# Zero

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"Anything free is worth what you pay for it."
—Robert A. Heinlein, Time Enough For Love

When I originally wrote this page (around the year 2000, when there were still neighbourhood bookstores), judging by the bookshelves at my neighbourhood bookstore, the concept of zero seemed to be one of the more popular concepts in popular and recreational mathematics at that time. Perhaps this was because there were several zeroes in the year, or perhaps the reason is that of historical interest, as the exact origins of the concept are foggy, and that zero was not accepted in many mathematical circles until rather recently.

One important thing to notice about zero is that there are two different uses of zero, both of which are important, although for different reasons. The first use of zero is as a placeholder in a positional numeral system. For example, 381 is a completely different number from 30810. The second use of the number zero is as a number, the number "0". It is unclear exactly when zero was first used in either of these two roles.

The use of zero as a placeholder probably first occurred in ancient Babylon. Surprisingly, even though the ancient Babylonians used a positional number system, they did not use zero as a placeholder until relatively late in their history.

The use of zero as an actual number probably originated in India. A positional number system was developed in India around the 2nd century B.C., and zero slowly gained acceptance, first as a placeholder, but later as a number in its own right. In the 7th century A.D., the mathematician Brahmagupta considered zero a number in his works and even gave rules for handling it in calculations. The Indian word used to represent zero was "sunya". This word became "sifra" in Arabic, which in turn became "zephirum" in Latin, which in turn became the English word "zero", as well as the English word "cipher" (or "cypher").

In Europe, it was not until the 1600s when zero finally started to become accepted as a number.