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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.

 You are watching: How to write all real numbers except 0SymbolRepresents 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

 SymbolRepresents∪Union of 2 sets ( ) An open interval (i.e. We do not encompass the endpoint(s)) See more: Why Do People Wear Rubber Bands On Their Wrist S? Major Reasons Men Wear Bracelets On Their Wrists< > 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, 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