Positive Numbers Less Than -3Date: 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 Check out our web site! http://mathforum.org/dr.math/ |
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