What are the different types of numbers?
I. A brief history of numbers
A. Natural numbers
As the adjective natural suggests, these are the first numbers we use: Just as a child learns to count using his fingers, early people began to count objects or animals. Naturally, we count: 1, 2, 3, etc.B. Whole numbers
The whole numbers consist of the natural numbers combined with the number zero.C. Rational numbers
Problems involving division and measurement of lengths gave rise to fractions of whole numbers, which are called rational numbers in mathematics, such as , for example. The Greeks knew about natural numbers and rational numbers.D. Decimal numbers
Decimal numbers come from fractions: They correspond to particular fractions. Nowadays, a decimal number indicates a number written with a decimal point and followed by a number of figures, 23.45 for example.E. Negative numbers
There is evidence that negative numbers were being used in India in the 7th century. It is important to note that Indians used zero, a necessary precondition to conceiving negative numbers. Negative numbers were called debt numbers for commercial reasons, just as today's bank statements have two columns entitled credit (for receipts) and debit (for expenditure).The use of negative numbers in the West came much later. Italian Renaissance mathematicians, who were specialists in algebra (the science of solving equations), understood that without negative numbers they could not solve certain equations (x + 7 = 0, for example). However, they were unsure whether to call these solutions proper numbers. And even in the 17th century, French mathematician Descartes described negative numbers as false numbers.
It was not until the 19th century that negative numbers were finally treated as true numbers.
F. Irrational numbers
The followers of Pythagoras proved that the length of a diagonal of a square of side 1 is not a rational number. Today, we write this number as and call this kind of number irrational because it cannot be expressed as the ratio of two whole numbers.II. The different types of numbers in mathematics
Relationships exist between the different types of numbers.A. Whole numbers
Every number used in mathematics is derived from a whole number. The letter W is used to denote this set.Examples: 12, 5, and zero are whole numbers.
B. Integers
Integers are whole numbers to which we add '+' for positive numbers or '-' for negative numbers. The letter Z (from the German Zahl, meaning “number”) is used to denote this set of numbers.Examples: +3, zero, and - 72 are integers.
We know that positive numbers can be written without the '+' sign, for example: +7 = 7.
Consequently, every whole number is an integer. In mathematics, we say that the set W is included in the set Z. This is written: W c Z .
C. Rational numbers
These are fractions of the type , where a and b are integers and b ≠ 0 .The letter Q is used to denote the set of rational numbers.
Examples: and are rational numbers.
D. Real numbers
As we said before, there are numbers, such as for example, that are not rational. We also acknowledge a set of numbers called real numbers containing all the numbers mentioned previously. Real numbers are denoted by the letter R. The real numbers usually suffice as a basis for the mathematics studied in school, though still other types of numbers exist, such as complex numbers and quaternions.Examples: 5; –29; –49.21; ; , and are real numbers.
So at school we work with four sets of numbers contained in one another: W c Z c Q c R .
Read more:
Reading and Writing Decimal Numbers
Multiplying or Dividing a Decimal Number by 10, 100, or 1,000
Multiplying Decimal Numbers
Dividing Decimal Numbers
Converting Decimals to Fractions
The Effect of Addition and Multiplication on the Order of Numbers
Dividing Whole Numbers with a Remainder
Comparing and Ordering Decimal Numbers
Adding and Subtracting Decimal Numbers