Principle of Mathematical Proofs

                                                         Induction Proofs:

The Principle of mathematical proofs (PMI) is not an easy proof at first, these types of proofs take practice. To set up (PMI) we need to choose a

 Base Case: prove that  is true

Induction Step: suppose that  is true.

                                               Prove that  is also true. 

It is important that the structure of the proof is correct. In the induction step we are assuming 

 is true. We actually assume  is true for all k. 

Example:  Prove 1+2+3+.....+100=? For all n in N, 

Proof by PMI: 

Base Case: we must show 

LHS: (left hand side) 

RHS: (right hand side) 

Right hand side and left hand side =1 so the base case is true. 

Induction Step: Suppose that 

 we want to prove 

.

 by the inductive hypothesis

 which is what we wanted to prove. 

Thereforefor all n in N. 

It is sometimes easier to work out the first steps to get a sense of how to prove the general inductive step, like i did up above. 

Potential Exam Question: For all n greater than of equal to Z, Prove the following statement: 

Citations: Professor Aaron Wong Proof Notes / Professor Arthur T. Benjamin's Video notes