1. The problem is to understand what a \textbf{set} is in mathematics. 2. A \textbf{set} is a well-defined collection of distinct objects, considered as an object in its own right. 3. These objects are called \textbf{elements} or \textbf{members} of the set. 4. Sets are usually denoted by capital letters, and elements are listed inside curly braces, for example, $A = \{1, 2, 3\}$. 5. Important rules about sets: - Elements are unique; duplicates are not counted. - The order of elements does not matter, so $\{1, 2\} = \{2, 1\}$. 6. Sets can be finite or infinite, and can contain numbers, symbols, or even other sets. 7. Understanding sets is fundamental in many areas of mathematics including algebra, calculus, and discrete math.