Marco Cimarosti <marco dot cimarosti at essetre dot it> wrote:

>> Maybe naively, I am thinking about a matrix, or an array, a table,
>> whatever you call it, as an invention, something like the concept of
>> zero.
>
> Oh, then we agree to disagree: I always thought that the "invention"
> of zero is a big misunderstanding.
>
> How can you "invent" a number? If you have three apples and eat all of
> them, you have *no* more apples! That "no" is the "concept of zero".

There was a time when that concept was considered to be outside the system of
counting and numbers in general. The rationale, roughly, was that you can't
count apples that aren't there; so since numbers were for counting, the idea
of "no apples" couldn't be described with a number. The difference between
one and zero was fundamental, unlike the difference between one and one
million, which was merely a matter of degree.

The "invention of zero" had to do with bringing the concept of zero into the
system of countable numbers. The invention of a symbol for zero was one of
the many effects of that intellectual breakthrough.

> You may say that someone invented a *symbol* to represent number zero
> in calculations, and you can certainly say that *digit* zero was a
> fundamental invention. But not zero itsefl.

Like "discovery of America," the phrase "invention of zero" describes an
undeniably important event of history in very misleading words.

-Doug Ewell
Fullerton, California
http://users.adelphia.net/~dewell/