Question Use set builder notation to express the set of squares of integers between 1 and 1000 exclusively, i.e not including 1 and 1000 . Select the correct answer below: \{ \( n^{3} \mid n \in \mathbb{Z} \) and \( \left.1

Ask by Bowers Wells. in the United States

Mar 09,2025

The correct expression in set builder notation for the set of squares of integers between 1 and 1000 exclusively is \( \{ n^{2} \mid n \in \mathbb{Z} \text{ and } 1 < n < 32 \} \). This is because the squares of the integers from 2 to 31 (since \( 31^2 = 961 \) which is less than 1000) will yield the desired set of squares—specifically, \( 2^2 \) to \( 31^2 \). Now let’s move on to some fun tidbits! Did you know that the earliest known use of squares can be traced back to ancient Egypt, where they used geometric forms in their practical mathematics? It’s fascinating to think about how these concepts laid the groundwork for modern theories! Also, if you’re looking to explore more about sets, consider diving into the world of functional notation and exploring how these foundational concepts are applied in computer science and data structures! It can be really eye-opening to see how abstract mathematical ideas find their way into programming and algorithms!