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Huhnkie Lee
  • 5/8/2025
coprime pair generation algorithm
Transcript
00:00:00Hello friends, welcome to Human RG 2233. Happy Thursday.
00:00:08Yeah, so let's see.
00:00:14There's this like kind of Italian French car brand Bugatti, right? This very luxurious famous
00:00:26international brand. So I looked up, well actually when I was watching some like
00:00:33either documentary or movie in, I think it was in Dailymotion,
00:00:40they have this subtitle in Croatian language, okay? So
00:00:48the word Bugatti came up in Croatian language, okay? So
00:00:52so I looked up in the internet, okay, what does Bugatti mean?
00:00:58And many web pages in the internet means like, oh, it's an Italian family name,
00:01:03it does not mean anything other than just family name, but there's many people in the internet
00:01:10said and they are wrong. Not so, okay? So Bugatti in Croatia means wealthy, okay?
00:01:17So I guess Bugatti family, maybe they're Croatian immigrants to Italy back in the days and
00:01:23maybe not just Croatia because Croatian language is also related to other Slavic languages.
00:01:31Slavic means like Eastern Europe, okay? Yeah, like Bosnian language, Croatian language,
00:01:37like Serbian language, there are a lot of common words there, okay? So
00:01:41so Bugatti means like wealthy, rich, wealthy in Croatian language and I'm sure it means the
00:01:49similar things in many different related languages, okay? All right. But yeah, it's
00:01:57so yeah, some Italian family Bugatti maybe migrated from northern parts of the
00:02:02so Baikan Peninsula somewhere, okay? Like Croatia somewhere around there, okay? Yeah.
00:02:16Yeah, so learning foreign language is so fun. We learn about history, their culture, customs,
00:02:21nice. Okay. Yeah. Okay, let's do some
00:02:26stretching. Sure. Yeah.
00:02:56Bye.
00:03:26Let me turn off that heat over there.
00:03:56I woke up in the morning, I just stayed in my bed, and I thought about some more mathematics
00:04:23like co-primes.
00:04:24Yeah.
00:04:25So I'll share the results with you.
00:04:26Yeah, I found something.
00:04:28Okay.
00:04:29Yeah.
00:04:30I'll share that with you.
00:04:31On my bed, I have notebooks.
00:04:34One notebook and one mechanical pencil.
00:04:37It has a test.
00:04:38On my bed, I have a small plastic trash can and bottle of water, cell phone, cell phone
00:04:51charger.
00:04:52Probably everything I need.
00:04:53Okay.
00:04:54Yeah.
00:04:55On my bed.
00:04:56Okay.
00:04:57As well as the electric heated blanket and other blankets and pillows, scarf, hat.
00:05:10On my bed.
00:05:12On my bed.
00:05:13Okay.
00:05:14Yeah.
00:05:15I have everything there.
00:05:16To keep myself warm and informed.
00:05:19on my bed.
00:05:20Yeah.
00:05:21My bedside is the inside.
00:05:22Okay.
00:05:23Yeah.
00:05:54Okay, now let's do a one leg squat and then we'll continue with the stretch, okay?
00:06:08One leg squat, right leg is easier than left leg.
00:06:24Okay, let's do a continue stretching and then we'll do one leg squat later again.
00:06:37Yeah, muscle and balancing, nice joints.
00:06:41Okay.
00:06:43Okay.
00:06:44Okay.
00:06:45Okay.
00:06:47Okay.
00:06:49Okay.
00:07:21Okay.
00:07:51Yeah, it's like acting, right?
00:07:54Kind of like occult, religion, leader.
00:07:59Okay.
00:08:03And...
00:08:05First of all, slides.
00:08:15All right.
00:08:17All right.
00:08:23All right.
00:08:35Okay.
00:09:05Yeah, yeah, thank you next on exercise very important
00:09:35Okay
00:10:05Now, back to one leg squat, just right leg, which is easier for me, left leg, okay, yeah
00:10:28That is all the way down, maybe in the future, okay, yeah, but good, yeah, five minutes, thank you. Good exercise there.
00:15:51Okay.
00:15:52Welcome to...
00:15:55Cumenology episode...
00:15:59Ah...
00:16:00Two, two...
00:16:02Three, three?
00:16:03Okay.
00:16:05We'll do mathematics a little bit later, okay?
00:16:07Yeah...
00:16:11Let me get some more water...
00:16:33Hey...
00:16:35Yes, so I looked at some housing in Anchorage because
00:16:54Okay, one possible scenario is this, okay, so I get a job in a lawyer job in Anchorage
00:17:02and then I might buy secondary housing but not house because I already have house here
00:17:13apartment, well apartment for sale is called condominium, okay, so yeah, you know
00:17:21apartment building apartment unit for sale is called condominium, okay, and that's more affordable
00:17:29than house, okay, yeah, and also it's like it's a unit and so I don't have to like manage it,
00:17:36you know, it's like apartment unit for sale is called condominium, so yeah, it's more
00:17:43easier to manage and
00:17:47yeah
00:17:48and it's quite affordable price range about one hundred thousand dollars more or less, okay,
00:17:57yeah, like one bedroom, one bath, apartment, condominium, okay, yeah,
00:18:04yeah, so that's one possibility, okay, so I moved some
00:18:08furnitures, clothings from this house to that condominium in Anchorage, okay, and stay there
00:18:16during the week, weekdays, and then spend the weekends here, okay, yeah, that's doable, okay,
00:18:24that's one possibility, okay, yeah, like zillow.com, realtor.com, those are good websites to
00:18:32put some criteria, you know, yeah,
00:18:34you know, trailer park, yeah, the so-called mobile homes, but they're not exactly mobile, okay,
00:18:44but yeah, they're even more affordable, like fifty thousand dollars, seventy thousand dollars,
00:18:49it's actually a house unit, but trailer park tend to be in a sketch neighborhood, okay, and I cannot
00:18:57take the risk of break-ins, squatters, because, uh,
00:19:05Anchorage, okay, uh, uh, some, there are some sketch neighborhood where there are some
00:19:11crimes, okay, and I cannot take the risk, okay, because, uh, that housing unit in Anchorage,
00:19:18it will be half the time empty, okay, so it has to be safe.
00:19:22So it's like an apartment building with many units, so just one unit, condominium,
00:19:30they'll be a lot safer, and, uh, easier to manage, because I don't,
00:19:35houses in Anchorage, Anchorage is big city, so houses, there's some homeowner association,
00:19:42codes, you have to mow your lawn, I'm not going to do that, okay, so,
00:19:48I have house here in Wassila, so, in Anchorage, it'll be condominium,
00:19:53apartment unit, okay, yeah, so that I don't have to mow the lawn and everything,
00:20:00I don't have to, like, clear the snow, no, none of that, okay, yeah,
00:20:07yeah, so that's that, good, yeah,
00:20:13okay,
00:20:13okay, now mathematics, okay,
00:20:30some more expansion from co-prime audition theorem,
00:20:36now we look at the flip side, non-co-prime audition and subtraction theorem, okay,
00:20:49yeah,
00:20:52now that we have small room here,
00:20:57okay,
00:20:57okay,
00:21:06okay, now,
00:21:12if a and b are non-co-primes,
00:21:17assume a is bigger than b, okay, like, seven and five, okay, so a and b are non-co-primes, then a,
00:21:37and a plus minus b,
00:21:40they're also non-co-primes, okay, proof,
00:21:43yeah,
00:21:51a and b are non-co-primes, so a and b have co-factors, multiplicative factors, okay,
00:21:58let's say alpha, x, b,
00:22:04alpha, y,
00:22:05alpha, x plus minus y, okay,
00:22:33so a and b co-factors, alpha,
00:22:42a plus minus b, it also has co-factor, alpha, okay,
00:22:49yeah,
00:22:49and also, that's, that means a and a plus minus b, they're non-co-primes, also b,
00:23:00and a and a plus minus b, okay,
00:23:11they're also non-co-primes, okay,
00:23:14because if your common factor alpha,
00:23:16and then you can see alpha, okay, nice, very good,
00:23:23yeah, so that's that, okay, easy proof, yeah,
00:23:34this sounds very powerful, okay,
00:23:36okay, now let's say five is rare, okay,
00:23:41all right,
00:23:45no, okay,
00:23:51yeah,
00:23:59yeah, this is what we just did, okay, yeah,
00:24:00non-co-prime audition subtraction theorem,
00:24:06that kind of corollary, like,
00:24:10from the co-prime audition subtraction theorem, okay, yeah,
00:24:14all right, fine, thank you.
00:24:30Perfect question.
00:24:41All right.
00:24:43Hi.
00:24:44Hi,
00:28:44Okay, I'm starting to cook my breakfast like tilapia fish, two pieces of chicken breast
00:29:04and canned kidney beans.
00:32:21Okay, now let's get back to the generative algorithm for co-prime pairs.
00:32:39Okay, I just realized that black pen happened to be magnetic, so we don't need pen holder.
00:32:51All right.
00:33:02Nice.
00:33:07Okay.
00:33:10Let's do mathematics.
00:33:12Oh, yeah.
00:33:23Who does mathematics when he or she is unemployed?
00:33:28Well, me, yeah, between jobs, sure, yeah.
00:33:38I mean, employed or unemployed, it doesn't make too much difference to me.
00:33:45Okay, I'd still do mathematics, study foreign languages, study history.
00:33:50Yeah.
00:33:52Okay, yeah.
00:33:54Okay, so we have that.
00:33:58Uh, let's look at number 12.
00:34:13Okay.
00:34:13Yeah, it's a nice composite number there.
00:34:37So, number 12, okay?
00:34:42Now, uh, 12 factorization, 4 times 3, okay?
00:34:51Uh, 2 to the second times 3, okay?
00:34:54Yeah.
00:34:55Yeah.
00:34:57So, then, um, prime factor set of 12.
00:35:07Uh, 2 and 3, okay, yeah, 1 is technically a prime number, but we will not do that, because it's everywhere, okay?
00:35:25So, yeah.
00:35:26Uh, yeah.
00:35:28So, when it comes to prime factor of some number, okay?
00:35:43You know what?
00:35:45Let me just include 1.
00:35:47Couple on this, okay?
00:35:50What is prime number, okay?
00:35:56Uh,
00:35:57Prime factor
00:35:58With exception of 1, okay?
00:36:07Uh,
00:36:07What is the exception of number?
00:36:12With exception of 2 as well.
00:36:18Well,
00:36:18Actually,
00:36:20With exception of prime numbers, okay?
00:36:24Okay, let's take a look at 7.
00:36:29Prime factor of 7.
00:36:341 and 7, right?
00:36:37Okay.
00:36:41But, when it comes to composite numbers,
00:36:45Like 12, okay?
00:36:46Uh,
00:36:47But, all the prime factors are less than half of that number.
00:36:51Very composite numbers, okay?
00:36:53Yeah.
00:37:02Okay?
00:37:02Like 47.
00:37:08Like 47.
00:37:08I mean, 49.
00:37:107 times 7.
00:37:1149, okay?
00:37:12So,
00:37:12All the prime factors are 49.
00:37:14Yeah, 1 and 7.
00:37:17Okay?
00:37:17Yeah.
00:37:18Uh,
00:37:18When it comes to composite numbers,
00:37:20All the prime factors,
00:37:21Uh,
00:37:21They are strictly less than one half of that number.
00:37:25Okay?
00:37:25Yeah.
00:37:25Well,
00:37:30Actually,
00:37:33Prime factor of 4,
00:37:371 and 2,
00:37:38Okay?
00:37:38So,
00:37:39Yeah,
00:37:39Less or equal to
00:37:42Half of that number.
00:37:43Okay?
00:37:44Very composite numbers.
00:37:46Okay?
00:37:47All right.
00:37:52Hoo-yah!
00:37:53Still number 12,
00:38:06Okay?
00:38:06Yeah,
00:38:07Let's look at number 12.
00:38:18We're gonna have some serious fun here,
00:38:19Okay?
00:38:23Okay?
00:38:34Okay?
00:38:34Now,
00:38:39We'll look at,
00:38:43Copeland pairs and non-copeland pairs.
00:38:48and symmetry, they are both symmetry distribution, okay?
00:38:52So...
00:39:00Let's put some colors.
00:39:02I'm putting this upside down because ink has
00:39:06weight, so that ink would come down
00:39:10to the tip
00:39:12of the pen, so that it doesn't
00:39:14get too light in color, okay?
00:39:16So, yeah.
00:39:18Gravitation, okay?
00:39:28Uh...
00:39:30Co-prime pairs?
00:39:38We mark it red.
00:39:441 and 11.
00:39:471 is co-prime with 12.
00:39:5011 is co-prime with 12.
00:39:52And 1 and 11, they are co-prime to each other as well.
00:39:56That's like a co-prime subtraction theorem.
00:40:00Okay? Yeah.
00:40:02If 12 and 1 is co-prime to each other,
00:40:06so it's 12 and 12 minus 1,
00:40:10which is 11.
00:40:12They are co-primes, okay?
00:40:14And also, uh...
00:40:16Okay.
00:40:18A and B are co-primes, that means...
00:40:28where A is larger than B, okay?
00:40:30Then A and B minus A, they are co-primes.
00:40:32Then A and B minus A, they are co-primes.
00:40:42Also, B and B minus A, they are also co-primes as well.
00:40:46And let's prove that real quick, okay?
00:41:02Let's assume they are non-co-primes.
00:41:06Let's assume they are non-co-primes.
00:41:08We'll prove by contradiction, which is proof of contra positive, okay?
00:41:12If they are non-co-primes, then B is equal to alpha x.
00:41:17If they are non-co-primes, okay?
00:41:19If they are non-co-primes, okay?
00:41:21B minus A is alpha y.
00:41:25And then, um...
00:41:27Subtract.
00:41:29A is equal to alpha x minus y.
00:41:35That means B and A, they are co-factor of alpha,
00:41:40so they are non-co-primes, okay?
00:41:43Contradiction.
00:41:45Okay, so Q, E, D.
00:41:49There's contradiction.
00:41:55Q, E, D, okay?
00:41:57So this contradiction is true.
00:41:59If not, we put X in there.
00:42:01But because it's true, we put circle in there.
00:42:04Okay?
00:42:05That's okay.
00:42:09Let's take five minutes break, okay?
00:42:11Vocal rest.
00:42:15Okay?
00:42:16Yeah, feel free to mark co-prime pairs and non-co-prime pairs, okay?
00:42:23Yeah.
00:42:24Five minutes break.
00:42:34What we have here?
00:42:39If 12 and 1 are non-co-primes...
00:42:41If 12 and 1 are primes, then 12 and...
00:42:4412 minus 1, they are also co-primes, okay?
00:42:4715 to 11, okay?
00:42:4815 to 11, okay?
00:42:49In addition to that,
00:42:521 and 11 themselves, they are co-primes as well.
00:42:55Okay?
00:42:56That's what we proved here.
00:42:57Okay?
00:42:59Yeah.
00:43:00All right.
00:43:01Five minutes break.
00:43:03Let me check on my breakfast.
00:43:04Sorry.
00:43:05Let me check on my breath.
00:43:06First,
00:43:11Oh,
00:43:12it takes a while,
00:43:13Let me check on.
00:43:14My breakfast.
00:43:15What's your...
00:43:16Okay.
00:43:17Let me check on my breakfast.
00:43:19Oh,
00:43:21Well,
00:43:23so...
00:43:24Yo.
00:43:25I don't know.
00:43:26You're...
00:43:27Well,
00:43:28I mean,
00:43:29beyond...
00:43:30ah,
00:43:31.
00:44:01.
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00:49:08Good sound effect, camera work, good music, background music, ah, nice.
00:49:15I mean, of course, some episodes not as good as others.
00:49:21I guess they want to give some chance to lesser known writers, I guess.
00:49:27But mostly, good stories, good productions, cheers.
00:49:38Okay, so we have that.
00:49:45To summarize, if a and b are co-primes, that means there are a lot of co-primes, okay?
00:50:01So a and a plus minus b, they are co-primes, and b and a plus minus b, they are also co-primes,
00:50:15okay, but so we have a, b, a plus b, a minus b, right?
00:50:30So let's draw a diagram, okay, you have a, b, a plus b, a minus b, and co-prime to each
00:50:46other, co-prime to each other, okay, co-prime to each other, and diagonal, okay?
00:51:00a and a minus b, and, okay, b and a plus b, they are co-primes, but here a plus b and
00:51:22a minus b, they are not always co-primes, okay?
00:51:24So like, uh, counter-example, counter-example, doing my cyber-apparel, okay, so, uh, three and
00:51:52seven, okay, yeah, counter-example, seven and three, they are co-primes, seven and three,
00:52:05but seven plus three, ten, seven minus three, four, ten and four, they are not co-primes,
00:52:11common factor of two, okay, so, yeah, okay, but otherwise, they are co-primes, except a plus b and a minus b,
00:52:30they are not always co-primes, okay, yeah, cheers, this is a nice diagram,
00:52:37okay, nice, beautiful,
00:52:48let's continue the symmetric co-prime pairing, one and eleven,
00:52:59ten, now, no, non co-prime pairing, 10.
00:53:12Yeah, this blue is too thick, it almost looks like black.
00:53:33It's a little bit lighter, okay.
00:53:35So 2 and 10, they're non-coprime pairs.
00:53:39So pairing, yeah, A plus B equal to 12, additive complements, okay.
00:53:46Binary partition, okay.
00:53:47So additive binary partition, okay.
00:53:533 and 9, non-coprime pairs, that's symmetric.
00:53:594 and 8, non-coprime pairs.
00:54:095 and 7, coprime pairs.
00:54:16Finally, 6 and 6, non-coprime pairs, okay.
00:54:31How about numbers beyond that, it's exactly the same, okay.
00:54:46It's periodic, same cycle, okay.
00:54:49Like row algebra, some number row 12, okay, yeah.
00:54:56So 2 and 10, they're non-coprime pairs to each other.
00:55:03Okay.
00:55:05So 2 and 10, they're non-coprime pairs to each other.
00:55:123 and 9, non-coprime pairs to each other.
00:55:194 and 8, non-coprime pairs to each other.
00:55:216 and 6, non-coprime pairs to each other.
00:55:221 and 11, coprime pairs to each other.
00:55:235 and 7, coprime pairs to each other.
00:55:24Okay, yeah.
00:55:25And we already proved that, okay.
00:55:26So, and the pattern is exact same.
00:55:4213, that's like a row 12 family.
00:55:48The number when divided by 12 remains as 1, okay.
00:55:56So, it's, it came from the coprime, I mean, coprime for each other theorem.
00:56:01Okay, yeah.
00:56:02Okay.
00:56:03So, we have 13 and 23 non-coprime pairs.
00:56:17Yeah.
00:56:22And then 17 and 19, okay.
00:56:38Yeah.
00:56:39Then, those are coprime pairs, okay.
00:56:41Now, non-coprime pairs.
00:56:4514 and 12.
00:56:5614 and 22.
00:57:04This is too loud.
00:57:0815 and 21.
00:57:2016 and 20.
00:57:2318 and 18.
00:57:2818 and 22.
00:57:40Okay.
00:57:41Yeah.
00:57:42But the difference is this.
00:57:43Here, when we add those symmetric pairs, they add up to 12.
00:57:48Here, we add those symmetric pairs, they add up to 36.
00:57:53Okay.
00:57:58Why?
00:58:01It's because we're adding 12, 12, and then on top of that 12.
00:58:12That's why.
00:58:13Okay.
00:58:14Yeah.
00:58:15There's a lot going on here.
00:58:27Yeah.
00:58:28Yeah.
00:58:29Yeah.
00:58:30No more theory.
00:58:31Cheers.
00:58:32Yep.
00:58:52Mm-hmm.
00:59:02One thing interesting is this.
00:59:23We're talking about the symmetric binary auditive partition of some even number.
00:59:41Okay?
00:59:43R number will divide that later.
00:59:46It's always the case that it's either co-prime plus co-prime or non-coprime plus non-coprime.
01:00:11Okay?
01:00:12It never happens where it's like co-prime plus non-coprime or non-coprime plus co-prime.
01:00:22Okay?
01:00:23It never happens that way.
01:00:28Which is another consequence from co-prime audition theorem.
01:00:35Okay?
01:00:36So, we looked at even number 12.
01:00:44Now, next time, after five minutes drag, we'll look at odd number, odd composite number, say.
01:00:53Oh, no, not too big.
01:00:57Okay.
01:00:5815?
01:00:59Yeah.
01:01:00Nine is too small, right?
01:01:01We'll do 15.
01:01:02Okay?
01:01:03Okay.
01:01:04Five minutes drag.
01:01:05Time check.
01:01:06I need some vocal rest.
01:01:08This is fun.
01:01:09It's been more than one hour.
01:01:11Yeah.
01:01:12Nice.
01:01:13Time flies.
01:01:14Okay?
01:01:15That's great.
01:01:16We are having fun.
01:01:18Okay?
01:01:19Yeah.
01:01:20Cheers.
01:01:21Five minutes drag.
01:01:23Yep.
01:01:24You have been very proactive.
01:01:25Nice.
01:01:26Hmm.
01:01:36Hmm.
01:01:37Hmm.
01:01:38Hmm.
01:01:39Hmm.
01:01:40You're being very productive.
01:01:41Nice.
01:02:10You're being very productive.
01:02:40You're being very productive.
01:03:10You're being very productive.
01:03:40You're being very productive.
01:04:10Now let's do a break from mathematics.
01:04:37Yeah, so this is like exhaustive enumeration and also non-redundant enumeration listing
01:04:49of all the co-prime pairs and non-co-prime pairs.
01:04:53We're going to start from one all the way to whatever number.
01:04:57Okay, so yeah.
01:04:59Okay, good.
01:05:02This is very, very significant.
01:05:05Great discovery here.
01:05:07Okay, nice.
01:05:07Now let's take a break from mathematics.
01:05:10Okay, so actually we may continue on this like tonight.
01:05:15Okay, so let's not do too much.
01:05:18Okay, so.
01:05:19So, yeah, in between jobs, I have applied to how many jobs have I?
01:05:29So like 12.
01:05:31Okay, so.
01:05:31Some in-house big corporations, in-house counsel jobs, government attorney jobs, and law firm jobs.
01:05:42Okay?
01:05:42Yeah.
01:05:43Okay.
01:05:43Cheers.
01:05:44Cheers.
01:05:48Teaching position jobs, law professor jobs.
01:05:50Okay?
01:05:50Yeah.
01:05:51So, in-house, government, law firm, and then university.
01:05:56Four categories.
01:05:58Nice.
01:05:59That's good coverage.
01:06:01Yeah.
01:06:03But law professor job is very nice and easygoing.
01:06:08Okay, and you get the summer semester off, and okay, so nice and relaxing.
01:06:16So, if I get low professor job, I mean, I'm not making that much money, but it'll be easygoing.
01:06:23So, I will not need secondary home in Anchorage.
01:06:26I'll just commute, okay?
01:06:28But governmental job is kind of in between when it comes to salary level, also workload.
01:06:38But law firm job and corporate counsel job, they'll be more high-end.
01:06:43It'll be a lot more money, and also a lot more workload.
01:06:50And then, in that case, I will need second home in Anchorage.
01:06:54Okay?
01:06:54So, yeah.
01:06:55So, I'm okay anyways.
01:06:58Okay.
01:07:01Yeah.
01:07:05In all different scenarios, we got game plan.
01:07:07Okay, so.
01:07:09Cheers.
01:07:16Yeah.
01:07:26Less to 15.
01:07:27Okay, let's work it out.
01:07:31Okay.
01:07:37Okay.
01:07:38Let's go.
01:07:40Okay.
01:07:53Let's go on.
01:07:54Okay.
01:07:55Bye.
01:07:56Bye.
01:07:56Bye.
01:07:58Hello.
01:07:58We have aerte hooder.
01:08:00We just have two more schedules from now.
01:08:02Okay.
01:08:02Sha star.
01:08:03Let's go ahead.
01:08:03Well, uh, we just have one.
01:08:04Okay?
01:08:04Oh, okay.
01:08:05Well, okay.
01:08:05Okay.
01:08:36Oh, yeah.
01:08:38No tunnels test, you know.
01:09:05Okay.
01:09:06Cheers.
01:09:18Uh, four prime pairs of 15, okay?
01:09:241 and 14.
01:09:36And, uh, no one called prime pairs.
01:09:453 and 12.
01:10:06Okay.
01:10:19Yeah.
01:10:24The other side is the exact same, okay?
01:10:31Uh, 6, 10 and 10 and 9.
01:10:47Yeah, adding to what?
01:10:4945, right?
01:10:50Yeah.
01:11:018 and 10 and 7.
01:11:068 and 10 and 7.
01:11:259 and 10 and 7.
01:11:30Okay, yeah, okay
01:11:37And I think it was yesterday we proved that actually this theorem co-prime auditions
01:12:02Subterranean theorem is bidirectional, okay, and that's why when they are non-co-primes then these are non-co-primes
01:12:09Okay, so, okay, yeah, the inverse
01:12:15Negation and all that stuff is fault of the logic, okay, so
01:12:19Yeah, and that's why if one is co-prime and the other has to be co-prime and one is non-co-prime, the other has to be non-co-prime, okay
01:12:27Yeah, no mixture between co-prime and non-co-prime, okay, that never happens, okay
01:12:31Yes, it's the implication the result consequence of co-prime non-co-prime audition subterranean theorem, okay
01:12:41Yeah, so it's proven, okay, yeah, nice
01:12:45I think we did enough mathematics for today, okay
01:12:48My breakfast is ready and then I'm hungry and
01:13:01Okay, let's take five minutes break and we'll talk about something else other than mathematics, okay
01:13:06Yeah, all right
01:13:10Very cool
01:13:18Okay
01:13:26Just some ventilation
01:13:27Okay
01:13:30All right
01:13:32Just some ventilation
01:13:34Okay
01:13:35Just some ventilation
01:13:36Okay
01:13:38Just some ventilation
01:13:40Okay
01:13:44.
01:14:14.
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01:17:24.
01:17:26.
01:17:28We have prime number and another prime number, they're always co-primes, okay?
01:17:42And prime number and non-prime number, which is composite number, okay?
01:17:49Also, non-coprime number, composite number, and another composite number, like 7 and, here
01:18:08let's say 7 and 5, okay, they're always co-primes, okay, two different prime numbers, okay?
01:18:16And prime number 7 and non-prime number 14, they are non-coprimes, okay?
01:18:31Not always co-primes, okay, so non-coprimes.
01:18:37Two composite numbers, let's say 14 and 21.
01:18:46They're non-coprimes, okay?
01:18:53Okay, yeah, some relationship between four-primes and primes, okay, why?
01:19:06Because we want to...
01:19:07Our later goal is that we want to think about the distribution of prime numbers based on distribution
01:19:19of co-prime numbers, co-prime pairs, okay?
01:19:24Why?
01:19:25Because there's the holy grail of number theory.
01:19:29Distribution of prime numbers, yeah, there's some knowns, but also there are a lot of unknowns
01:19:36there.
01:19:37Okay?
01:19:38You can imagine maybe we can come up with some kind of differential equation, something like
01:19:43that, okay?
01:19:44About prime numbers, okay?
01:19:45About prime numbers, okay?
01:19:46So, that'd be cool.
01:19:47Yeah, cheers.
01:19:48Okay?
01:19:49But that's for later, okay?
01:19:50So, now let's put this behind us.
01:19:51We'll continue this later.
01:19:52Maybe tonight.
01:19:53Some other time.
01:19:54I don't know.
01:19:55Okay?
01:19:56We did enough.
01:19:57Alright.
01:19:58Oh yeah.
01:20:00Yeah...
01:20:01Yeah.
01:20:02Whew.
01:20:03Some other time, I don't know. We did enough.
01:20:12Yeah.
01:20:17Yeah.
01:20:25Vocal rest. Let's play some guitar.
01:20:33A couple of days ago, I went to Point McKenzie, and I walked in water stride
01:21:02stridor insect. How does it float on surface of the water stridor? They need to
01:21:10study some more about that mechanism. Water stridor does not sink underneath
01:21:16water. It always floats, right? Six legs. They need to study some more of that
01:21:24mechanism, okay? Scientists. There are some unknowns, okay? So, man. Physics. Cheers.
01:21:40Okay, let's tune this.
01:21:48I downloaded some more web browsers because like Opera and DuckDuckGo are nice.
01:21:53Because I looked at multiple websites, right? So, multiple web browsers in my cell phone, okay? Nice.
01:22:01Okay.
01:22:23Okay.
01:22:29Okay.
01:22:31Okay.
01:22:33Okay.
01:22:39Okay.
01:22:41Okay.
01:22:43Okay.
01:22:45Okay.
01:22:47Okay.
01:22:49All right.
01:23:06Okay.
01:23:09Okay.
01:23:11um
01:23:29uh
01:23:41you
01:24:11good
01:24:18i'll get some more water
01:24:25you
01:24:32you
01:24:34you
01:24:36you
01:24:43you
01:24:45you
01:24:47you
01:24:54you
01:24:56you
01:24:58you
01:25:00you
01:25:01yeah
01:25:05cheers
01:25:07so in that mathematics algorithm uh basically this exhaustive and non-redundant listing of all the co-prime pairs and also all the known co-prime pairs as well
01:25:19okay
01:25:20uh
01:25:21uh
01:25:22our next step would be to compare that with a finite sequence algorithm which is totally different algorithm but
01:25:29supposedly generate also exhaustive and non-redundant co-prime pairs okay our algorithm is better in a sense that it also generates all the known co-prime pairs as well
01:25:41okay yeah okay yeah
01:25:51now
01:25:52let's play guitar
01:25:54you
01:25:56you
01:25:58you
01:26:00you
01:26:02you
01:26:04you
01:26:06you
01:26:08you
01:26:11you
01:26:18you
01:26:20you
01:26:21it's been a while
01:27:36So yesterday I finished watching the last DVD disc of the season 4 in Twilight Zone.
01:27:46Over the past month or so I watched all the episodes in season 4 of Twilight Zone TV show.
01:27:56Next I'm gonna watch all the episodes of season 3 of Twilight Zone.
01:28:01I look forward to it.
01:28:04Oh yeah.
01:28:06Really?
01:28:07Yeah.
01:28:08Yeah.
01:28:09I'll see you tonight.
01:28:10Happy Thursday.