1. August 2006 Copyright © 2006 by DrDelMath.Com 1 Interval & Set-Builder Notations Basic, Essential, and Important Properties of Sets

2. August 2006 Copyright © 2006 by DrDelMath.Com 2 Notation An interval is a connected subset of numbers. Interval Notation is an alternative to expressing your answer as an inequality. A parenthesis ( or ) means the endpoint is excluded, while a bracket [ or ] means the endpoint is included.

3. August 2006 Copyright © 2006 by DrDelMath.Com 3 Example – Interval Notation 410

4. August 2006 Copyright © 2006 by DrDelMath.Com 4 Example – Interval Notation 410

5. August 2006 Copyright © 2006 by DrDelMath.Com 5 Notation Set builder notation has the general form Set builder notation has the general form {variable | descriptive statement }. {variable | descriptive statement }. The vertical bar (in set builder notation) is always read as “such that”. The vertical bar (in set builder notation) is always read as “such that”. Set builder notation is frequently used when the roster method is either inappropriate or inadequate. Set builder notation is frequently used when the roster method is either inappropriate or inadequate.

6. August 2006 Copyright © 2006 by DrDelMath.Com 6 DO NOT PANIC !!! notation, you just need to be able to interpret a set described using set-builder notation. You will never have to describe a set using set builder notation, you just need to be able to interpret a set described using set-builder notation.

7. August 2006 Copyright © 2006 by DrDelMath.Com 7 Example – set builder notation {x | x < 6 and x is a counting number} is the set of all counting numbers less than 6. Note this is the same set as {1,2,3,4,5}. {x | x < 6 and x is a counting number} is the set of all counting numbers less than 6. Note this is the same set as {1,2,3,4,5}. {x | x is an even positive integer} is the same as {2,4,6,…}. {x | x is an even positive integer} is the same as {2,4,6,…}.