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Huhnkie Lee
  • 6/4/2025
designing the bezout coefficient formula
Transcript
00:00:00Hello friends welcome to humanology episode 2248. Happy Wednesday morning.
00:00:14Yeah so last night I did drink alcohol. I think it's okay to drink alcohol like on a special occasion.
00:00:23Not in a habitual basis but special occasions. I think that's a good thing
00:00:28actually okay yeah just on a special occasion sure sure yeah cheers.
00:00:37Okay and also so yeah we also did like the Instagram live as well right yeah
00:00:43for celebratory occasion and then after that I watched some music videos and some
00:00:51movie clips like Russia movie clips in YouTube and also music videos in YouTube
00:00:56like yeah like I hope you dance yeah also darling loving you is so easy not love
00:01:04is easy and I also bet by our friends though yeah in the rock band okay so uh-huh and
00:01:19and uh yeah and uh so I hope you dance that's a kind of country song and I actually cried
00:01:29while listening to that lyrics uh music very moving motivational good song yeah okay
00:01:37crying is very healthy okay yeah so I cry like uh these days I guess once a month I guess
00:01:44crying is very healthy okay yeah yeah listening to good music sure sure that's good okay let's do uh
00:01:51uh stretching I did some running outside yeah good morning happy wednesday morning I had some running
00:01:58outside and then uh let's do stretching and then uh we get back to mathematics okay yeah sure
00:02:06cheers
00:02:06and I finished watching movie slow video that's korean movie oh that was nice yeah cool movie okay
00:02:22she's also free on youtube okay
00:02:24okay
00:02:41okay
00:02:45okay
00:02:51okay
00:04:24Ah, very sweet air, sweet water.
00:04:30Nice.
00:04:31Nice morning, Ron.
00:04:44Empty streets.
00:04:46Nice.
00:04:47Fresh air, fresh water, very sweet water.
00:05:00Oh, yeah.
00:05:01Okay.
00:05:06Okay.
00:05:06Yeah, I also watched some Hidden Dragon Crouching Tiger movie clips, that was good too.
00:05:31Okay, very short of exercise.
00:06:31Yeah, straight, you know.
00:06:38Yeah, straight, you know.
00:06:40Okay.
00:06:45Okay.
00:06:52Okay.
00:06:54Okay.
00:07:01Okay.
00:07:08Okay.
00:07:09Okay.
00:07:10Now, give me one second.
00:07:15Let me go to the restroom.
00:07:22Okay.
00:07:23Okay.
00:07:24Now, let me go to the restroom.
00:07:30Okay.
00:07:31Okay.
00:07:32Now, let's do some ground stretching, like splits.
00:07:37No?
00:07:38All right.
00:07:44All right.
00:07:45All right.
00:07:46All right.
00:07:47All right.
00:07:53All right.
00:07:54All right.
00:07:55All right.
00:07:56All right.
00:08:00Okay.
00:08:01Okay.
00:08:02Okay.
00:08:03Okay.
00:08:07Okay.
00:08:08Okay.
00:08:10Okay.
00:08:14Wow.
00:08:15Oh.
00:08:16Oh.
00:08:17Okay.
00:08:18Okay.
00:08:19Okay.
00:08:20Okay.
00:08:21Okay.
00:08:22Okay.
00:08:23Okay.
00:08:24Okay.
00:08:25Okay.
00:08:26Wow.
00:08:27Oh.
00:08:28Oh.
00:08:29Deep breathing.
00:08:37Oh.
00:08:54Oh
00:09:05Oh
00:09:21Okay
00:09:24All right
00:09:29Oh
00:09:31Ah
00:09:34Ah
00:09:38Ah
00:09:39Ah
00:09:41Ah
00:09:43Ah
00:09:47Ah
00:09:49Ah
00:09:51Ah
00:09:52Ah
00:09:53Ah
00:09:54Ah
00:09:58Ah
00:10:00Ah
00:10:02Ah
00:10:03Ah
00:10:04Ah
00:10:10Ah
00:10:13Ah
00:10:16Ah
00:10:21Ah
00:10:23Ah
00:10:25Oh, yeah.
00:10:38Oh.
00:10:55Okay, very good.
00:11:15Okay.
00:11:20Let's take five minutes break, please.
00:11:22Yeah, very good exercise, stretching, nice.
00:15:52Good morning.
00:15:59Welcome to Humanology episode number 10 to 48.
00:16:10Yeah.
00:16:10Let me get some water.
00:16:52Now let's continue to do mathematics.
00:17:22Okay.
00:17:23Okay.
00:17:24Okay.
00:17:25So we have a matrix here.
00:17:39Let's give it a name, right?
00:17:40Yeah.
00:17:41Yeah.
00:17:42What is this matrix about?
00:17:43We call it the remainder matrix, okay?
00:17:47Yeah.
00:17:48Remainder matrix.
00:17:49So we have a base 7 here.
00:17:56So we have a base 7 here.
00:17:58So we have base 7 here.
00:17:59Meaning we have number 1 through 6.
00:18:02So 6 by 6.
00:18:324.
00:18:33Okay.
00:18:34Okay.
00:18:35Okay.
00:18:3618 is 14 plus 4, right?
00:18:37Yeah.
00:18:38And...
00:18:39So 6 times 3 is 18.
00:18:42Right?
00:18:4318 row 7 is 4.
00:18:47That's the...
00:18:494 is the number of this row.
00:18:52Okay?
00:18:53Okay?
00:18:54Not row algebra row, but column row row.
00:18:58Okay?
00:18:59Yeah.
00:19:00Okay?
00:19:01That's how we construct this matrix.
00:19:05Okay?
00:19:06Yeah.
00:19:07Cheers.
00:19:08Okay.
00:19:09Okay.
00:19:10Now, once we fill this out...
00:19:18By the way, here, why does this number only occurs once and only once?
00:19:23That's like a multiplicative singularity theorem.
00:19:27Okay?
00:19:28Yeah.
00:19:29So we already proved that.
00:19:30Okay?
00:19:31But here, why this occurs only once and once?
00:19:33Probably the similar reason.
00:19:34Okay?
00:19:35Yeah.
00:19:36Okay?
00:19:37Okay. Now, but those former proof, we'll do that later. Okay?
00:19:46Yeah. Cheers.
00:19:53Well, we already did former proof. Multiplicative singularity theorem, right? Yeah.
00:20:00Okay. Co-prime. Okay. Now, let's observe this. But, okay.
00:20:071, 2, 3, 4, 5, 6. So you have 1, 1, 1, 1, 1. 6, 6, 6, 6, 6. Okay? Yeah.
00:20:24And you have 1, 2, 3, 4, 5, 6. All right? And then 1, skip 2, skip 3.
00:20:38Now, what's hidden here?
00:20:447. Okay?
00:20:497 and blank.
00:20:52We just put blank. It's not 0. It's just blank. Okay?
00:20:57So that rotation base. Okay? Just like your permutation groups theory. Okay?
00:21:02So 1, skip 2, skip 3, skip 4, skip 5, skip 6.
00:21:13Okay.
00:21:13Okay? There's second row. Second column. Third column. 1, skip skip 2, skip skip 3, skip skip 4, skip skip 5, skip skip 6.
00:21:275, skip skip skip skip 5, skip skip skip 6.
00:21:43Six column.
00:22:016 column, 1, skip skip skip skip skip skip 2, skip skip skip skip skip skip 3, skip skip skip skip skip skip skip 4, skip skip skip skip skip skip skip 5, skip skip skip skip skip skip skip skip skip 6.
00:22:17Okay, so that's the pattern.
00:22:22Now, we did base 7. How about some other numbers like base 11?
00:22:27Will it follow the same pattern? I'm pretty sure it will.
00:22:31But did I see that yet? No.
00:22:34Then why am I so sure?
00:22:36It's because there is absolutely no reason why this pattern only occurs when it is 7.
00:22:45It's an educated guess.
00:22:48If this pattern is true for 7, I'm pretty sure it's true for every number.
00:22:57That's my educated guess.
00:23:00Okay? I haven't tried any other numbers.
00:23:02And we will in the future.
00:23:10Okay?
00:23:11So that formula I showed you yesterday, that's based on this only.
00:23:16I did not test any other cases.
00:23:18And we will in the future.
00:23:19Okay?
00:23:24Now let's take 5 minutes break.
00:23:25Okay?
00:23:26Yeah.
00:23:27Oh, I'm hungry.
00:23:28I'm cooking my breakfast in the microwave.
00:23:33Okay?
00:23:34Yeah.
00:23:35Okay.
00:23:36Okay.
00:23:37Okay.
00:23:38Okay.
00:23:39Okay.
00:23:40All right.
00:23:41Five minutes break.
00:23:43Ooh.
00:23:44I'm hungry.
00:23:45Ooh.
00:23:46There we go.
00:23:47Yeah.
00:23:48Five minutes.
00:23:51There we go.
00:23:52Yeah.
00:23:53Five minutes.
00:23:55Yeah.
00:23:56Five minutes.
00:23:57Yeah.
00:23:58Five minutes.
00:27:57Okay?
00:27:58So, do I know the reason why it behaved this way?
00:28:06I do not.
00:28:08I don't know why.
00:28:09Not yet.
00:28:10Later on, we'll prove it and understand the mechanism behind the rationale behind this pattern.
00:28:18But, it's not necessary to understand the reasoning behind this pattern in order to come up with a formula.
00:28:31All we need to design a formula is the pattern recognition.
00:28:38That's good enough.
00:28:39Cheers.
00:28:40Cheers.
00:28:41Okay.
00:28:42Yeah.
00:28:43Proof.
00:28:44We'll do that later.
00:28:45Okay.
00:28:46Yeah.
00:28:47Proof.
00:28:48We'll do that later.
00:28:49Okay.
00:28:50Yeah.
00:28:51It won't be too difficult.
00:28:53Do you want to be too difficult?
00:28:54Okay.
00:28:55Uh...
00:28:56And then, based on this pattern, yeah, we can come up with a formula.
00:29:11We did.
00:29:12Okay.
00:29:13I showed you yesterday.
00:29:14Right?
00:29:15And...
00:29:16Uh...
00:29:17Uh...
00:29:18Which is not too difficult a task.
00:29:23Then, what was difficult?
00:29:33For me, to come up with this matrix, I mean, brand new.
00:29:42I mean, okay, God created this long time ago.
00:29:46Okay?
00:29:47But, to discover this.
00:29:49Well, we discovered many different matrices in the past.
00:29:53The ones that we erased.
00:29:56They are erased.
00:29:57Okay?
00:29:58And those were interesting matrices.
00:30:01We gave it a name, like energy matrix.
00:30:04Right?
00:30:05But, it didn't quite work out.
00:30:08It didn't really help us.
00:30:11This one does.
00:30:13Okay?
00:30:15Yeah.
00:30:16So, trial and error.
00:30:18Okay?
00:30:19Yeah.
00:30:20Cheers.
00:30:25But, in the past, other matrices, it really helped us.
00:30:31Why?
00:30:32Because we did get better at mathematics.
00:30:35We came up with some formula for those matrices.
00:30:40That same training, same technique, methodology that we used in the past, are being recycled here.
00:30:49So, we were ready.
00:30:55To tackle on this one.
00:30:56Okay?
00:30:57Yeah.
00:30:58Okay.
00:30:59Cheers.
00:31:00Yeah.
00:31:01Okay.
00:31:02Cheers.
00:31:03Yeah.
00:31:04Okay.
00:31:05Okay.
00:31:06Okay.
00:31:07You got him.
00:31:08That's perfect.
00:31:17What?
00:31:26Okay.
00:31:28How did your dance dominion startling?
00:31:32Nothing.
00:31:33Oh...
00:31:52But let's try to understand all the other, okay?
00:32:00Uh...
00:32:031 times 2, row 7 is 2, okay?
00:32:131 times 3, row 7 is 3.
00:32:16Yeah, that's why it's row 11111.
00:32:20Just easy enough, right? Yeah.
00:32:27And then...
00:32:302 times 2, row 7, 4.
00:32:40Okay? Yeah.
00:32:41Now, 3 times 2, row 7, 6.
00:32:46But when bass is not 7, when it's 11, it will be the exact same.
00:32:52Right? Yeah, of course.
00:32:56So, when it comes to second column, it skips 1 because it's 2, okay?
00:33:02When it comes to column 3, it skips 2 because it's 3, right?
00:33:10So, number of skips is like a column number minus 1.
00:33:16And then all we need to figure out is the function for all these indices, like row number,
00:33:27column number, row index, column index, based on this pattern, which is not that difficult.
00:33:34Okay?
00:33:36Yeah.
00:33:37It's...
00:33:39Nothing fancy.
00:33:40It's just algebra at the level of maybe college, high school, middle school.
00:33:51Middle school.
00:33:53Nothing fancy.
00:33:54We just have multiplication, audition, division.
00:34:02That's about it.
00:34:03There's not even subtraction there in the formula.
00:34:08Yeah, we have iVos in brackets, which is easy if than else.
00:34:12That's more in the computer program language, okay?
00:34:14So, and some row operator, yeah, which is easy.
00:34:18It's just remainder, okay?
00:34:19Yeah.
00:34:25Once we found it, yeah, it's not that difficult.
00:34:28I know it's quite complicated, I know, but it's not too difficult.
00:34:35Okay?
00:34:38Yeah, cheers.
00:34:39No, time check.
00:34:54It's been more than 30 minutes.
00:34:58Okay.
00:35:01Let's take five minutes break, and then I'll grab a whiteboard to erase.
00:35:07And then we'll start designing the formula.
00:35:16Well, I already did, and I showed you yesterday, right?
00:35:20But we'll design it together again.
00:35:23Okay?
00:35:24I'll show you how to design this.
00:35:30Okay?
00:35:31Yeah.
00:35:32But if you're not designing on your own, go for it, okay?
00:35:34Yeah.
00:35:35Yeah.
00:35:36And then we can compare the answers, okay?
00:35:41Yeah.
00:35:42It's fun.
00:35:43It's very enjoyable experience, okay?
00:35:50Yeah.
00:35:51Okay.
00:35:52Five minutes break, okay?
00:35:53Sure.
00:35:54Let me continue to cook my breakfast.
00:35:58Yeah.
00:35:59Yeah.
00:36:08Uh-huh.
00:36:14.
00:36:44.
00:37:02.
00:37:06.
00:37:08.
00:37:10.
00:37:12.
00:37:22I did not know how to drink again, but yesterday I did drink again.
00:37:26That's fine.
00:37:28Once in a while, you know?
00:37:30Yeah.
00:37:32Hmm.
00:37:42Hmm.
00:37:46Hmm.
00:37:48.
00:38:02.
00:38:04.
00:38:06.
00:38:08.
00:38:24.
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00:41:45.
00:42:46We'll erase this one, okay?
00:42:52Okay, I found one, all right.
00:43:02Yeah, it's not an easy decision to pick a whiteboard to erase because some whiteboards I cannot erase until I write this down and publish it as a paper.
00:43:16I can't even pay for it, you know?
00:43:18This phone I can't erase.
00:43:20Alright.
00:43:22Okay?
00:43:24I mean, yeah.
00:43:28I mean, yeah, drinking, I think it's okay to drink once in a while on a special occasion.
00:43:46That makes sense to celebrate, you know?
00:43:48Yeah.
00:43:49Not drinking at all, that's too extreme.
00:43:52Okay?
00:43:53Yeah.
00:43:54Once in a while, once in a while.
00:44:02And how much did I drink yesterday?
00:44:04I drank a lot.
00:44:06During the show, after the show.
00:44:08Okay?
00:44:09That's fine.
00:44:10Once in a while.
00:44:11Okay?
00:44:12Cheers.
00:44:13No, let me go to that.
00:44:14Okay?
00:44:15Okay.
00:44:16Okay.
00:44:17Okay.
00:44:18No, let me go to best.
00:44:48Okay, so let me get some water.
00:45:18Okay, and let me copy down the remainder matrix.
00:45:48One, four, five, two, three, six.
00:46:18Two, one, three, four, six, five, three, five, one, six, two, four, four, two, six, one, five, three.
00:46:48Five, six, four, three, one, two, six, three, two, five, four, one.
00:47:06So the last row here, that's the Bezu coefficient for number seven, okay?
00:47:14So just looking at this number, six, three, two, five, four, one, it looks like a random sequence of numbers, okay?
00:47:22And, but, see, I tried to find some pattern, but I couldn't.
00:47:29But if we generalize that concept of the remainder using raw operator, then we can see the pattern, okay?
00:47:41And you can generalize things in mathematics in so many different, many ways, okay?
00:47:48So I had to find the kind of generalization where the pattern is clearly visible.
00:47:57So, that's why it took me such a long time, okay?
00:48:02Yeah.
00:48:06Yeah.
00:48:10Okay.
00:48:19So the formula, okay.
00:48:22So, first column, okay?
00:48:42Actually, I feel like drinking.
00:48:44I feel like, I don't feel like drinking, okay?
00:48:46But is it okay to drink?
00:48:49No.
00:48:50I drank yesterday, okay?
00:48:51So next time, when will I drink next time?
00:48:54Maybe on my birthday.
00:48:56My birthday is coming in June, okay?
00:48:58So, sure.
00:49:00Yeah.
00:49:02Because if I drink every day, then it will hurt my toes again, and I don't want that, okay?
00:49:12Okay.
00:49:12Okay.
00:49:16So, first column, is this, okay?
00:49:30E is element of this matrix, okay?
00:49:33E, column number one, and I, I throw.
00:49:45So, column number one, and I throw.
00:49:50Is it good too?
00:50:02I, right?
00:50:06Yeah.
00:50:06In first column, yeah, the element in this matrix is same as the row index.
00:50:18Easy enough, right?
00:50:19Yeah.
00:50:24Later on, we'll come up with different formula for this because, you know, to fit into the general schema of things, okay?
00:50:31Yeah.
00:50:31Now, second column, that is more tricky, okay?
00:50:40So, second column is like this, okay?
00:50:53For second column.
00:50:54So, second column, that's row index, we have one, two, three, and then four, five, six.
00:51:14Okay?
00:51:24Okay.
00:51:24And...
00:51:24If you calculate...
00:51:44I
00:51:49Row 2
00:51:52Okay, I is the row index, okay?
00:51:591 row 2, 1
00:52:012 row 2
00:52:030
00:52:043 row 2, 1
00:52:074 row 2, 0, 5 row 2, 1
00:52:106 row 2, 0, okay?
00:52:14So
00:52:16So
00:52:18Based on this
00:52:22Okay
00:52:26Based on this information
00:52:28If you want to
00:52:30Come up with formula
00:52:32Element
00:52:34Second column
00:52:36I throw
00:52:38If you want to
00:52:40Come up with formula
00:52:42Element
00:52:44Second column
00:52:46I throw
00:52:48If you want to, okay?
00:52:50Come up with formula
00:52:52Yeah, design a function based on this
00:52:54Design a function based on this
00:52:56Okay
00:52:58Yeah
00:53:00Yeah, 5 minutes break, okay?
00:53:02Thank you
00:53:03This is fun
00:53:04This is very, very
00:53:06Entertaining
00:53:08Enjoyable
00:53:09Oh, this is fun
00:53:11Yeah
00:53:12Fun stuff
00:53:14Okay
00:53:165 minutes
00:53:185 minutes
00:53:19Thank you
00:53:205 minutes
00:53:21Thank you
00:53:22Yep
00:53:23Let's ventilate the room
00:53:26Let's ventilate the room
00:53:56Thank you
00:53:58You
00:53:59Thank you
00:54:00I
00:54:02I
00:54:03I
00:54:04I
00:54:06I
00:54:07I
00:54:08I
00:54:10I
00:54:11I
00:54:12I
00:54:13I
00:54:14I
00:54:15I
00:54:16I
00:54:17I
00:54:18I
00:54:19I
00:54:20I
00:54:21I
00:56:53All right.
00:57:05Let's see.
00:57:41This first set, one, two, three, first, it's a row divided by two, right?
00:57:48Yeah.
00:57:49Okay.
00:57:51Okay.
00:57:52Okay.
00:57:53Okay.
00:57:54Okay.
00:57:55Okay.
00:57:56Okay.
00:57:57Okay.
00:57:58And again, we have some hidden row here, seven.
00:58:00Okay, and again we have some hidden row here, seven, okay?
00:58:11Seven blank blank, okay, so.
00:58:19Then, how about four, five, six, how do we calculate that?
00:58:30So, yes, circling back, okay, just like a permutation group, okay?
00:58:45That was the good inspiration from group theory that I talked about, okay?
00:58:50So, imagine the row index, extension of row index, okay?
00:58:59So, one, two, three, four, five, six, seven, and then eight, nine, ten, eleven, twelve.
00:59:12That extended row index concept, in that case, four is eight divided by two, five is ten divided by two, six, twelve divided by two, okay?
00:59:30Okay? Yeah.
00:59:36Okay.
00:59:40How about one, two, three?
00:59:43Yeah, one plus zero.
00:59:48And zero is equal to?
00:59:50Zero times seven.
00:59:54Two?
00:59:55Yeah.
00:59:58Two plus zero.
00:59:59Two plus zero times seven, okay?
01:00:01And three?
01:00:02Three plus zero.
01:00:03Three plus zero times seven, okay?
01:00:06And then, it's like this.
01:00:31was in bracket, okay? If I was where it is like if then else that one program
01:00:41language, okay? So if I roll 2, roll index divided by 2
01:01:01what's the remainder, okay? If that reminder is 0, then
01:01:15you multiply
01:01:19row index i plus
01:01:357 times 0 divided by 2, okay?
01:01:43plus
01:01:45if
01:01:47i
01:01:49row 2
01:01:51is equal to 1
01:01:55times
01:01:59i
01:02:01plus
01:02:037 times
01:02:051
01:02:07divided by 2
01:02:13Okay?
01:02:15That's it.
01:02:23Cheers, yeah.
01:02:25For example, when i is 3, this one is 0 because it's false, okay? Yeah. So this one is 1 because it's true, okay? Okay? 3
01:02:49root 2
01:02:511, okay? Yeah.
01:02:53Now then 3 plus
01:02:557
01:02:57which is 10 divided by 2, which is 5.
01:03:01Okay? Yeah.
01:03:05So that's how it works. Now time check.
01:03:09we have less than 1 hour left, okay? So
01:03:21more than 30 minutes, okay?
01:03:25Okay, good. All right?
01:03:27Now, let's go to column number 3.
01:03:52Column number 3.
01:03:553
01:03:57Let's go to column number 3.
01:03:59Okay?
01:04:00Okay?
01:04:01Column number 3, okay?
01:04:03We
01:04:08group them, okay?
01:04:13We have 1 and 2.
01:04:153 and 6.
01:04:16Okay?
01:04:17Column number 3, okay?
01:04:19We group them, okay?
01:04:20We have 1 and 2.
01:04:223 and 6, okay?
01:04:24Three and six, okay.
01:04:29One,
01:04:32two,
01:04:36and three, four.
01:04:40Four.
01:04:53Then five and six.
01:05:02Okay.
01:05:03Now, this time, if we calculate i, rho, three.
01:05:20Rho index, rho three, okay.
01:05:22When rho index is divided by three, what's the remainder, okay.
01:05:27We have one,
01:05:29two,
01:05:33one, two, zero, one, two, zero.
01:05:46Okay.
01:05:52Now, based on this information,
01:05:54just like this.
01:05:59If you want to design function for third row,
01:06:06as a function of i,
01:06:08rho index, okay.
01:06:10If you want to.
01:06:13Okay.
01:06:14Yeah.
01:06:15Now, let's take five minutes break, okay.
01:06:20It will be similar to this, okay.
01:06:22Yeah.
01:06:22Nice.
01:06:24Yeah.
01:06:25Five minutes break.
01:06:38Yep.
01:06:54Bye.
01:06:55Bye.
01:06:55Bye.
01:07:15Bye.
01:07:16Bye.
01:07:17Bye.
01:07:17Bye.
01:07:18Bye.
01:07:18Bye.
01:10:04Okay, let's continue, okay, cheers, okay, so, all right,
01:10:34uh, similar, okay, so, yeah, 3 is equal to 7 plus 2, which is 9, divided by 3, okay, 4, 4 is equal
01:11:00to, uh, 7 plus 5, which is 12, divided by 3, okay, now, 5 is equal to 14 plus 1, and, and,
01:11:12uh, yeah, sure, uh, 14 plus 1, divided by 3, 6, yeah, 14 plus 4, 18, divided by 3, okay, yeah,
01:11:22so that's how it goes, now let me go to the rest room, look, uh,
01:11:30you
01:11:32you
01:11:34you
01:11:35you
01:11:37you
01:13:39So, all right, let's do this.
01:13:43All right.
01:13:44Okay, when I rho 3 is equal to 0, I times I plus 7 times 0 divided by 3.
01:14:12Okay, plus if I rho 3 is equal to 1, the second set, I plus 7 times 1 divided by 3.
01:14:32Okay, plus if I rho 3 is equal to 2 times I plus 7 times 2 divided by 3.
01:14:48Okay, so as you can see, as we can see, there's definitely pattern here.
01:14:56And to fit this pattern, we can express first column over there.
01:15:14If I rho 1 is equal to 0, if I rho 1 is equal to 0, which is always true.
01:15:29So, this I version bracket is always 1, I times, times I plus 7 times 0 divided by 1.
01:15:43Okay, yeah.
01:15:44Okay, so we are halfway done.
01:15:52Okay, we did column 1, column 2, column 3.
01:15:55Okay.
01:15:56Okay, tonight, we'll continue on this.
01:16:00We'll do column 4, 5, 6.
01:16:02And if you want to do it on your own, go for it.
01:16:04Okay?
01:16:05Yeah, cheers.
01:16:05Now, let's take 5 minutes break, and then we'll do one more segment, and then we'll wrap it up for this episode, okay?
01:16:17Because I gotta eat my bread first.
01:16:19Okay.
01:16:20Okay.
01:16:21Bye, Ms. Blake.
01:16:24Very nice.
01:16:27Yep.
01:16:33Hey.
01:16:33Hey.
01:16:36Hey.
01:16:36Hey.
01:16:37Hey.
01:16:37Hey.
01:17:03Hey.
01:17:21What's up?
01:17:22Hey.
01:17:22Hey.
01:17:26Hey.
01:17:27Hey.
01:17:30Hey.
01:17:30Hey.
01:17:31Hey.
01:19:04Okay, my breakfast is about ready.
01:19:07Let's put this behind us.
01:19:11Yeah, I'll go about something else.
01:19:17So what movie am I going to watch eating breakfast?
01:19:20I'm thinking about Korean movie, Korean YouTube, like The Card.
01:19:30It's about labor union in Korea.
01:19:38I read the plot summary in Wikipedia.
01:19:41So, yeah.
01:19:44So, that's what I'm thinking.
01:19:51That's what I'm thinking, okay?
01:19:52I may watch something else, but...
01:19:56Uh-huh.
01:20:01Yeah.
01:20:04But the Korean movie I watched last night was slow video.
01:20:14That was nice.
01:20:16Yeah.
01:20:17Good comedy.
01:20:18Good comedy.
01:20:19Romantic comedy.
01:20:20It was nice.
01:20:21Yeah.
01:20:22Great storytelling.
01:20:32How impressive.
01:20:34Yeah.
01:20:35Yeah.
01:20:36Yeah.
01:20:37Yeah.
01:20:38Okay.
01:20:39That's pretty much what I have to say.
01:20:53Okay.
01:20:54So, and...
01:20:55Yeah.
01:20:56So, in my bedroom, I read some history in Wikipedia, like basic biography of some entertainment business.
01:21:11Right?
01:21:12Yeah.
01:21:13Interesting.
01:21:14Yeah.
01:21:21Yeah.
01:21:22Okay.
01:21:27Okay.
01:21:28See you tonight.
01:21:30Okay?
01:21:32Happy Wednesday.
01:21:33Yeah.
01:21:35My proud future leaders.
01:21:36Yeah.
01:21:37Marshall, education, current development.
01:21:38Be ambitious.
01:21:39Okay.
01:21:41Yeah.
01:21:42Mm-hmm.