Zero is often equated with "nothing," but that is not a good analogy. Zero can be the absence of a quality, but it can also be a starting point, such as 0° on a temperature scale. In a mathematical system, zero is the additive identity. It is a number which can be added to any given number to yield a sum equal to the given number. Symbolically, it is a number 0, such that a + 0 = a for any number a.

In the Hindi-Arabic numeration system, zero is used as a placeholder as well as a number. The number 205 is distinguished from 25 by having a 0 in the tens place. This can be interpreted as no tens, but the early use of 0 in this way was more to show that 2 was in the hundreds place than to show no tens.

Zero is used in some ways that take it beyond ordinary...