Tag Archives: interval notation

Homework Hints: Intervals of real numbers – unions and intersections

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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.  Consider the intervals of real number A = [2, 5) and B = (4,\infty).  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.  The set A includes all numbers that are great than or equal to 2 and less than 5.  This means that A includes 2, 3 and 4, but also decimals such as 3.5 or 4.9998.  The set B includes all numbers greater than 4, such as 4.1 or six billion.

The intersection will be the places where these two overlap – it will include numbers greater than 4 but less than 5 (NOTE: it does not include the numbers 4 and 5 themselves, but it does include, for example, 4.3).  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:  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.  To do this, connect them with a union symbol (just use the capital U on your keyboard).  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