Tuesday, October 20th, 2009
How to Write Proofs by Exhaustion
Description
A detailed tutorial on writing proofs by exhaustion. Step by step tutorial including several examples of how to write proofs by exhaustion for reference.
Overview
A proof by exhaustion is one of the easier types of proofs to write. All this proof involves is testing cases – every case possible for what you are trying to prove. This can be made easier by using variables instead of numbers, or by testing for an even number and odd number, positive and negative number, etc. That way you do not have to test many numbers in order to prove. If even one of the cases does not work out, then whatever you are testing for has been disproven.
Tags: cases, discrete math, disproven, even, exhaustion, Math, method, negative, odd, positive, possibilities, proof, proofs, proven, variable, write
Posted in Discrete Math | No Comments »
Thursday, October 8th, 2009
Introduction to the Principle of Mathematical Induction
Description
A detailed tutorial of the principle of mathematical induction. Step by step tutorial including several examples of the principle of mathematical induction for reference.
Overview
The principle of mathematical induction is basically a method of proof-writing, which involves trying to prove that a certain statement is true for all natural numbers. The first statement will be proved, and then the next statement, and the next one. In this way, it is similar to a proof by exhaustion. However, since the statement must be proven for all numbers, eventually an integer will be used in the calculations. This should not be confused with mathematical induction – the principle of mathematical induction is actually a type of deductive reasoning.
Tags: deductive, discrete math, exhaustion, induction, interger, k, Math, mathematical, n!, natural, number, principle, proof, reasoning, statement
Posted in Discrete Math | No Comments »
