Set-builder notation and interval notation

College Algebra Students:

Question: Why would you want to master the use of set-builder notation and interval notation to describe a set of numbers?

One Answer: We will be using them to describe our solutions to inequalities. Unlike equations that will usually have just one answer like x = 30 or x = 12, inequalities usually have more than one answer. For example, the inequality x + 7 > 16 has many solutions. It turns out that x = 30 and x = 12 are both solutions to this inequality. But there are many more. We need a way to describe all of the numbers in a compact form.

Another Answer: We will need them to describe the domain or range of a function. The function f(x) = log x does not make sense for certain values of x, like x = 0 or x = -10. We need a way to describe this too.

Check out these sites for additional information on using set-builder notation and interval notation:

http://id.mind.net/~zona/mmts/miscellaneousMath/intervalNotation/intervalNotation.html. A very straight-forward discussion of the relationship between the inequality symbols and the brackets and parentheses used in interval notation.

http://regentsprep.org/Regents/math/ALGEBRA/AP1/IntervalNot.htm. Note: This site uses the classic method of open circles and closed circles to graph intervals. Our textbook uses parentheses and brackets in the graphs. Our textbook's method is a little more awkward if you ask me, but I think it makes it easier to describe a group of numbers using interval notation.

http://www.math.ohio-state.edu/files/interval.pdf. This document actually uses the parentheses and brackets on graphs the way our textbook uses them. Each row shows an inequality in interval notation, in set-builder notation, and as a graph. You can replace the "a"s and "b"s with numbers to show the answers to similar problems with actual numbers in them.