The Classification of Numbers

1. Natural Numbers

It is claimed as the most familiar type of number for almost all of people in the world. It is also called as the counting numbers and you can simply call the number as one, two, three, four, five and so on. This is the real traditional system of numbering and the order is started from 1. This principle is based on the culture of Ancient Greek where zero was not considered as number. As the time goes by, the mathematicians set the new theories which claim zero as the beginning of natural numbers.
In today’s world, people use the base ten to deal with the digital numeral system. In this system, the rightmost digit of the natural number has a place value of one. The natural numbers can be represented by the classes of equivalent sets too. As the example, the number 3 is used to represents the entire classes of sets which have precisely three elements. In this case, many different representations can be used by people and the key thing to represent 3 in more formal way is to inscribe the particular pattern or symbol of symbols three times.

2. Integers

The next type of number is called the integers. This is commonly called as the negative form of natural number. It is defined as the number which will produce zero when the positive number is added. Absolutely, the negative numbers are smaller or less than zero. The common way to write it is by adding the negative or minus sign. If you take number 4, so the negative form will be -4. In a simple mathematical explanation, you can get zero as a result of 4 + (−4).

3. Rational Numbers

What can you say about the rational number? The definition of such number is a number which can be possible expressed as the fraction with integer numerator as well as a non-zero natural number denominator. You must write the fractions n two numbers. The first number is called numerator, while the second number is called denominator. The first and the second number are separated by the dividing bar and people have two choices to write it down. They can use m⁄n or . In this case, the value of fraction will be greater than 1 if the numerator is greater than denominator. In further calculation, you will also find that the fraction is possibly greater than, less/smaller than or even the same/equal to one, depend on the numerator and denominator. It can be positive and negative too.
What you have to remember is that it can be written in the form of decimal which will be learnt in the following explanation too.

4. Real Numbers

What can you say about the numbers? The group of this number include all of the measuring numbers. In this case, the rural numbers are commonly used and written in the form of decimal numerals. The decimal point should be placed and written to the right. If you write 456. 123, so you can read it as four five six point one two three. There is a difference about the way to write the decimals in several countries and you must understand it rightfully to make sure that you will not make the fault with it.
If you live in US or UK 9and also some countries) you should use ‘period’ to write the decimal point. In other countries, the decimal point is represented by comma. What you must always remember is that all rational number is real number too. If people use real number to represent the particular measurement, they will always find the margin of error. This cannot be avoided and they commonly truncating or rounding the decimal, thus the rounded digit will offer the greater accuracy than the real exact measurement.

5. Complex Numbers

The complex numbers will male you assume that you would have to move to the greater level of abstraction. The word ‘abstract’ is enough to give the imagery for you about the meaning of complex numbers. Yes, you are right, this is done to explain that you will talk about the mathematical operation which is not merely symbolized by numbers, but also the letters to replace the number. People can find the exact value of the letter after using some patterns based on the given instruction.
It can be in the form of simple idea about a+b, but it sometimes can come in the form of square root and require some patterns to do it,. Absolutely, the value of one of the two letters has been given to let people find the answers. If you write a+b=25, with a=13, thus you can easily find the answer about the value of b. You can subtract 25 with 13. So, you can claim that b=12.

6. Computable Numbers

The types of numbers above have been explained in details. If you learn more about mathematics, you can find those numbers in many different topics and start to process or calculate them based on the given pattern and instructions. But, how can you deal with the computable numbers? This type of number is actually about the set of real numbers which are used to do the computing task. In this case, the computable numbers are popular as the recursive numbers. Other people call it computable real too and the equivalent definitions can be found if someone uses μ-recursive functions, λ-calculus or even the Turing machines. Very often, those numbers are used to be the
formal representation of algorithms.