Re: [External] : Re: How to make M-x TAB not work on (interactive) declaration?

[Yuri Khan]

On Mon, 16 Jan 2023 at 11:44, Jean Louis <bugs@gnu.support> wrote:

> > >> (+) ➜ 0
> > >
> Send me references on what is additive identity.
>
> Though that it is so, it does not answer why is it so.

Consider a sum of n elements: S = (+ x_1 … x_{n-1} x_n).
By definition, it is equal to the sum of the first n-1 elements, plus
the nth element: S = (+ x_1 … x_{n-1}) + x_n. No problem this far?
(except for me mixing prefix and infix notation)

Now, plug n=1 into this general formula.
S = x_1 = (+) + x_1.
Therefore, the sum of an empty list (+) has to be 0.

In the same vein, a product of n elements: P = (* x_1 … x_{n-1} x_n) =
(* x_1 … x_{n-1}) * x_n, which in the case of n=1 becomes P = x_1 =
(*) * x_1. Therefore, the product of the empty list (*) has to be 1.