RE: Mathematical proof..
September 25, 2014 at 5:17 pm
(This post was last modified: September 25, 2014 at 5:20 pm by Alex K.)
(September 25, 2014 at 5:05 pm)Rhythm Wrote: You take the rules of the system, you plug in variables, and show that by following those rules those variables yield 'x".
Exactly. In principle you start with
1. Axioms which are defined as true and
2. rules of logic which allow you to generate new true statements from known true statements.
You then try to find a logical chain from the axioms to the theorem youd like to prove. If you find one, it's proven.
In reality, it's often messier cause no mathematician sticks to making all elementary steps explicitely, which would take forever. By using natural Language and shortcuts, it becomes harder to check which steps in a proof are valid.
The art is in formulating the question properly and finding intermediate steps which get you closer to the desired theorem. Sometes, proving seemingly completely unrelated intermediate "lemmas" suddenly open a path to the actual goal because they can be applied to it somehow.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition
