Problem 117 - Introductory Algebra for College Students

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

The statement makes sense given that interval notation is more concise and takes less space than set-builder notation. However, this is a matter of personal preference and could vary among different individuals.

Step 1: Understanding interval notation

Interval notation is a simplified form of writing the set of numbers in a particular interval or set. It uses parentheses '()' or brackets '[]' for indicating the intervals, thus keeping it brief and less space consuming.

Step 2: Understanding set-builder notation

The set-builder notation is another form of representing specific numbers of a set. It is a more detailed and explanatory way of writing sets. It uses curly brackets '{}' and descriptive conditions to describe the elements of the set.

Step 3: Comparing the two notations

Both interval notation and set-builder notation serve the same purpose: to describe sets of numbers. However, interval notation is typically more concise than set-builder notation, which may be why it might be preferred when space is a concern. It should be noted though that preference is subjective and depends on the individual’s rather than a absolute rule.