WEBVTT
00:00:00.900 --> 00:00:04.310
Which of the following expressions represents the set shown on the number line?
00:00:04.500 --> 00:00:10.780
Is it (a) the set of all real numbers minus the set of numbers greater than negative four and less than or equal to one?
00:00:11.090 --> 00:00:16.190
Is it (b) the set of all real numbers minus the set of numbers in the closed interval negative four to one?
00:00:16.430 --> 00:00:25.670
Is it (c) the union of the set of numbers greater than negative ∞ and less than or equal to negative four and the set greater than or equal to one and less than ∞?
00:00:25.920 --> 00:00:30.950
(d) is the set of all real members minus the set of numbers in the open interval negative four to one.
00:00:31.150 --> 00:00:37.210
And (e) is the set of all real numbers minus the set of numbers greater than or equal to negative four and less than one.
00:00:37.460 --> 00:00:39.120
Let’s go right back to our number line.
00:00:39.300 --> 00:00:41.700
And we begin by recalling the meaning of these dots.
00:00:41.820 --> 00:00:48.770
An empty dot means greater than or less than whereas a solid dot means greater than or equal to or less than or equal to.
00:00:48.930 --> 00:00:54.160
And so, let’s imagine the set of numbers we’re interested in are the set of numbers for some unknown 𝑥.
00:00:54.270 --> 00:01:00.030
We can see that 𝑥 can take values less than or equal to negative four and greater than one.
00:01:00.310 --> 00:01:03.090
So how do we represent these using interval notation?
00:01:03.230 --> 00:01:09.240
Well, we can see that our value for 𝑥 can take all real numbers except those in this underlined part.
00:01:09.330 --> 00:01:13.290
Those are the values including negative three, negative two, negative one, zero, and one.
00:01:13.480 --> 00:01:16.980
Well, we know that this letter ℝ represents the set of all real numbers.
00:01:17.100 --> 00:01:21.050
And we want to subtract some set from negative four to one.
00:01:21.130 --> 00:01:26.880
We don’t want to subtract negative four from all real numbers because we know that 𝑥 could be negative four.
00:01:26.910 --> 00:01:29.900
But we use the closed interval notation next to the one.
00:01:29.960 --> 00:01:33.720
And that’s to show that we don’t want to include the number one in our set.
00:01:33.780 --> 00:01:43.610
And so, the expression that represents the set shown on the number line is the set of all real numbers minus the set containing numbers greater than negative four and less than or equal to one.
00:01:43.770 --> 00:01:45.340
And we can see that’s (a).