Concept explainers
To state: Whether the set of negative integers is finite or infinite by listing the elements of the set.
Answer to Problem 1T
The set of negative integers is
Explanation of Solution
Given:
The set of negative integer’s element.
Definition used:
Integers are the set of whole numbers or numbers that are not fractions.
The natural numbers is the set of numbers which is defined as
Two type of sets are possible on the basis of counting, one that has finite number of elements and one that has infinite number of elements.
Also in infinite set, there are two possible types one that can be listed in elements form and one that can’t be listed in elements form.
Calculation:
Negative integers are the numbers that are obtained by negating the natural numbers. The set of negative integers is as follows:
Here,
By the definition stated above, set of natural number
Therefore, the set of negative integers will also be an infinite set as it is obtained by negating the natural numbers.
Thus, the set of negative integers is
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