Zero is a fascinating little number, and it has some very distinctive properties. Ever since zero was invented, mathematicians have struggled to define it and to use it in their work, with the properties of zero being arrived at through the use of mathematical proofs which are intended to illustrate those properties at work. Even with proofs to support the rationale behind some of the properties of zero, this number can be quite slippery.
People haven't always used zero. A crude form of zero as a placeholder appears to have been used by Babylonian mathematicians, but Indian mathematicians are usually credited with coming up with the idea of zero as a number, rather than just a placeholder. Almost immediately, people struggled to define the number and learn how it worked, and explorations into the properties of zero got quite complex.
Numbers can be classified as positive or negative, depending on whether they are greater or less than zero, but zero itself is neither. Zero is also even, something which comes as a surprise to some people when they learn about the properties of zero, as they often assume that it is either odd or outside of the even/odd dichotomy. In fact, extensive math could be used to show you how zero is classified as even, but the simplest way to show how zero is even is to think about what happens when you have a multiple digit number which ends in an even number. 1002 ends in a 2, an even number, so it is considered even. Likewise with 368, 426, and so forth. Numbers which end in zero are also treated as even, illustrating that zero is itself even.
The Addition Property of Zero states that adding 0 to a number does not change that number. 37+0 equals 37, for example. In the Multiplication Property of Zero, mathematicians state that multiplying a number by zero always ends in zero: if you multiply six oranges zero times, you end up with no oranges. Some other properties of zero have to with addition and subtraction. Subtracting a positive number from zero ends in a negative number, and subtracting a negative number from zero ends in a positive.
Zero has another property which is familiar to anyone who has tried to divide a number by zero with a graphing calculator. Division by zero is simply not allowed in mathematics, and if you attempt it, a calculator usually returns the message “undefined,” “not allowed,” or simply “error.” The Indians actually tried very hard to prove that you could divide by zero, but they were unsuccessful. However, you can divide zero by other numbers (although not by zero), although the result is always 0. 0/6, for example, equals 0.