The integers are all those numbers that, as a set, bring together positive, zero and negative numbers; They used to add or remove units and are denoted with the letter Z .
Thus, the integers can be seen as the union of natural numbers (IN), the zero and; the set of opposites each natural number/
Since the integers are used to count either by adding, subtracting or multiplying the number of elements belonging to a set; then the result or total of any of these operations is a new integer , so it will be a positive, negative or even zero (0) number.
Properties of integers (Z)
Basically, the following properties are recognized :
- Addition or subtraction of two integers, gives as a result another integer , it is said that the set of integers is closed .
- The associative and are fulfilled for addition and multiplication or product of integers.
- The Distributive property of the product is fulfilled.
- There is an element in integers, zero ; which acts as a neutral element for the sum . Examples: 5 + 0 = 5; -2 + 0 = -2; -14 + 0 = -14
- Every whole number has an opposite for the sum. Thus, -2 is the additive opposite of 2; 8 is the opposite of -8 ; -5 is the additive opposite of 5.
- Finally, there is an element in the integers, the one (1); which acts as a neutral for multiplication ; this can be seen in the examples : 3 × 1 = 3; -7 × 1 = -7.
The name that the whole numbers have , is because they represent units that cannot be divided; as in the case of people , animals or objects, all those numbers used to determine whole quantities fall into this type. In addition, the fact that they contain negative numbers allows operations that involve missing numbers .
You want to travel a 20 km track and; only 12km were covered,
How many km were missing?
Answer: 20-12 = 8.
Likewise, these numbers are usually the result of basic mathematical operations such as subtraction, addition and multiplication. This means, that its use dates from ancient times and; there is concrete evidence that Hindu mathematicians already affirmed the existence of negative numbers during the 6th century.
Examples of whole numbers
- 2. 3