# Homework Hints: Intervals of real numbers – unions and intersections

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. Â Consider the intervals of real number $A = [2, 5)$ and $B = (4,\infty)$. Â Find their intersection $A\cap B$ and their union $A\cup B$.

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. Â The set $A$ includes all numbers that are great than or equal to 2 and less than 5. Â This means that $A$ includes 2, 3 and 4, but also decimals such as 3.5 or 4.9998. Â The set $B$ includes all numbers greater than 4, such as 4.1 or sixÂ billion.

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

• $A\cap B = (4,5)$

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

• $A\cup B = [2,\infty)$

WeBWorK Tip: Â 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. Â To do this, connect them with a union symbol (just use the capital U on your keyboard). Â Here is a (made up) example:
$[1,7] \cup (15,17]$

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