A proof of proof by infinite descent
relatedwork.blogspot.com
A proof of proof by infinite descent
1–10 of 60 posts
Re: A proof of proof by infinite descent
#2> I imagine that one could also prove that √−1 is not rational
I feel like this was a marvellous joke but I can’t prove it.
Re: A proof of proof by infinite descent
#3> I imagine that one could also prove that √−1 is not rational I feel like this was a marvellous joke but I can’t prove it.
You'd be surprised at the number of things that appear to be self-evidently true that turn out to depend on tacit assumptions. For example, is 7 prime? Not if you're doing modular arithmetic.
Re: A proof of proof by infinite descent
#4> I imagine that one could also prove that √−1 is not rational I feel like this was a marvellous joke but I can’t prove it.
You'd be surprised at the number of things that appear to be self-evidently true that turn out to depend on tacit assumptions. For example, is 7 prime? Not if you're doing modular arithmetic.
i think they were joking, but i can't prove it
Re: A proof of proof by infinite descent
#5> I imagine that one could also prove that √−1 is not rational I feel like this was a marvellous joke but I can’t prove it.
You'd be surprised at the number of things that appear to be self-evidently true that turn out to depend on tacit assumptions. For example, is 7 prime? Not if you're doing modular arithmetic.
It's also independently pretty tedious to explain that 7 is prime to a proof checker.
Re: A proof of proof by infinite descent
#6Earlier quoted context omitted.
You'd be surprised at the number of things that appear to be self-evidently true that turn out to depend on tacit assumptions. For example, is 7 prime? Not if you're doing modular arithmetic.
It's also independently pretty tedious to explain that 7 is prime to a proof checker.
Is it? You can tell the checker about the remainder of division by 2 to 6.
Re: A proof of proof by infinite descent
#7Re: A proof of proof by infinite descent
#8> I imagine that one could also prove that √−1 is not rational I feel like this was a marvellous joke but I can’t prove it.
You'd be surprised at the number of things that appear to be self-evidently true that turn out to depend on tacit assumptions. For example, is 7 prime? Not if you're doing modular arithmetic.
It's a joke about `i` being imaginary.
Re: A proof of proof by infinite descent
#9Re: A proof of proof by infinite descent
#10Earlier quoted context omitted.
You'd be surprised at the number of things that appear to be self-evidently true that turn out to depend on tacit assumptions. For example, is 7 prime? Not if you're doing modular arithmetic.
It's also independently pretty tedious to explain that 7 is prime to a proof checker.
The proof is not too bad in Lean4. I'm nothing special and I've got it down to 9 lines. But, maybe that is considered pretty tedious vs. what expectations one might have. In any case, it is an exercise in Heather MacBeth's free book: The Mechanics of Proof,
https://hrmacbeth.github.io/math2001/04_Proofs_with_Structur...
btw, that book is a lot of fun to work through.