An interval can include either endpoint, both endpoints or neither endpoint. To distinguish between these different intervals, we use interval notation. An open interval does not include endpoints. The exclusion of the endpoints is indicated by round brackets in interval notation.
When the interval is represented by a segment of the real number line, the exclusion of an endpoint is illustrated by an open dot.
For example, the interval of numbers between the integers 3 and 8, excluding 3 and 8, is written as. As a segment of the real number line, it would be represented by the line below. A closed interval includes the endpoints. The inclusion of the endpoints is indicated by square brackets [] in interval notation. Finally, note that if the characterization of the set is rather complex, the set notation becomes preferable to the interval one, which would require a great number of intervals in the union.
In some other cases, it could be literally impossible to write a set in interval notation, for example is you consider only irrational numbers, you write. In this notation we define the characteristics of all x belonging to this set A Interval notation is other way to say the same but assuming that [ means the extreme a is IN the interval and means extreme a is not.
What is the difference between set notation and interval notation? The table below outlines the possibilities. Remember to read inequalities from left to right, just like text. The table below describes all the possible inequalities that can occur and how to write them using interval notation, where a and b are real numbers. In the previous examples you were given an inequality or a description of one with words and asked to draw the corresponding graph and write the interval.
In this example you are given an interval and asked to write the inequality and draw the graph. In the box below, write down whether you think it will be easier to draw the graph first or write the inequality first. In the following video, you will see examples of how to write inequalities in the three ways presented here: as an inequality, in interval notation, and with a graph.
Set-builder notation is a method of specifying a set of elements that satisfy a certain condition. Interval notation is a way of describing sets that include all real numbers between a lower limit that may or may not be included and an upper limit that may or may not be included. The endpoint values are listed between brackets or parentheses.
A square bracket indicates inclusion in the set, and a parenthesis indicates exclusion from the set. For example,. Describe the intervals of values shown below using inequality notation, set-builder notation, and interval notation. Remember that, when writing or reading interval notation, using a square bracket means the boundary is included in the set.
Using a parenthesis means the boundary is not included in the set. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Related 5. Hot Network Questions.
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