Negative one and four, but I don't want to include Let's say that I want to talk about the values between negative one and four. An open interval just so that we clearly can see the difference. So let's- Let me drawĪ number line again. So these are allĭifferent ways of denoting or depicting the same interval. Such that x is a member of this closed set, I'm Member of the real numbers such that x is a member, This vertical line here means "such that," negative three is less x is less than- negative three is less than or equal to x, is less than or equal to two. I'm using the Greek letterĮpsilon right over here. These curly brackets say that we're talking about a set of values, and we're saying that the set of all x's that are a member of the real number, so this is just fancy math notation, it's a member of the real numbers. And I could put these curlyīrackets around like this. Sometimes you might see things written a little bit more math-y. These brackets tell us that we include, thisīracket on the left says that we include negative three,Īnd this bracket on the right says that we include Talking about the interval between, and we can use brackets because it's a closed interval, negative three and two, and once again I'm using brackets here, Another way that we couldĭepict this closed interval is we could say, okay, we're Than or equal to positive two, so that means that x couldīe equal to positive two, so it is a closed interval. That x could be equal to, that x could be equal to negative three.
Three is less than or equal to x so that's telling us I could say these are all of the x's that are between negative three and two. Let's say this number line is showing different values for x. 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. This is actually a pretty good question and it's good to see that you ate paying attention.
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