The zero is the identity element in the addition of real numbers, i.e., \(a+0=0+a, \forall a \in \mathbb R\).

It is the only complex number which is considered as a real number and as a purely imaginary number.

The zero also represents the probability of an impossible event, i.e., \(P \left( \varnothing \right)=0\).

We also have \(0=\log_{a}1\) and \(a^{0}=1\), since \(a \neq 0\).

By convention, no real number can be divided by zero.

Theoretically, \(0 \times \infty\) and \(\frac{0}{\infty}\) are indeterminations in the calculation of limits of real functions of a real variable.

It is the only real number that is neither positive nor negative.

It is also the existing number of magic squares \(2 \times 2\).

Zero is one of the greatest inventions of the World! In \(200\) BC Hindu scholars worked with nine symbols and a point which supposedly bring order to the world of mathematical chaos. The point and the nine symbols are the oldest known precursors of \(0, 1, 2, 3, 4, 5, 6, 7, 8, 9\). Composed only by ten symbols and based on multiples of ten, Hindu numeral system was easily learned and used.

The word "zero" was invented by the Italian mathematician Leonardo Fibonacci. He has transformed the Arabic word "صِفْر" (sifr, "empty"), which is equivalent in Italian to "zefiro" and which was later reduced to "zero".

Many languages have adopted the word "zero": English, Catalan, Portuguese, French (zéro), Romanian, Spanish (cero), ...

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