Zero

Introduction

“Zero” is a number which, when added to any number, leaves the latter unchanged. The symbol for the number zero is "0". The word zero comes originally from the Hindi “sunya” which means ‘empty’, and travelled through Arabic (sifr), Latin (zephirum), eventually to become the English zero. Zero is also used as a placeholder in place value systems as a digit. It came into existence around 200 A.D. and it was the Indians who developed the use of zero. Indians were the first to recognize a mathematical representation of concept of no quantity. If there are zero things, there are not any things. There are none.

Zero - a special number

In mathematics, zero is a special number for the following reasons:

• Sum of zero to any number equals to that number. For example, sum of seven and zero equals to seven.

Symbolically it is represented as: 7 + 0 = 7.

• Subtraction of Zero from any number equals to that number. For example, subtracting zero from four equals to four.

Symbolically it is represented as: 4 – 0 = 4.

• Multiplication of zero to any number equals to zero. For example, multiplying zero to five equals to zero.

Symbolically it is represented as: 5 x 0 = 0.

• Division of zero by any number results in zero.
• Division of any number by zero is impossible as dividing any number with zero will give error. It can also be said that division of any number by zero gives infinity as quotient.

Some other properties about zero

• Zero is a whole number.
• Zero is not a positive number.
• Zero is not a negative number.
• Zero is an even number.
• Zero divided by zero is an indeterminate form which means that it is undefined.
• Zero is divisible by any number and leaves no remainder.
• Any number to zero power is equal to 1 and zero power to any number equals to zero only.
• The sum of 0 numbers is 0, and the product of 0 numbers is 1.
• Zero neither a prime number nor a composite number.
• Zero is not a unit.

Uses of Zero in Mathematics

• Zero is used as a place indicator in place value number system. For example, in a number 5203, the zero is used so that the positions of the 5 and 2 will be correct.

• Zero is used as a number in the form we use it as 0.

• In geometry, the dimension of a point is zero.

• In linear algebra, a zero matrix is a matrix with all its elements as zero.

• In set theory, the number zero is the cardinality of the empty set.

Magical number using zero

Using six 0’s, we can get a magical number 48.

i.e., (0!+ 0!+ 0!+ 0!)! x (0!+ 0!)

= (1+1+1+1)! x (1+1) because 0! = 1.

= 4! x 2

= 4 x 3 x 2 x 1 x 2 because 4! is 4 x 3 x 2 x 1

= 48

Applications

• In mathematics, zero plays a very important role in number systems.
• In physics, zero plays a very valuable role for many physical quantities like mass, volume etc.
• In chemistry, it is considered as the atomic number of the theoretical element tetraneutron.
• In computer science, zero is often used as the starting point.

Conclusion

As we discussed about zero on various aspects, one thing is certain that it plays a pivotal role in mathematics as well as other fields. Some problems cannot be solved in mathematics without zero. It plays a role of additive identity in integers, real numbers and many other algebraic functions.