# One isn't the loneliest number

Updated on October 30, 2010

## Is zero a number? Is zero odd or even? Is zero a positive or negative number?

The word "zero" is derived from the Arabic sifr meaning "something empty" ("cipher" is a related word). The use of zero as a visible mark of absence was a striking innovation of the Arabic notation that reached Europe in the 12th century. In Greek and Roman arithmetic, the ambiguity resulting from the absence of a zero symbol was a serious hindrance to scientific progress. Familiar though it is, the use of zero must be reckoned as one of the basic intellectual inventions of modern culture.

The standard use of zero is to indicate the absence of some countable or measurable magnitude whose precise nature is determined by the context. Thus, in the numeral 205, the zero symbol indicates that the intended number is composed of 2 hundreds and 5 units, but no tens; "zero velocity" means no velocity, or rest; "zero degrees Centigrade" means a temperature that is no degrees above the arbitrarily chosen starting point of the thermometric scale, which is a temperature equal to that of melting ice; and "zero degrees absolute" or "absolute zero" refers to the theoretical low point on the absolute temperature scale, that is, a temperature at which it was once assumed there would be no molecular motion whatsoever. As a rule of thumb, "0" or "zero" may be replaced by the adjective "no", in the manner illustrated by the examples given. Like other adjectives, "zero" needs to be attached to a noun or noun clause whose reference it modifies.

An obvious way to indicate absence is by means of a blank space. But such a notation as 2 5, with a mere gap between the 2 and the 5, is easily confused with an error in transcription and fails to indicate what and how much is intended to be omitted; hence the early use of a dot, as in 2.5, to mark the gap. Our present oval sign 0 seems to have evolved from the hexagonal or other closed line originally drawn around the dot as a precaution against ambiguity or forgery. In this way, an auxiliary device for showing mere absence took on the appearance of a substantial symbol, apparently standing for a genuine number on a par with the so-called natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9.

Considered as a number, zero seems to have odd and mysterious properties that set it apart from the natural numbers. Plausible though it is for the addition of zero to make no difference (on the principle that nothing is being added), the parallel for multiplication by zero has to be rejected. The prohibition of division by zero seems reasonable, but the learner finds it hard to attach clear meaning to the symbol i" (x to the power zero) and is puzzled by the supposed demonstration that the value of x° is alway 1. The truth is that such symbols as x° and 0! (factorial zero) have to be given stipulated definitions that are not derivable from any natural equation of "zero" with "no" or with "nothing."

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