WEBVTT
00:00:03.370 --> 00:00:06.610
So in this lesson, what we’re gonna be looking at is expressing a set.
00:00:07.080 --> 00:00:12.960
What this means is actually listing values that could be in a particular set of parameters.
00:00:13.350 --> 00:00:15.310
And each of these values is known as an element.
00:00:17.000 --> 00:00:24.810
So even though we say values, as I said, we should say elements because they don’t have to be numbers, for example, the set of vowels a, e, i, o, u.
00:00:25.270 --> 00:00:29.510
But then we can have numbers like the set of odd numbers, which is one, three, five, et cetera.
00:00:31.430 --> 00:00:34.610
So we now know a little bit about what expressing a set is.
00:00:35.250 --> 00:00:40.070
Now what we’re gonna do is take a look at some questions that will show us how we would express particular sets.
00:00:41.770 --> 00:00:43.720
So ready, set, go.
00:00:43.770 --> 00:00:45.160
Let’s have a look at the first question.
00:00:48.530 --> 00:00:51.990
Using the listing method, express the set of the days of the week.
00:00:53.440 --> 00:00:59.580
So what this question means by the listing method is listing out each of the elements of the set that we’re looking at.
00:01:00.890 --> 00:01:03.170
It is important to remember to use the correct terminology.
00:01:03.370 --> 00:01:06.920
So if we’re talking about a part of our set — a part of our set is called an element.
00:01:08.460 --> 00:01:15.150
And we can already say that we know that our set is gonna have seven elements because if we’re talking about the days of the week, we know that there are seven days of the week.
00:01:16.910 --> 00:01:22.520
And whenever we’re about to list a set, what we use is some set notation to represent that we’re gonna be listing a set.
00:01:22.920 --> 00:01:25.280
And that is the curly bracket that we have here.
00:01:25.280 --> 00:01:26.990
We’re gonna have one at each end of our set.
00:01:28.360 --> 00:01:30.010
So our first element is gonna be Saturday.
00:01:30.170 --> 00:01:31.090
You could start with any day.
00:01:31.090 --> 00:01:38.490
I’ve chosen to start with Saturday, then Sunday, Monday, Tuesday.
00:01:39.640 --> 00:01:44.560
Then next, we have Wednesday and then Thursday and, finally, Friday.
00:01:46.090 --> 00:01:50.110
And we can quickly double check to make sure that we’ve got the seven elements we expected, and we have.
00:01:50.460 --> 00:01:58.250
So therefore, we can say that the set of the days of the week is Saturday, Sunday, Monday, Tuesday, Wednesday, Thursday, and Friday.
00:02:00.380 --> 00:02:00.960
Okay, great.
00:02:01.010 --> 00:02:04.780
So what we’ve done is we’ve expressed a set and we’ve shown how to do that using the listing method.
00:02:04.820 --> 00:02:08.480
And we used a little bit of notation with our curly brackets.
00:02:08.480 --> 00:02:11.760
And we’ve also talked about the elements being each part of our set.
00:02:13.350 --> 00:02:18.210
So now what we’re gonna do is take a look at an example which includes numerical values and see how we’d list those.
00:02:21.300 --> 00:02:25.130
𝑌 is the set of digits in the number 90,590.
00:02:25.720 --> 00:02:27.460
Write 𝑌 using the listing method.
00:02:29.040 --> 00:02:38.170
Well, the first thing we need to do in this question, to enable us to write 𝑌 using the listing method, is identify the digits within our number.
00:02:40.140 --> 00:02:43.280
Well, first of all, we can see that the digit nine appears twice.
00:02:44.820 --> 00:02:50.500
Then we have the digit zero, which also appears twice, and finally the digit five.
00:02:51.150 --> 00:02:59.050
Now, when we’re gonna list these digits, so we’re gonna list the set of digits, which is 𝑌, we only need to list each digit once.
00:03:00.430 --> 00:03:04.490
So therefore, the set 𝑌 would equal nine, five, and zero.
00:03:04.490 --> 00:03:13.850
And it’s worth noting here that a common mistake would be to list all of the digits that we have, for instance, two nines, two zeros, and a five.
00:03:13.880 --> 00:03:17.330
So, It’s also worth noting that it doesn’t matter which order we put them in.
00:03:17.670 --> 00:03:19.450
I’ve just put them here in descending order.
00:03:23.070 --> 00:03:29.700
So we’ve looked at a couple of examples now, one that involved nonnumerical values, one that involves numerical values.
00:03:29.730 --> 00:03:31.570
What would we take a look at next?
00:03:33.210 --> 00:03:41.670
Well, next, we’re gonna have a look at what we do if we’ve got a very big set or, in fact, an infinite set.
00:03:44.600 --> 00:03:47.220
𝑋 is the set of odd numbers greater than eight.
00:03:47.340 --> 00:03:49.160
Write 𝑋 using the listing method.
00:03:50.900 --> 00:03:58.780
Well, in this question, if we want to list our set and find each of the elements, then what we’re gonna need to do is take a look at these two key bits of information.
00:03:59.420 --> 00:04:04.520
We want the set to be odd numbers, but they must be greater than eight.
00:04:06.200 --> 00:04:07.400
Well, we’ve got one problem.
00:04:08.300 --> 00:04:11.130
The odd numbers greater than eight is gonna be a lot of numbers.
00:04:11.570 --> 00:04:15.510
In fact, it’s gonna be ∞ numbers.
00:04:16.080 --> 00:04:21.890
So our set is gonna have ∞ elements because it’ll keep going on and on and on.
00:04:22.420 --> 00:04:23.370
So what are we gonna do?
00:04:25.070 --> 00:04:30.520
Well, first of all, what we’re gonna do is list our first value because the first odd number that’s greater than eight is nine.
00:04:31.820 --> 00:04:35.430
And then, what we’re gonna do is list a couple more values, 11 and 13.
00:04:37.320 --> 00:04:45.270
But then, instead of having to list lots and lots and lots of different values or lots of different elements, all we do is we put three little dots.
00:04:45.300 --> 00:04:51.350
And this means continued, because, as we’ve said, there’ll be infinite number of different elements within this set.
00:04:51.760 --> 00:05:00.210
So we can say that if 𝑋 is a set of odd numbers, then 𝑋 can be written as nine, 11, 13, et cetera.
00:05:00.470 --> 00:05:07.340
And I’ve put that inside of our curly brackets, which are part of our set notation and tells us that it represents a set of values.
00:05:10.320 --> 00:05:15.860
So we’ve looked at listing different sets and we’ve shown how we can do this using different notation.
00:05:16.430 --> 00:05:21.230
So finally, what we’re gonna do is we’re just going to show you how you’d list elements on their own.
00:05:21.230 --> 00:05:25.460
So not entire sets, but just still elements of a set.
00:05:27.940 --> 00:05:34.920
Write the elements of the set, the odd numbers between, but not including, 799 and 805.
00:05:36.490 --> 00:05:43.140
So the keyword here in this question is element because what it means is we want to write the individual parts of our set.
00:05:43.270 --> 00:05:44.620
And these are known as elements.
00:05:46.250 --> 00:05:48.210
We can also see the next bit of useful information.
00:05:48.260 --> 00:05:49.840
And that is that we’re looking at odd numbers.
00:05:51.620 --> 00:05:57.710
And it must be between, but not including, 799 and 805.
00:05:59.430 --> 00:06:07.630
So our first value will not be 799; it will be 801 because this is the next odd number.
00:06:09.540 --> 00:06:16.110
Then, the next odd number that meets our criteria is 803 and then, finally, 805.
00:06:16.300 --> 00:06:21.670
This will also not be included because we’re told in the question that 799 and 805 are not included.
00:06:23.520 --> 00:06:33.040
So therefore, the elements of the set, the odd numbers between, but not including, 799 and 805 are 801 and 803.
00:06:33.320 --> 00:06:34.640
There are two elements.
00:06:36.770 --> 00:06:41.410
So we’ve now come to the end of the lesson because we’ve shown how we can list sets.
00:06:41.640 --> 00:06:44.920
And we’ve listed sets that include numerical and nonnumerical values.
00:06:45.400 --> 00:06:48.490
We’ve also looked at elements and how we can list individual elements.
00:06:48.690 --> 00:06:53.230
And we’ve shown how you’d list sets that have infinite number of values.
00:06:54.730 --> 00:06:57.140
So now what we’re gonna do is take a look at the key points.
00:06:57.310 --> 00:07:01.020
The first key point we’ve got is that an element is a value or part of a set.
00:07:01.440 --> 00:07:04.130
So any individual part of our set is called an element.
00:07:05.950 --> 00:07:07.880
We’ve also seen that we use set notation.
00:07:07.880 --> 00:07:11.970
So we have these curly brackets that show that something is in fact a set.
00:07:13.950 --> 00:07:24.590
And we’ve also shown that if we have an infinite number of elements in a particular set, then we can show this by listing the first two or three elements, then having these three dots after, which says that it’s gonna carry on infinitely.
00:07:24.700 --> 00:07:31.780
And what we’ve shown is with our examples that a set can be numerical or nonnumerical.
00:07:32.290 --> 00:07:38.800
And any set can have any number of parameters, which help us decide upon what that set is gonna be and what the elements within it are.