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Zero is a unique number with properties that mathematicians have struggled to define. It was first used as a placeholder by Babylonian mathematicians, but Indian mathematicians are credited with the idea of zero as a number. Zero is neither positive nor negative, but it is considered even. It has properties related to addition, subtraction, and multiplication, but division by zero is undefined.
Zero is a fascinating little number and has some very distinctive properties. Ever since zero was invented, mathematicians have struggled to define it and use it in their work, arriving at the properties of zero through the use of mathematical proofs that are meant to illustrate those properties at work. Even with evidence to support the rationale behind some of the properties of zero, this number can be quite slippery.
People haven’t always used zeros. A crude form of zero as a placeholder appears to have been used by Babylonian mathematicians, but Indian mathematicians are usually credited with the idea of zero as a number, rather than just as a placeholder. Almost immediately, people struggled to define the number and learn how it worked, and explorations into the properties of zero became 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 that surprises some people when learning about the properties of zero, as they often assume that it is odd or outside the even/odd dichotomy. Indeed, extended math could be used to show you how zero is classified as even, but the easiest way to show how zero is even is to think about what happens when you have a multi-digit number that ends in an even number. 1002 ends in a 2, an even number, so it is considered even. Likewise with 368, 426 and so on. Numbers ending in zero are also treated as even, proving that zero itself is 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 up in zero: if you multiply six oranges zero times, you end up with no oranges. Some other properties of zero have to do 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 familiar to anyone who has tried dividing a number by zero with a graphing calculator. Division by zero is simply not allowed in math, and if you try, a calculator will usually return the message “undefined”, “not allowed”, or just “error”. The Indians actually tried very hard to prove that one could divide by zero, but they were unsuccessful. However, you can divide zero by other numbers (even if not by zero), although the result is always 0. 0/6, for example, equals 0.
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