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Set-Builder and Interval notations

Set-Builder Notation

Set-builder notation is commonly used to compactly stand for a set of numbers. We deserve to use set-builder notation come express the domain or range of a function. Because that example, the collection given by,

x ,

is in set-builder notation. This set is check out as,

“The collection of all real numbers x, such that x is not equal to 0,”

(where the price | is read as such that). That is, this set contains all actual numbers except zero.




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Symbol
Represents

Denotes the collection
|
Such the

Another example of set-builder notation is,

{x | − 2 expression Notation

We can additionally use expression notation come express the domain the a function. Expression notation supplies the complying with symbols


Symbol
Represents

Union of 2 sets
( )
An open interval (i.e. We do not encompass the endpoint(s))



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A closeup of the door interval (i.e. We do include the endpoint(s))

Interval notation have the right to be used to express a variety of different sets of numbers. Below are a few common examples.

A collection including all real numbers other than a single number.

The union symbol have the right to be used for disjoint sets. For example, we can express the set,

x ≠ 0,

utilizing interval notation as,

(−∞, 0) ∪ (0, ∞).

We use the union prize (∪) in between these 2 intervals due to the fact that we space removing the allude x = 0.

We deserve to visualize the above union of intervals utilizing a number heat as,

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Notice the on ours number line, an open up dot indicates exclusion of a point, a close up door dot suggests inclusion of a point, and also an arrowhead indicates extension to −∞ or ∞.

Open and closed intervals

Now let"s look at another example. The collection given by,

{x| − 2

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In the following section we will describe summation notation.

Summation Notation