And I just showed you how I can depict it on a number line, by actuallyįilling in the endpoints and there's multiple ways to talk about this interval mathematically. And when you include the endpoints, this is called a closed interval. Negative three and two are part of this interval. So this right over here, I'mįilling negative three and two in, which means that Negative three and two, then I would fill them in. Negative three and two, or maybe I'm just including one of them. Am I including negative three and two, or am I not including I care about all the numbersįrom negative three to two. Let's say I wanted to talkĪbout the interval on the number line that goes from That we can show an interval, or interval notation. To do in this video is get familiar with the notion of an interval, and also think about ways If the boundary expressions do both things, we use both notations. We have a square bracket after -1 because -1 IS included in the interval. We have a parenthesis in front of -4 because -4 is NOT included in the interval. In this case we mix the parenthesis and the square bracket. In the third example (the one you are citing), the one boundary expression includes "equal to" and one does not ( x is greater than -4 and x is less than or equal to -1). When the boundary does NOT includes the number (greater than or less than, but not equal to), we use parentheses to notate the interval. When Sal shows the notation for the second interval (pink writing), the boundary expressions do NOT include "equal to" ( x is greater than -1 and x is less than 4). When the boundary includes the number (equal to), we use the square brackets to notate the interval. If you go back and watch Sal show the notation of the first interval (blue writing), both boundary expressions include "equal to" ( x is greater than or equal to -3 and x is less than or equal to 2). Keep in mind that this is a type of mathematical notation and not Grammar of any language that uses this type of punctuation. In Interval Notation, you actually can have a parenthesis on one side and a bracket on the other and have the notation be correct. If this was not true, we would say A ⊄ B meaning A is not a subset of B.This is actually a pretty good question and it's good to see that you ate paying attention. When we have two or more sets, we can look at how they are the same or how they differ in lots of different ways.įor example, if set A completely fits into set B, we can say that A ⊂ B. This contains everything we are interested in and has the symbol '∪', ∪ or \(\upvarepsilon\) (sometimes other symbols are used too). This set could also be defined by us saying:įinally, there is one more important set – the universal set. This is read as 'Z is a set of the factors of 18'. We can also use notation to create our sets: We can define our own sets and choose any letter we want to represent them: N is the set of counting or natural numbers: Sets are named using capital letters with some sets having a predefined name. Objects placed within the brackets are called the elements of a set, and do not have to be in any specific order. Set notation uses curly brackets which are sometimes referred to as braces. Set notation is used in mathematics to essentially list numbers, objects or outcomes.
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