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Apr 18, 2014 · That said, the main reason for proving obvious things is that proofs are the fundamental building blocks of mathematics. If something is true, a mathematician should be able to prove it. If something cannot be proven, that will (or should) stick in the mathematician's craw.
Students sometimes object that mathematicians are too picky about proving things that are ‘obvious’. But the fact that something is obvious in the real world counts for very little in the constructed world of mathematics.
A proof, in mathematics, is the validation of a proposition or theorem by the application of specified rules in a series of logical steps. In layperson's terms, this means that a proof is a carefully constructed set of arguments laid out so that nobody, no matter how smart or creative, could refute the logic.
What Does \Obvious" Mean in Mathematics? (and why do we have to prove things?) Bruce Blackadar. January 2015. \ `Obvious' is the most dangerous word in mathematics." E. T. Bell. \Since people have tried to prove obvious propositions, they have discovered that many of them are false." Bertrand Russell.
Jul 20, 2014 · As math majors and math educators we take for granted the importance of proofs and being precise. However with I have found that non-math majors are content with anything that looks reasonably quantitative, whether the logic is correct or not. I get two types of responses why it is a waste of time.
Axioms are mathematical statements which are true, and are self-evidently so and therefore cannot be proved. They should be things so obviously true or so universally accepted, that when you read them, you say to yourself, “ Duh, of course! ” 11.
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May 29, 2016 · Once it is known that a statement has a proof, it is known as a theorem, lemma, corollary, proposition, or law. So, a proof of a statement in mathematics is a convincing argument that establishes the truth of that statement.
