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542 sats \ 9 replies \ @Scroogey 25 Oct \ on: [Daily puzzle] is this number rational science
We can use the trigonometric addition formula
in an inductive proof by contradiction:
- Assumption:
is rational. - Step: if
is rational then must also be rational, because the above formula is the ratio of two rational numbers. - But
which is irrational, hence the assumption must be wrong.
Nice job. This was supposedly an entrance exam question for the University of Kyoto in 2006.
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I understand the Kyodai and Todai exams are literal nightmares! They have people going to special exam schools for several years on end to get the score high enough to be accepted.
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Yeah looks pretty extreme. You really need to be trained on this to be able to solve this kind of problem with tight time constraints.
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Nice. Are you a mathematician, @Scroogey?
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Pulling out an inductive proof by contradiction, along with an obscure (to me) formula, is impressive for someone who doesn't do proofs on a regular basis :)
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Proof by contradiction was my favorite method in college. I think it's easier because you know where to start and you just move forward. So even to prove that things are true, I'd just assume the converse and show a contradiction.
Because a non-contradiction based proof seems harder. You know where you want to go, but you don't know where to start.
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Yeah, Reductio ad Absurdum were also my favorites.
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