What Is Numbers? Type of Numbers & Integer

List of types of numbers

  1. Natural Number
  2. Whole Number
  3. Rational Number
  4. Real Number
  5. Irrational Number
  6. Imaginary Number
  7. Complex Number
  8. Hyper complex Number
  9. Integers

Numbers are classified based on its types. It could be a natural number, whole, signed number, rational numbers etc. The example of natural numbers is given below –

1, 2, 3, 4, 5, 6, …

The next popular category is the whole number starting with zero as shown below –

0, 1, 2, 3, 4, 5, 6, …

The number zero was discovered in India and used everywhere today in mathematical calculations. A number could be rational or irrational too. Here is an example of negative numbers below –

…, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, …

Rational numbers are technically written as the division or fraction of numbers or integers. In simple words, fractions are formed by dividing one integer by another integer.

Number representations

You must be confused about how to express or represent numbers in mathematics. For this purpose, we use the number system with special mathematical notations given by digits or symbols in a consistent manner.

There is one unique way to present every number and special arithmetic or algebraic structure is used for the same. It can also be given by arithmetic operations like addition, subtraction, division etc. Different type of number system in mathematics or computer world too are given below –

  • Decimal number system (Base- 10)
  • Binary number system (Base- 2)
  • Octal number system (Base-8)
  • Hexadecimal number system (Base- 16)
  • Computer numeral system
  • Fraction
  • Scientific Notation

Every time you type a number or alphabet, it is translated to special binary numbers that are quickly understood by the computer. A computer can hold only a few symbols depending on the position and the value of the digit is calculated by –

  • The digit
  • It’s position in the number
  • The base of the number system

Signed numbers

In mathematics, numbers are represented bya sign as well that are named as the signed numbers. Here, we have given the example of numbers with positive and the negative sign.

  1. Positive Number Signe
  2. Negative Number Signe

…, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, …

Sign and magnitude are frequently used together and they have its special meaning too. Instead of giving any special symbol, just add minus sign that is popular with the name negative binary.

Types of integer

Taking a step ahead in numbers, let us read out what is an integer and its different types too. Again, not every integer could be a whole number or a natural number. But all whole numbers and natural numbers could not be integers. The integers are also given in the form of negatives like -1, -2, -3 etc. and so on. This is easy to present the integers on graphs too either it is positive or negative.

  1. Even and Old Number
  2. Prime Number
  3. Composite Number
  4. Polygonal Number
  5. Square Numbers
  6. Pentagonal numbers
  7. Hexagonal numbers
  8. Heptagonal numbers
  9. Octagonal numbers
  10. Nonagonal numbers
  11. Decagonal numbers
  12. Dodecagonal numbers.

Non-standard numbers

As we have discussed earlier, standard numbers are written simply in the mathematics world like 0, 1, 2 …. etc. For non-standard numbers in mathematics, there are some additional elements available outside the initial segment.

  1. Transfinite numbers
  2. Ordinal numbers
  3. Cardinal numbers
  4. Infinitesimals
  5. Hyperreal numbers
  6. Surreal numbers


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