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Apr 18, 2014 · 144. Because sometimes, things that should be "obvious" turn out to be completely false. Here are some examples: Switching doors in the Monty Hall problem "obviously" should not affect the outcome. Since Gabriel's horn has finite volume, then it "obviously" has finite surface area. "Obviously" we cannot decompose sphere into a finite number of ...
Jul 30, 2022 · Proofs are the whole point of mathematics. They are how we verify and explain that we know things instead of merely guess at them. When I personally teach discrete mathematics, the first-day opening that I use to address this issue is this: Consider a function defined on natural numbers n: f(n) = n2 − n + 11.
- 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...
Jul 20, 2014 · Sorted by: to verify the truth or falsehood of a statement. to provide insight as to why a statement is true. as an entry point into the development of a new idea. as a structure for communicating mathematical knowledge. as an impetus for the use of precise mathematical language. Share. answered Jul 19, 2014 at 18:14.
Why do We Need Proofs? It's clear why we need to prove mathematically something that's not obvious, like the Pythagorean Theorem, but why should we prove something that "common sense" tells us is obviously true. First, if something cannot be proved, there may be something missing. For example, suppose we set up some equations that describe a ...
Nov 9, 2018 · A proof is a good bet, but it does not give us certainty. If it fails, we can (eventually) fix it, or replace it, or withdraw it. The last of these is equivalent to refunding your money and ...
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Apr 10, 2015 · Dividing both sides by a 2 − a b gives 2 = 1. Mathematics is all about proving that certain statements, such as Pythagoras' theorem, are true everywhere and for eternity. This is why maths is based on deductive reasoning. A mathematical proof is an argument that deduces the statement that is meant to be proven from other statements that you ...
