Questions tagged [proofs]

For questions about mathematical proofs in an educational context.

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17
votes
5answers
9k views

Good examples of proof by contradiction?

In later courses on automata theory, many students just seem incapable of getting a proof that a language isn't regular right, be it using the pumping lemma (see also the many questions on the matter ...
13
votes
7answers
401 views

What different ways do people use to show students that $\mathbb{R}$ is uncountable?

In particular, if you use Cantor's diagonalization argument, do you ignore the repeating decimal annoyance? Or prove that it's not a problem? Is there another clean way that gives students intuition ...
29
votes
7answers
2k views

Teaching logic with a proof assistant

I am thinking about teaching a university-level "introduction to proofs" class (mainly for math and CS majors) making use of a computer proof assistant like Coq. I feel like there is a lot of ...
41
votes
25answers
10k views

Good, simple examples of induction?

Many examples of induction are silly, in that there are more natural methods available. Could you please post examples of induction, where it is required, and which are simple enough as examples in a ...
4
votes
1answer
77 views

What are ideas and strategies on improving at discovering counterexamples? [closed]

What are ideas and strategies on improving at discovering counterexamples? I originally posed this as an Example Question.
13
votes
3answers
319 views

Any suggestions on how to approach recursion and induction?

Much mathematics is intimately tied to recursion, be it in definitions (like factorials and integer powers) and proofs by induction. This is also very relevant in computer science and programming. ...
20
votes
4answers
371 views

Multiple Solutions Methods vs. Encouraging a Particular Approach

It happens frequently in math that problems have multiple possible solutions. This might become troublesome, e.g. when students use some other approach, hence, not learning the current topic. One ...
22
votes
0answers
557 views

What are some good simple examples that getting the right result is not enough? [closed]

When I want to point out to my students that getting the right result is not enough, I like to show them the example: $$\frac{16}{64} = \frac{1\hskip-.1cm- \hskip-.4cm{6}}{-\hskip-.2cm{6}\,4} = \...
28
votes
8answers
3k views

Is there a good age/level to start learning mathematical proofs?

I know from my experience I learnt proofs myself way before I learnt them in school and I felt it gave me a far better understanding of math. What is a good point to start learning proofs? what are ...

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