## Saturday, January 3, 2015

### INVENTION OF ZERO

Everybody of us must be very well aware of the number 0 in the counting system. We know that this number zero increases the value of a digit when placed next to the any number but when placed before any number makes no sense. Moreover, when multiplied or divided by any number, the result comes out to be zero. In all, we cannot deny this that this number 0 is a magical invention in our number system. Let us see the story behind its invention.

The number 0 is the smallest non-negative integer immediately preceding 1 . However, this may or may not be considered a natural number, but actually it is a whole number so considered as a rational number and a real number (as well as an algebraic number and a complex number).

The number 0 is neither positive nor negative, it lies in the middle of a number line. It cannot be prime because it has an infinite number of factors and cannot be composite because it cannot be expressed by multiplying prime numbers (0 must always be one of the factors). Zero is an even number because it is divisible by 2.  Zero is a number which quantifies a count or an amount of null size. It is believed that zero was identified before the idea of negative things (quantities) that go lower than zero was accepted.

Sumerians were the first people in the world to develop a counting system 4,000 to 5,000 years ago. The Babylonians got their number system from the Sumerians. Zero was invented independently by the Babylonians, Mayans and Indians. In the Sumerian system, number system was positional that is the value of a symbol was evaluated on its position relative to other symbols.

During Akkadian Empire, the Sumerians’ number system passed to the Babylonians around 300 B.C. There a symbol was assigned which indicate clearly a placeholder with the agreement of scholars to signify that there is an empty space just like to signify that in the number 2,025, there is no number in the hundreds place. The Babylonians added a symbol of double angled wedges to represent the empty column due to the confusion when they left an empty space in their cuneiform number system. However, they never developed the idea of zero as a number.

By 130 AD, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero i.e. a small circle with a long overbar within a sexagesimal numeral system. Another zero was used in tables alongside Roman numerals by 525 AD but it was used as a word,nulla meaning "nothing", not as a symbol. When division produced zero as a remainder, nihil, also meaning "nothing", was used. The initial "N" was used as a zero symbol in a table of Roman numerals by Bede or his colleague around 725 AD.

Using an empty space in tabular arrangements or the word kha "emptiness”  is known to be used in India from the 6th century. The glyph for the zero digit was written in the shape of a dot, and consequently called bindu ("dot"). The dot had been used in Greece during earlier ciphered numeral periods.

The concept of zero first appeared in India around 458 AD. Poetry or chants were used for mathematical equations rather than symbols. In 498 AD, Indian mathematician and astronomer Aryabhata stated that "sthānāt sthānaṁ daśaguṇaṁ syāt;"i.e. "from place to place each is ten times the preceding," which is the origin of the modern decimal-based place value notation.

In 628 AD, another Hindu astronomer and mathematician named Brahmagupta developed a symbol for zero that was a dot underneath numbers. He wrote rules for reaching zero through addition and subtraction, and the results of using zero in equations. This was the first time in the world that zero was recognized as a number of its own, as both an idea and a symbol.

Mathematicians normally do not assign a value when a zero divided by zero, whereas computers and calculators sometimes assign NaN, which means "not a number." Moreover, non-zero positive or negative numbers when divided by zero are either assigned no value, or a value of unsigned infinity, positive infinity, or negative infinity.

An Italian mathematician Fibonacci used zero to do equations without an abacus, then developed the most prevalent tool for doing arithmetic. This development was highly popular among merchants, who used Fibonacci’s equations involving zero to balance their books.
12,000 miles away from Babylon, the Mayans developed zero as a placeholder around 350 AD and used it to denote a placeholder in their elaborate calendar systems. Despite being highly skilled mathematicians, the Mayans never used zero in equations.

The number  zero is not the same as the digit zero, used in numeral systems using positional notation. Successive positions of digits have higher weights.

By the 1600s, zero was used fairly widely throughout Europe. It was fundamental in Rene Descartes’ Cartesian coordinate system and in Sir Isaac Newton’s and Gottfried Wilhem Liebniz’s developments of calculus. Calculus paved the way for physics.

So we can say invention of zero solves out many problems in mathematics, physics and in many other field. It was really a great invention.