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Positive Numbers Less Than -3

Date: 01/30/98 at 14:27:27
From: Mrs. Heather
Subject: Algebra 1

Problem: Write using roster notation and set-builder notation.

 1) the set C of positive multiples of 3 less than -3

How can a positive number be less than 3?  That is what's really 
stumping me! Also, "negative integers greater than -3" only include 
-2 and -1, right?

Thank you for your time.

Date: 02/01/98 at 22:42:36
From: Doctor Jaffee
Subject: Re: Algebra 1

Greetings Mrs. Heather,

There's a good reason that you can't find any positive numbers less 
than -3. There aren't any! Consequently, there are no positive 
multiples of 3 less than -3.

Now, roster notation is a system in which one lists all the elements 
of a set in brackets. If there are no elements in the set, then just 
make 2 brackets with nothing in between them like so: {  }. (This is 
called the "empty set".)

In set builder notation we want to establish some kind of rule or 
equation that generates all the numbers of the set. So, if we use the 
variable x to represent an integer, all the elements of the set are 
numbers in the form 3 times x where 3x is less than -3, but 3x is 
greater than 0 and 3x is an integer.  We would write
{3x:0<3x<-3, x an integer}. Of course, the inequality 0 < 3x < -3 has 
no solution, so this notation would generate the empty set.

You were also right when you stated that -2 and -1 are the only 
negative integers greater than -3.

Thanks for writing and I hope this has helped. 

-Doctor Jaffee,  The Math Forum
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