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Interval & Set-Builder Notations

Basic, Essential, and Important Properties of Sets

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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.

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Example – Interval Notation

 

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Example – Interval Notation

 

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Notation Set builder notation has the

general form

{variable | descriptive statement }.

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.

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DO NOT PANIC !!!

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.

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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 is an even positive integer} is the same as {2,4,6,…}.