Question 1: Write the following sets in set builder notation:
\((iii)\) \(\quad\) \(\{0, \pm 1, \pm 2, \ldots, \pm 1000\}\)
Solution:
We observe in the set \(\{0, \pm 1, \pm 2, \ldots, \pm 1000\}\), the smallest number is \(-1000\), the greatest number is \(1000\), and the numbers increase by steps of \(1\). Therefore, this set consists of integers.
Set Builder Notation:
\(\{ x \mid x\in Z \land -1000 \leq x \leq 1000 \}\)