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Jimmy Stephens,Webmaster
Jimmy Stephens,Webmaster
2 comments:
In order to be a proof, a statement must be invulnerable to any possibility of a counterexample that can disprove it. It must be tested thoroughly and with as many variables as possible in order to be secured. In order to reach a proof, hypotheses are also changed in order to accommodate a certain set of numbers that the statement can cover, as opposed to creating a blind generalization which could later prove wrong. A proof is also tested by the assumption that it is incorrect, and if it consistently proves to be correct, its certainty is even more emphasized. A last way a proof is tested for certainty is to take the proof and run through one stage to another, creating a frame of mathematical induction.
Proofs may sometimes prove to be difficult because very few people have a complete grasp of the whole argument or purpose of the statement. There are also arguments that arise among mathematicians. They make disagree over logic and how it is "merely sleight of hand and doesn't tell us how to actually construct a concrete solution." Others would argue that disregarding proofs would mean blindly looking for solutions to every problem denying similar results that have been proven time and time again to be certain or reliable.
I agree with Patricia's post on both subjects. A proof is a statement that must be flawless in our perceivable world. That applies to out known logic and can have no counterargument, but if new knowledge is obtain it can be refined to try and accommodate what we already know and learned recently. Proofs are not simple to follow which makes it very hard for the common person to truly understand them. If someone can't understand the base of the proof then they will not be able to understand the entirety of it, and many can barely grasp the idea of the base itself making proofs very hard to understand. Even to those who do understand the amount of rules to follow makes it difficult.
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