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Example 3 - Write A = {1, 4, 9, 16, 25, ...} in set-builder

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Example 3 Write the set A = {1, 4, 9, 16, 25, . . . } in set-builder form. A = {1, 4, 9, 16, 25, . . . } A = {12, 22, 32, 42, 52, . . . } Here, 1, 2, 3, 4, 5 are all natural numbers and 1, 4, 9, 16, 25 are their squares Hence, we may write the set A as A = {x : x is the square of a natural number} or A = {x : x = n2, where n ∈ N}

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.