WEBVTT
00:00:01.380 --> 00:00:06.000
Find the set of natural numbers that are less than seven.
00:00:07.490 --> 00:00:12.980
Remember that a set in maths is a collection of numbers or objects.
00:00:13.550 --> 00:00:17.900
And we can think of the set as representing an object by itself.
00:00:18.710 --> 00:00:22.330
We’d expect the set in this question to contain different numbers.
00:00:23.060 --> 00:00:29.120
But as a whole, we could talk about it as a set of natural numbers that are less than seven.
00:00:30.260 --> 00:00:33.900
We sometimes say that natural numbers are the numbers that we used to count with.
00:00:34.530 --> 00:00:37.970
Another definition is a nonnegative whole number.
00:00:38.710 --> 00:00:43.850
So we can’t go lower than zero, but all the whole numbers from zero onwards.
00:00:44.530 --> 00:00:46.320
You could draw this on a number line.
00:00:46.930 --> 00:00:56.130
If we draw arrows on both ends of our number line, it shows that the numbers continue to the left into negative numbers and to the right into positive numbers.
00:00:56.920 --> 00:01:03.050
All the natural numbers are the numbers that we see to the right of and including with zero.
00:01:03.800 --> 00:01:06.410
These are all nonnegative whole numbers.
00:01:07.310 --> 00:01:09.720
So we can label our natural numbers on the number line.
00:01:09.720 --> 00:01:18.410
Zero, one, two, three, four, five, six, and seven.
00:01:19.370 --> 00:01:21.950
Of course we could continue eight, nine, and so on.
00:01:22.250 --> 00:01:26.140
But we only need to think about these particular natural numbers in this question.
00:01:27.250 --> 00:01:31.210
We’re asked to find the set of natural numbers that are less than seven.
00:01:31.870 --> 00:01:37.880
The only two numbers on our number line that we really need to think about is, do we need to include zero.
00:01:38.620 --> 00:01:40.940
And should we include seven itself?
00:01:41.600 --> 00:01:42.750
Let’s think about zero.
00:01:43.110 --> 00:01:45.640
Is zero nonnegative?
00:01:46.290 --> 00:01:48.380
Yes, it’s not a negative number, is it?
00:01:49.120 --> 00:01:50.980
And is it a whole number?
00:01:51.630 --> 00:01:53.020
Well, it’s not a decimal.
00:01:53.480 --> 00:01:55.920
So we can consider it as a whole number.
00:01:57.060 --> 00:02:00.040
We should include zero as part of our set.
00:02:00.810 --> 00:02:02.500
What about the number seven?
00:02:03.340 --> 00:02:04.540
This is nonnegative.
00:02:04.540 --> 00:02:05.660
And it’s a whole number.
00:02:06.440 --> 00:02:08.260
So it must be a natural number.
00:02:08.690 --> 00:02:12.930
But we were asked to find all the natural numbers that were less than seven.
00:02:13.660 --> 00:02:16.450
Could we say that seven is less than seven?
00:02:17.330 --> 00:02:18.580
No we can’t.
00:02:18.980 --> 00:02:21.870
So we can’t include seven as part of our set.
00:02:22.460 --> 00:02:26.920
Remember that when we write a set, we write it within braces.
00:02:28.110 --> 00:02:33.500
So let’s do that with our answer now as we recall the set of natural numbers that are less than seven.
00:02:34.120 --> 00:02:37.460
And we need to use commas to separate each number in the set.
00:02:37.900 --> 00:02:52.740
The set of natural numbers that are less than seven are zero, one, two, three, four, five, and six.