Doug Ewell wrote:

> > 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.

There even was a time when the concept of "number" itself did not exist.

And, IMHO, the concept of zero already existed even at that time: I would
not be surprised if the concept of "number" was invented eactly as a cover
term to include zero and the positive units used for counting in the same
category.

IMHO, a mathematics which does not have zero is a mathematics which does not
have subtraction. I.e., hardly a "mathematics" at all.

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

You are comparing a well-documented historical event and an undocumented
hypothesis.

America was "discovered" on the 12th of October of AD 1492, when a
trans-oceanic expedition led by Cristobal Colón (or Cristoforo Colombo,
Christopher Columbus), a Spanish explorer of Italian origin, arrived in the
American islands now called Bahamas.

Now, can you provide similar details about when, where and by whom zero was
"invented"?

Or, as a minimum, can you cite any evidence of an early *documented*
mathematics which lacks the concept of zero and a way to express it (a
symbol, a blank cell, the phrase "Sorry, no more of it")?

--
Marco