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@mathemagical @soaproot @highergeometer I know all about infinity in the projective geometry sense! (I have a PhD in projective geometry.)
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David K Butler (Uni of Adel)
@DavidKButler@mathstodon.xyz
mastodon 4.7.2Lecturer at Maths Learning Centre, Uni Adelaide (my views here). Grad Dip Ed & PhD Finite Geom. Love maths and helping people learn. he/him #MTBoS #100factorial
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Joined November 11, 2022
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@mathemagical @soaproot @highergeometer Ah thanks for clarifying. I’m glad that real people use ideas from the maths that is most dear to my heart.
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@soaproot @highergeometer I’m glad you both like it!
I helped a student make sense of direct proof, proof by contradiction and proof by contrapositive today, and it was quite successful, so I want to share it with you.
When you prove the statement “If A, then B” directly, your proof usually goes like this:
Suppose A
[insert arguments here]
Therefore B.
When you prove the statement “If A, then B” by contradiction, your proof usually goes like this:
Suppose A.
Suppose not B.
[insert arguments here]
C
But already, not C.
Contradiction!
Therefore B.
When you prove the statement “If A, then B” by contrapositive, your proof usually goes like this:
Suppose not B.
[insert arguments here]
Therefore not A.
Hence if A, then B.
It really helped the student to see how the two clauses in the original statement become sentences in the proof and where they go.
“Everybody is so terribly sensitive about the things they know best.”
- from The Phantom Tollbooth, by Norton Juster
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I shall also tell you at this time that 101 and 9901 are both prime numbers such that if you remove the 0s the resulting numbers are also prime numbers.
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@soaproot@sfba.social @andrejbauer@mathstodon.xyz Interestingly I was talking to the student about what indicates contraction might be a good thing to try, and it’s often that the goal is stated as a negative to begin with.
@andrejbauer@mathstodon.xyz @soaproot@sfba.social And I’m sorry that my PhD in pure maths did not provide me with the training you think it should have. Feel free not to explain it to me, I’m just a stranger on the internet as are you.
@andrejbauer@mathstodon.xyz @soaproot@sfba.social I just don’t see why they’re distinct. If the statement “B” in my proof by contradiction happened to be “not B” then it would be the same as your refutation by contradiction. (In a land where not not B is B, and I have never lived in a land where it’s not.) And vice versa.
@andrejbauer@mathstodon.xyz @soaproot@sfba.social I don’t see why this is an issue.
@andrejbauer@mathstodon.xyz @soaproot@sfba.social It was a typo. I meant contradiction.
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@marshray@infosec.exchange @andrejbauer@mathstodon.xyz @soaproot@sfba.social Ahh. That makes more sense. I forget that when people talk about logical reasoning they are sometimes/often talking about everyday reasoning, not things in pure maths proofs.