Proof by Induction – Mathematical Preliminaries Part 4 Computability Theory by ComputeNow - October 28, 2018October 28, 20180 A proof by induction is the powerful and important technique for proving theorems, in which every step must be justified. For each positive integer n, let P(n) be a mathematical statement that depends on n. Assume we wish to prove that P(n) is true for all positive integers n.A proof by induction of such a statement is carried
Mathematical Statement Computability Theory by ComputeNow - October 16, 20180 Mathematical Statement For understanding any mathematical statement we first need to recollect what maths is basically. When we solve any problem in maths our solution is either right or wrong. There is no midway to the problems! Similar is the situation with any mathematical statement. A mathematical statement is either true
Pigeon Hole Principle Mathematical Preliminaries Part 3 Computability Theory by ComputeNow - October 8, 20180 Pigeon Hole Principle If n+1 or more objects are placed into n boxes, then there is at least one box containing two or more objects. In other words, if A and B are two sets such that |A| > |B|, then there is no one-to-one function from A to B. Theorem 1: Let n be a
