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MAT 1033
WORKSHEET # 1
INTERVAL NOTATION (SECTION 1.1)
A set is a collection of objects whose contents can be clearly determined.
The objects in the set are called the elements of the set.
Sets of real numbers can be represented using one of the following forms:
1. SET – BUILDER NOTATION. In this notation the elements are described, but not listed.
Ex: N = {x|x is a natural number}
(Note: The small vertical line “|” stands for the phrase “such that”)
2. GRAPH. Visually represents the set of numbers on a number line by placing a dot at the
correct location for each number. The value of the numbers increase from left to right.
If we are considering an entire span or interval of numbers rather than just a set of
individual values, we use shading to indicate ALL the numerical values in that interval.
If the set we are considering is an entire span or interval of values on the number line we can also use a
form called Interval Notation.
3. INTERVAL NOTATION. Represents a shaded span of numbers on the number line by showing
the numbers at the end of the interval separated with a comma.
The numbers are surrounded by symbols that indicate whether or not those endpoints are included.
(Parentheses) indicate endpoints that are NOT included in the interval (when graphing you may have
used open circles to indicate this.)
[Brackets] indicate endpoints that are included in the interval (when graphing you may have used closed
or solid circles to indicate this.)
NOTE: (Parentheses) are ALWAYS used to surround ∞ and –∞.
