Problem 146 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I prefer interval notation over set-builder notation because it takes less space to write solution sets.

Step-by-Step Solution

Answer

Yes, the statement does make sense given that interval notation often requires less space to write. However, the preference of one notation over the other can be subjective and may vary based on the complexity of the set being represented.

Step 1: Understand Interval Notation

Interval notation is a method used to express the set of solutions in mathematics which involves writing the solutions as intervals. This notation can be simpler and take less space to write than other methods, as the student pointed out. For example, the solution set \( -3 \leq x < 2 \) can be written as \([-3,2)\) in interval notation.

Step 2: Understand Set-Builder Notation

Set-builder notation is a method in mathematical notation for describing a set by indicating the properties that its members must satisfy. While it may take more space compared to interval notation, it allows a clear, formal, and precise representation of more complex sets. For example, the solution set \( -3 \leq x < 2 \) can be written as \(\{x| -3 \leq x < 2\}\) in set-builder notation.

Step 3: Making sense of the statement

The preference for one notation over the other can vary among individuals based on factors such as complexity of the set being represented and space constraint. Here, the statement does make sense if the individual prefers a shorter notation and is dealing with relatively simple sets. However, when dealing with more complex sets, set-builder notation may be preferred despite being more lengthy.