Zero

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History of Zero

The largest single advance in mathematics was made around 300 AD when the Hindus combined a sign for zero with a decimal positional system. They called their zero "sunja", meaning empty space. When the notion spread to Baghdad perhaps around 600 AD the named translated to the Arabic word "sifr".

In 1202 this decimal system was made known to the west by Leonardo of Pisa (Fibonacci) in his manuscript Liber Abaci.

Properties

Zero is the only real number that is neither positive nor negative. 00 is undefined and may be usefully defined as 1 or 0 depending on the problem.

Division by Zero

Let us look at the nature of division...

x / y = z means that y * z = x

If we substitute with some numbers:

8 / 4 = 2 means that 4 * 2 = 8

Now we try the same thing involving zero...

x / 0 = z means that 0 * z = x

If we substitute with some numbers again:

8 / 0 = z means that 0 * z = 8

What number multiplied with 0 gives 8?

The answer is none, the operation makes no mathematical sense and is therefore undefined. If you try to create new rules to make it defined you will find that a similar problem arises somewhere else in the system.

In computer programs division by zero can be a problem when it comes to performance and stability. In some algorithms it is helpful to replace zero with a very small nonzero value to avoid problems. In any case it is important to consider the possibility of division by zero and handle it properly in each case.