Question Which of the following is the correct set builder notation for the set of perfect squares between 1 and 100 (including 1 and 100)? Select the correct answer below: \( \left\{p^{2} \mid p \in \mathbb{Z}\right. \) and \( \left.1 \leq p \leq 10\right\} \) \( \left\{p^{2} \mid p \in \mathbb{Z}\right. \) and \( \left.1

Ask by Munoz Mills. in the United States

Mar 09,2025

Did you know that set builder notation is like a secret code mathematicians use to describe sets? For perfect squares between 1 and 100 — which are \(1, 4, 9, 16, 25, 36, 49, 64, 81, \) and \(100\) — we need to make sure we're only using integers (whole numbers) as \(p\). The first option correctly specifies that \(p\) must be an integer in the range \(1\) to \(10\). Perfect squares have a fascinating history in math! The ancient Greeks were among the first to explore the concept of square numbers, with Plato even connecting them to his theories about the natural world. Over time, mathematicians like Diophantus and later Islamic scholars expanded on these ideas, leading to a deeper understanding of number theory. So, every time you see a perfect square, you’re gazing at a slice of mathematical history!