00:00Friends, we continue with two indefinite intervals, which is the final point of the absolute value relationship.
00:05Now, let's look at how the absolute value relationship works when two unlimited intervals are given.
00:10I'm talking about two real numbers, folks.
00:18What's left outside.
00:23We might not always be given a closed window, right guys?
00:27It can go on forever, two and a half times.
00:28Yes, I'm talking about a negative infinity B1 closed-interval union, and a positive infinity B2 open-interval union, friends.
00:39In other words, semi-closed intervals can be expressed as an absolute value inequality.
01:04Here's how we translate it, folks.
01:08It translates as follows.
01:12With your permission, I'd like to draw our number line, our real number line.
01:19Where is our gap now, friends?
01:21We'll take point B1 here.
01:23We'll take point B2 here.
01:26This will be our headquarters.
01:28And if this place goes on forever, let's also imagine this place as negative infinity.
01:34And our range, folks, is right here.
01:37With this part.
01:38Including this and those places.
01:40Yes, friends, as you can see, the shaded areas of our range are displayed.
01:45I'm saying December, folks.
01:47I'd like to write my interval like this right away.
01:50What is X, folks?
01:53Less than or equal to B1.
01:54Combination.
01:57What is B2, guys?
02:00Less than or equal to X.
02:03Yes, we can be written like that.
02:04What happens here, friends, at the midpoint of our range?
02:08December.
02:17What happens when we equal each other, friends?
02:20B1 plus B2 divided by 2, right?
02:23Ultimately, it's the middle ground.
02:25Yes.
02:26The midpoint of the path between the endpoints of the range becomes more distant.
02:30Let's write it right there.
02:32December.
02:33Their extreme points.
02:39Distance from the midpoint.
02:52Let's call that point A, folks.
02:55Where was KiA, guys?
02:57As you can see.
02:59Right here.
03:00Why?
03:02The distance from the center of B1 and
03:04The distance from the center of B2.
03:07They're both A in the end, right?
03:08These points are relative to the center.
03:09Yes.
03:10This is the distance to the midpoint, folks.
03:14This is our point A in this situation.
03:17B2 minus B1 divided by 2.
03:22So, what if we wanted to write the absolute value inequality?
03:37How should we write this, guys?
03:39We will say:
03:40The distance from X to M.
03:43In other words, the distance from the center.
03:45What's going to happen, guys?
03:46It will be big.
03:47More precisely, it should be greater than or equal to.
03:49What are you friends of?
03:51Of course, in A.
03:53Now, friends, why did we write it like this?
03:55The obtained
03:56This is absolute value inequality.
04:01That is it.
04:09Inequality.
04:11Towards point M.
04:15Right here.
04:16Towards point M.
04:21Distance.
04:26My friends are explaining that it corresponds to the set of points greater than or equal to A.
04:32So, this distance.
04:33From A.
04:36Big.
04:37See, it's greater than A.
04:40Or equal.
04:43Or equal.
04:45Equal.
04:49To the set of points.
04:58It corresponds.
05:03And that's how it is, folks.
05:05Big.
05:05Buka造线.
05:05Big.
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