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From: Paul S Person <psperson@old.netcom.invalid>
Newsgroups: rec.arts.sf.written
Subject: Re: (ReacTor) Defining Our Terms: What Do We Mean by "Hard SF"?
Date: Wed, 21 Aug 2024 08:19:00 -0700
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On Tue, 20 Aug 2024 22:13:12 -0400, Joy Beeson
<jbeeson@invalid.net.invalid> wrote:

>On Tue, 20 Aug 2024 08:09:49 -0700, Paul S Person
><psperson@old.netcom.invalid> wrote:
>
>> They never even once mentioned that integration and differentiation
>> are inverses of each other? With various caveats and details, to be
>> sure.
>
>It was asserted, but never explained.  The two courses were entirely
>separate.

Ah, that would explain it. Neither course felt any obligation to
mention the other.

>I've read that the proof is childishly simple.

I found this with Bing:
<https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/05%=
3A_Integration/5.03%3A_The_Fundamental_Theorem_of_Calculus#:~:text=3DProo=
f%20Since%20f%28x%29%20is%20continuous%20on%20%5Ba%2C%20b%5D%2C,a%29%20%E=
2%89%A4%20%E2%88%ABb%20af%28x%29dx%20%E2%89%A4%20M%28b%20%E2%88%92%20a%29=
..>

How simple it is depends, I suppose, on how far into math a person
happens to be.

As one professor remarked to a class on Algebra (that is, groups,
rings, etc): students start the course finding it's topics
unbelievably abstract -- and finish it finding them very real.

It's all in what you're used to, and that varies from time to time.
--=20
"Here lies the Tuscan poet Aretino,
Who evil spoke of everyone but God,
Giving as his excuse, 'I never knew him.'"