00:03
The set of all x such that the absolute value of x minus 1 is less than 2.
00:09
Find the least upper bound and the greatest lower bound of this set.
00:14
Let's go ahead and try to graph this on the number line.
00:21
All right.
00:22
The absolute value of x minus 1 is less than 2.
00:26
So let's put some numbers in here.
00:28
0, 1, 2, 3, 4, and let's go down, negative 1, negative 2, negative 3, and that should be enough.
00:46
Now, the absolute value of x minus 1, that means the difference between x and 1, of course, in absolute value turners, but the difference between x and 1.
00:57
So 1 is basically going to be the center of our graph.
01:01
The distance between x and 1 is less than 2.
01:05
So the distance between wherever x is and one is less than two.
01:11
So the distance that we can move, the distance that x can be from one is at most two spaces away.
01:21
So two spaces away here would be three, but we've got to be strictly less than two spaces away, so we're not going to really quite get to three...