An integer is a whole number having no decimal part. An integer can be a positive whole number, a negative whole number, or zero. Examples of integers are 24, -142, and 0. The symbol for the set of natural numbers is a double struck capital N: ℕ. The definition of the set of integer in set notation is ℕ = {…, -3, -2, -1, 0, 1, 2, 3, …}.
In math, we can represent integers in ways that may not look like integers at first. For example, the fraction can be reduced to 2, and so is an integer, even if it is represented by an improper fraction.
Another example is 5.00. While it is represented using decimal notation, it has a decimal part of 0, which is the same as no decimal part. However, in most computer based systems, 5.00 would be stored as a decimal number, not as an integer.
Here are some examples of numbers that are not integers: 5.2, (can not be reduced to a single whole number), p (has been proved to be irrational), and 0.3 (contains non-zero digits after the decimal point).
Property | Description |
---|---|
Associativity | The set of integers is associative with respect to addition, subtraction, multiplication and division. |
Commutativity | The set of integers is commutative with respect to addition and multiplication. The set of integers is not commutative with respect to subtraction or division. |
Additive identity | The additive identity for integers is 0. |
Multiplicative identity | The multiplicative identity for integers is 1. |
Closure | The set of integers is closed with respect to addition, subtraction and multiplication. The set of integers is not closed with respect to division. |
Discrete | The set of integers is a discrete (not continuous) set. |
Cardinality | The cardinality of the set of integers is ℵ_{0}. |
Table 1: Properties of the integers. |
Decide if each number represents an integer. Then click either 'integer' or 'not an integer'.
Number | Is an integer? |
---|---|
15 | Integer Not an integer The number '15' is an integer. It has no digits to the right of the implied decimal point, is not an unreducible fraction, and does not represent an irrational number. |
-6.4 |
Integer Not an integer The number '-6.4' is not an integer. It has nonzero digits to the right of the decimal point. |
Integer Not an integer This number is not an integer. It is a nonreducible fraction. | |
-2.0000 |
Integer Not an integer The number '-2.0000' is an integer. It has no digits to the right of the implied decimal point, is not an unreducible fraction, and does not represent an irrational number. It can be written as '-2'. |
Integer Not an integer This number is not an integer. It represents an irrational number. | |
Integer Not an integer This number is an integer. The fraction reduces to the integer 4. | |
π |
Integer Not an integer The number 'π' is not an integer. It represents an irrational number. |
Integer Not an integer This number is an integer. The square root of 4 evaluates to 2. |
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