Question

Which of the following sets is an infinite set?

A.){1, 2, 3 . . . 100}
B.)empty set
C.)the set of whole numbers less than one billion
D.)the set of natural numbers
E.)none of the above

Answer 1

Answer;

D.)the set of natural numbers

Step-by-step explanation;

-A set is said to be an infinite set whose elements cannot be listed if it has an unlimited (i.e. uncountable) by the natural number 1, 2, 3, 4, ………… n, for any natural number n is called a infinite set. A set which is not finite is called an infinite set.

-Set A cannot be infinite because it only goes to 100 and Set B is empty so that also has nothing infinite. However set of Natural numbers as they continue number by number getting in to an bigger number is infinite.

-On the other hand; A set is said to be a finite set if it is either void set or the process of counting of elements surely comes to an end is called a finite set.

Answer 2

Answer: the correct answer is D) The set of natural numbers.

A set that contains infinite number of elements is called as infinite set.

Natural numbers are those that start from one and go till infinity. Thus, set of natural number is infinite as this set contains infinite number of elements, satisfying the property of infinite set.

On the contrary, option A), B), and C) contains finite numbers, which can be counted. Thus, they are not the example of infinite set.

Thus, D) is the right answer.