Set of natural numbers N is countable or (denumerable). N= { 1,2,3,…….}. It is an infinite set. Now set 3N would be {3,6,9,…..}

Set 3N will be countable if strict one to one relationship is established between the elements of set 3N and the elements of set N.

Let the elements of Set 3N be marked as a_1, a_2, a_{3 ……..} Now strict one to one relationship is easily established from a₁ to 1 and 1 to a_1, from a₂ to 2 and 2 to a₂ , and so on. There is no element in set 3N which corresponds to more than one element of set N and vice-versa

Hence set 3N is countable or say denumerable.

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