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- A proof provides evidence that a theorem is true, but some proofs also produce insight into what is going on.
www.scientificamerican.com/article/proofs-and-guarantees/
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.
Jul 30, 2022 · Trying to prove things challenges you to find patterns, abstractions, and similar that are useful beyond the specific problem you are trying to solve. Formulating these is often the main accomplishment of a proof, while “the proof itself” can be a mere technical exercise or calculation.
- Why Does Math Need Proofs?
- Why Do I Need to Learn Proofs?
- Where Will I Need Proofs?
- Logic in Law
First, from 2000: I replied: Math, that is, is abstract reasoning, which is guaranteed to be true as long as the assumptions we make are true. In arithmetic, we start with basic assumptions about how numbers combine, and reach a conclusion that will be true as long as the things we are counting are actually suitable for counting (as opposed to, say...
Consider this question from 2002: Doctor Roy answered, starting with a teaser and some parallel questions: The same could be said of many things taught in schools. He went on to give examples where school teaches ways of thinking, not just specifically useful facts. He concluded:
Here’s one more question, focused on a particular kind of proof in geometry but really applicable to all of math. This is from 2000: We’ve seen above that all of math is built on provable facts, not just blind assumptions. But why learn it when you will not be a mathematician? Two of us replied, starting with Doctor Ian, mentioning facts you might ...
Doctor Alicia added her thoughts: Of course, they don’t really use “two-column proofs”, which are a particular way to organize a proof meant to help beginners be sure that every step of reasoning is justified. Step by step, we would use the given information to show, in the end, that angles A and B are complementary. (This is a typical very brief p...
Apr 10, 2015 · A proof is a logical argument that establishes, beyond any doubt, that something is true. How do you go about constructing such an argument? And why are mathematicians so crazy about proofs? Which way around? What can maths prove about sheep?
Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation".
Nov 30, 2021 · Why we want proof — What are mathematical proofs, why do we need them and what can they say about sheep? The origins of proof — Part I — This article explores deductive reasoning and looks at the earliest known example of a proof.
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Nov 9, 2018 · Why do we believe that 3 < 5 and that there are infinitely many primes? Most would say that’s an easy question with an obvious answer: proof. Here is a tougher question: Is proof the only sort ...
