Re: (*)->1

[Michael Heerdegen]

Michael Heerdegen <michael_heerdegen@web.de> writes:

> Jean Louis <bugs@gnu.support> writes:
>
> > Thus (+) ➜ 0 without value result should not be zero. If no values
> > where given to addition, no addition has taken place. Value of zero
> > should not get out of nothing.
>
> Mathematically it is neither right nor wrong.  It is a convention to
> assign 0 to an empty sum.  This is for convenience, and it doesn't lead
> to contradictions.

Some more comments:

1. The mathematical background is the associative property in monoids:

  https://en.wikipedia.org/wiki/Monoid

2.  You surely never complained about a^0 = 1 although "it's an empty
product".  You surely used that often because it's convenient.

3.  Similar things in Lisp are

(append) ==> ()
(concat) ==> ""
(or) ==> nil
(and) ==> t

The result is always the neutral element of the associative operation.

Michael.