proof would be one where all possible examples include just a few integers that can easily be tested as individual cases.

How do I prove my deductions?

Examples of Proof by Deduction Firstly, choose n and n + 1 to be any two consecutive integers. Next, take the squares of these integers to get n 2 and ( n + 1 ) 2 where ( n + 1 ) 2 = ( n + 1 ) ( n + 1 ) = n 2 + 2 n + 1 . The difference between these numbers is n 2 + 2 n + 1 − n 2 = 2 n + 1 .

What is method of exhaustion in discrete math?

Method of exhaustion, in mathematics, technique invented by the classical Greeks to prove propositions regarding the areas and volumes of geometric figures. Although it was a forerunner of the integral calculus, the method of exhaustion used neither limits nor arguments about infinitesimal quantities.

Is it possible to prove a proof by exhaustion?

Proof by exhaustion requires conclusion for every case. In many situations, proofs by exhaustion are not possible. For example, “show that every multiple of 3 is odd”. In this case, it is not possible to check each case at any stage, because there are huge numbers that are multiples of 3, but it can be shown false by counterexample.

What are the stages of a proof by exhaustion?

A proof by exhaustion typically contains two stages: A proof that the set of cases is exhaustive; i.e., that each instance of the statement to be proved matches the conditions of (at least) one of the cases. A proof of each of the cases.

How to prove a result by exhaustion in Edexcel?

Home Edexcel A Level Maths: Pure Revision Notes 1. Proof 1.1 Proof 1.1.3 Proof by Exhaustion What is proof by exhaustion? How do I prove a result by exhaustion? Try a simpler case if you are stuck. For example, if you are asked to prove that 97 is a prime number you could try thinking about what you would do for smaller primes such as 7 or 11.

How to prove that a set of cases is exhaustive?

A proof that the set of cases is exhaustive; i.e., that each instance of the statement to be proved matches the conditions of (at least) one of the cases. A proof of each of the cases.