Hi everyone,

This is a followup to Thursday’s lecture, and should provide a little help with some of the homework problems (I’m looking at you, Problem 7).

**Example.** Ā Consider the intervals of real number and . Ā Find their intersection and their union .

One key idea is that these are intervals of the real numbers, so they include not just the whole numbers but *all* numbers between the endpoints. Ā The set includes all numbers that are great than or equal to 2 and less than 5. Ā This means that includes 2, 3 and 4, but also decimals such as 3.5 or 4.9998. Ā The set includes all numbers greater than 4, such as 4.1 or sixĀ billion.

The intersection will be the places where these two overlap – it will include numbers greater than 4 but less than 5 (NOTE: it doesĀ *not* include the numbers 4 and 5 themselves, but it does include, for example, 4.3). Ā In interval notation, we write:

The union will include all numbers greater than or equal to 2, written:

**WeBWorK Tip:** Ā To enter the infinity symbol, just use the word “infinity” like this:

[2, infinity)

**WeBWorK Tip:** Sometimes in WeBWorK, your answer will consist of two different intervals – you want to include them both in the answer. Ā To do this, connect them with a union symbol (just use the capital U on your keyboard). Ā Here is a (made up) example:

Not sure if these will help, but they may give you a little more to go on – feel free to leave a comment here or send me an email if you have questions.

Best of luck!

Prof. Reitz