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Re: [Coq-Club] π>e


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  • From: Alex Shkotin <alex.shkotin AT gmail.com>
  • To: coq-club AT inria.fr
  • Subject: Re: [Coq-Club] π>e
  • Date: Sun, 24 Oct 2021 07:53:35 +0300
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Agnishom,

to continue your way: e ≝ exp(1). PI ≝ 2*arcsin(1).
subgoal1 e<3. subgoal2 3<PI.

Alex

пт, 22 окт. 2021 г. в 22:58, Agnishom Chattopadhyay <agnishom AT cmi.ac.in>:
Sounds like a difficult task!

I think this is the most common approach by regular mathematics people: First, define the exponential function. Now, set e = exp(1). Next, show that the function x => exp(i x) is periodic and has a smallest period. Call this pi. Now, compute two significant digits of both and compare.

This path is extremely complex to build from the ground up. This requires defining the real numbers, defining complex differentiation and some results about numeric computation.

There are a lot of math libraries in Coq. I don't know how mature they are, but that seems like the rational place to start looking.

On Fri, Oct 22, 2021, 13:45 Alex Shkotin <alex.shkotin AT gmail.com> wrote:
Hi All!

How in Coq define π and e and prove that π>e?

Alex



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