Question

Classify $C = \{ ..., - 3, - 2, - 1,0\} $ as ‘finite’ or ‘infinite’.
A) Infinite
B) Finite
C) Data insufficient
D) None of these

Answer 1

Hint: We will make use of the definition of integers here:
The term integers contain all the positive as well as all the negative numbers including zero.
Now it is clear from the given set ‘C’ that it is a subset of the set of integers as it contains all the negative integers and zero also which is an integer as well.

Complete step-by-step answer:
As we can see, the given set $C = \{ ..., - 3, - 2, - 1,0\} $ contains only integers.
Here we will discuss the definition of integers:
Integers are those real numbers which come under the group of real numbers and contain all the positive as well as all the negative numbers up to infinity including zero.
Here, the maximum limit of the given set C is given as 0.
But it contains an infinite number of negative real numbers from -1 to $ - \infty $.
So, it contains an infinite number of negative numbers irrespective of the maximum limit 0 and does not contain infinite positive numbers except 0.
Since there are infinite elements in the given set C, it is an infinite set.

Therefore, the correct answer is option A.

Note: If a set contains a finite amount of elements, it is a finite set. The set of even prime numbers is an example of a finite set.
If a set contains an infinite number of elements, it is an infinite set. The number sets like the set of natural numbers, whole numbers, rational numbers and irrational numbers come under infinite sets.
Integers are those numbers which come under real numbers and contain all positive and all negative numbers.
The domain and range of integers lies in between $( - \infty ,\infty )$.