Tagged Questions

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On ambiguity in statements expressed in natural language, where the statements use an indefinite article, e.g. “a”.

Please consider the following example statements and judge the meaning of the article "a". Example: A house is a building. Example: A house is being built next to our house. In example 1, "a" is ...
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A question on mathematical writing.

One of the problems I am grading this week is as follows: Given a simply connected bounded domain $\Omega$ on $\mathbb{R}^{2}$, prove that there exist a line that separates it into two parts of equal ...
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A Good Example of an Argument That Cannot Be Reversed

My students are having a hard time with assuming what they must prove. A good example of what they are doing is when one wishes to show that $\lim_{x\to 3}(2x+1)=7$. They will assume that ...
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“$n$ is even iff $n^2$ is even” and other simple statements to teach proof-writing

I am supposed to teach undergraduate students who do not major in mathematics and I would like to give them a short introduction to mathematical reasoning and to the concept of proof. I am looking for ...
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Proofs as games?

A long time ago (but I can't remember when), I was introduced to the (pedagogical) concept of writing a proof as giving a winning strategy for a game. Basically, given a statement \$\forall x\exists y ...
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Difference between a Lemma and a Theorem [duplicate]

What essentially is the difference between a lemma and a theorem in mathematics? More specifically, suppose you come across a general result while solving a mathematical problem, what are the ...