Re: (ReacTor) Defining Our Terms: What Do We Mean by "Hard SF"?

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=Proof%20Since%20f%28x%29%20is%20continuous%20on%20%5Ba%2C%20b%5D%2C,a%29%20%E2%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.
--
"Here lies the Tuscan poet Aretino,
Who evil spoke of everyone but God,
Giving as his excuse, 'I never knew him.'"