Question

Which of the following sets are finite or infinite
(i) The set of months of a year
(ii) $\{1,2,3,....\}$
(iii) $\{1,2,3,....99,100\}$
(iv) The set of positive integers greater than $100$
(v) The set of prime numbers less than $99$

Answer 1

(i) The set of months of a year is a finite set because it has $12$ elements.
(ii) $\{1,2,\mathrm{3....}\}$ is an infinite set as it has infinite number of natural numbers.
(iii) $\{1,2,3,...99,100\}$ is a finite set because the numbers from $1$ to $100$ are finite in number.
(iv) The set of positive integers greater than $100$ is an infinite set because positive integers greater than $100$ are infinite in number.
(v) The set of prime numbers less than $99$ is a finite set because prime numbers less than $99$ are finite in number.