For each set, given below, state whether it is finite set, infinite set or the null set

vii. {squares of natural numbers}

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Solution

Step: Check whether the given set is finite, infinite or null set

Given set: {squares of natural numbers}

Squares of natural numbers

$= 1^{2}, 2^{2}, 3^{2}, 4^{2}, 5^{2}, . . . .$

$= 1, 4, 9, 16, 25, . . . . .$

There are countless natural numbers and so their squares are also countless.

And we know that a set is said to be an infinite set, if it has an uncountable number of elements in it.

Hence, the given set is an infinite set.

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