1. ## How to prove

Hi,

I want to learn the art of constructing proofs but it proves difficult namely because I don't know how to begin. I've become familiar with a variety of methods such as proof by contradiction, deduction, exhaustion, induction etc.

How I approach trying to prove something is that I read it out in words and then write it down. It's as if I know it's true but I struggle to piece it together through maths though. I've come from an engineering maths syllabus and I enjoyed it so much it's become an addiction but I feel like I lack the essence and purity of it all. I've taken a step back and decided to study the theory of sets and grammar books for a start. I'm absorbing definitions and theorems a lot more seriously now, but again its the rigor.

Could any members suggest some good books or even provide a learning curve for where to begin in learning how to prove?

2. ## Re: How to prove

Originally Posted by PilgrimsPath
Hi,

I want to learn the art of constructing proofs but it proves difficult namely because I don't know how to begin. I've become familiar with a variety of methods such as proof by contradiction, deduction, exhaustion, induction etc.

How I approach trying to prove something is that I read it out in words and then write it down. It's as if I know it's true but I struggle to piece it together through maths though. I've come from an engineering maths syllabus and I enjoyed it so much it's become an addiction but I feel like I lack the essence and purity of it all. I've taken a step back and decided to study the theory of sets and grammar books for a start. I'm absorbing definitions and theorems a lot more seriously now, but again its the rigor.

Could any members suggest some good books or even provide a learning curve for where to begin in learning how to prove?

YES it is the rigor.

For example starting with the axioms of the real No system can you write a single rigorous proof ??

If Iwas YOU i would never start with the theory of sets you going to get confused and when you ask for help you going to get even more

The rigor there is very complicated and you have to be an expert in Logic

3. ## Re: How to prove

Originally Posted by PilgrimsPath
Could any members suggest some good books or even provide a learning curve for where to begin in learning how to prove?
THIS TEXTBOOK is the best text I ever used for a basic abstract mathematics proofs course.
Note that it is available in a DOVER paperback. Any edition would work for your purposes.