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0 (zero)

There has been discussion for centuries about whether or not the digit 0 is a number. Nowadays we call it a number, and for writing decimal numbers we just need it.

 


Explanation

With addition and subtraction there are no problems

1 + 0 = 1     and    1 − 0 = 1

A multiplication works well

1 × 0 = 0     and    0 × 0 = 0

In a division only the numerator can be zero and the denominator may never be zero, so

Surprisingly, dividing by zero produces two results

However, zero divided by zero is

Exponentiation is possible, and so

10 = 1

Only zero to the power of zero cannot be calculated, and is determined by definition as

00 ≝ 1

The square root of zero is

 


History

In 628, the Indian astronomer Brahmagupta was the first to give rules to compute with zero.


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