(*) -> 1

[Jean Louis <bugs@gnu.support>]

* Eduardo Ochs <eduardoochs@gmail.com> [2023-01-17 05:39]:
> a few months ago I had to prepare some figures to explain to my
> students what should be the "neutral elements" for some operations...
> The main idea is that we want all these expressions to yield the same
> result, including the two last ones, that are weird,
> 
>   (+ (+ 2 2) (+ 2 2 2 2 2))
>   (+ (+ 2 2 2) (+ 2 2 2 2))
>   (+ (+ 2 2 2 2) (+ 2 2 2))
>   (+ (+ 2 2 2 2 2) (+ 2 2))
>   (+ (+ 2 2 2 2 2 2) (+ 2))
>   (+ (+ 2 2 2 2 2 2 2) (+))

That still does not make sense to me. I translate that to ordinary
notation:

 (2 + 2) + (2 + 2 + 2 + 2 + 2)
 (2 + 2 + 2) + (2 + 2 + 2 + 2)
 (2 + 2 + 2 + 2) + (2 + 2 + 2)
 (2 + 2 + 2 + 2 + 2) + (2 + 2)
 (2 + 2 + 2 + 2 + 2 + 2) + 2
 (2 + 2 + 2 + 2 + 2 + 2 + 2) + -- this is impossible situation as
 summand is missing because 
 "14 + " lacks summand. There must be some number first. 

People speak how Lisp follows mathematical conventions, but obviously
it follows some, but not all. 

Convention in multiplication is that there must be two numbers, that
is not followed, something else is followed. The reason behind is what?

> and my real objective was to convince them that we had very good
> reasons to decide that the result of (or) should be false the result
> of (and) should be true, and then extend these ideas to "for all" and
> "exists".

I wish I could see that good reason. 

Just by placing (+) and expecting it to yield something is not clear
that it is good reason.

I expect it then also here, but it does not work:

(/ (/ 2 2) (/))

So the above alone can't explain my why is it that Lisp uses
identities.

-- 
Jean

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