Choose the correct statement about the set {n² : n ∈ N}.
Answer and explanation
Correct answer: It is infinite
For every natural number n, the set contains the square n². Its beginning is 1, 4, 9, 16, 25, and so on. As n can be chosen arbitrarily large, the squares continue without an ending largest element. Also, different natural numbers give different squares, so infinitely many distinct elements occur. Therefore the set is infinite.
Frequently asked questions
What is the correct answer to this question?
It is infinite
Why is this the correct answer?
For every natural number n, the set contains the square n². Its beginning is 1, 4, 9, 16, 25, and so on. As n can be chosen arbitrarily large, the squares continue without an ending largest element. Also, different natural numbers give different squares, so infinitely many distinct elements occur. Therefore the set is infinite.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
