A Guide to Numbers
Numbers are the basic pillars of counting and measuring. Numeral is the notational symbol to represent a number. However, the word number is used for both abstract object as well as symbol. Numerals apart from being used in measuring and counting are also used for labels, for codes. With time, mathematics has seen more and more development regarding numbers. There have been numerous varieties like zero, negative numbers, rational numbers, irrational numbers, and complex numbers.
Numerical operations in numbers are the procedures that take one or more numbers as input and produce a number as output. There are two types of numerical operation. One is the unary operation and the other is the binary operation. Unary operation are those which take a single input number and produce a single output number whereas a binary operation is the one which takes two input number and produces one output numbers. In fact, abstract algebra is a particular branch of mathematics that deals with the structure in number systems by the help of groups, rings and fields. Moreover, there are different types of number as well.
Types of Numbers
Natural numbers – Natural numbers are the most commonly used numbers. The numbers start from 0 and goes up to any limit you can think of. No matter how large a number you choose, the right most digit will have a place value of one and thereafter each place to the left increases the value by 10 times. Natural numbers are denoted by the symbol N.
Integers – The numbers that are less than zero are called negative numbers and the numbers more than zero are called positive numbers. Negative numbers are represented by a negative sign before the number. When the set of negative numbers are represented along with natural numbers then they are called set of integer numbers. Integers are represented by Z.
Rational numbers – When a number is expressed as a fraction with an integer as numerator and a natural number other than zero as a denominator, then it is called a rational number.
Real numbers – Real numbers are the ones, which contain all the irrational, rational, integers and natural numbers. Usually, real numbers bear decimals.
Complex numbers – There is also a genre of numbers called the complex numbers, which are denoted by ‘i’. If you consider calculating the square root of a negative number, then the imaginary number is called complex number. All these collection of imaginary numbers are called complex numbers.
Even numbers and Odd numbers
Apart from these categories of numbers, there are also specific distinctions between numbers and these are odd numbers and even numbers. Odd numbers are the ones that are not divisible by 2. For example 1, 3, 5, 9 are some of the odd numbers because they are not divisible by 2. Even numbers are those that are divisible by 2. For example 2, 4, 6, 8 are even numbers because they are all divisible by 2. However, though 0 is divisible by 2 yet it is neither a odd number nor an even number.