humanology 2085 .

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Transcript
00:00:00Hello friends. Welcome to Humanology 2085.
00:00:09Let's martial arts. Let's do some defense.
00:00:31Okay.
00:00:35Okay. Five minutes break please. Thank you.
00:00:40Okay. We're like dodging like this.
00:00:45Okay. Okay. Five minutes break here.
00:00:55Okay.
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00:04:47Okay.
00:05:00Welcome to Humanology episode
00:05:102085. Yeah. Welcome.
00:05:14Let's continue the mathematics. We found something very cool yesterday.
00:05:24Okay.
00:05:29Okay.
00:05:32So, Gaussian operators. It's like you know the function. Function is one variable.
00:05:42Input, any number, real number, output, integer. Okay, so it's integer function.
00:05:48This is actually one more I can remember from high school.
00:05:55Yeah, I mean the notation may be different in textbooks.
00:06:01But yeah, but before that, let's talk about politics a little bit, okay?
00:06:07I read about this Democratic National Convention, DNC's speeches, and they've got some good reviews.
00:06:15So I checked them out by Biden and by Hillary Clinton in YouTube and prerecorded.
00:06:22And actually I liked some parts of it, even made me almost cry, okay?
00:06:28Good orators, yeah.
00:06:32Some parts, I fast forward the other part which was just too boring, okay?
00:06:36But I like some parts, like finishing parts, okay?
00:06:39Also when they make fun of Donald Trump, of course, that was fun.
00:06:45Yeah.
00:06:48Hillary Clinton, 2016, when she got nomination, the way she looked was so repulsive.
00:06:55She's just so arrogant. She was.
00:06:58But yesterday in DNC, her speaker, more humble, humble, likeable even.
00:07:08Unlike 2016 when she was absolutely arrogant, repulsive.
00:07:13Yeah, and she toned down quite a bit.
00:07:17Good.
00:07:20Good-looking lady, yeah.
00:07:24And Biden looking very strong. Yeah, that's good.
00:07:27That day with June Debate, he was tired from international trouble.
00:07:31That's what it was.
00:07:37Okay.
00:07:42Pen.
00:07:57So ceiling function is we are basically rounding off if it's fraction.
00:08:02If it's integer, leave it alone.
00:08:05Flooring function, rounding down if it's fraction to the nearest integer, okay?
00:08:13If it's integer, leave it alone, okay?
00:08:15And this third function, Gaussian unary function, integer function, okay?
00:08:23This is like either round up or round down to the nearest integer, okay?
00:08:30So 2.5, yeah, depending on the combination, right in the middle, right?
00:08:37You just round up, okay?
00:08:39So 2.5 becomes 3.
00:08:412.7 becomes 3.
00:08:433, stay the same, 3.
00:08:453.1, now round down to the nearest integer, okay?
00:08:49Becomes 3.
00:08:503.3 becomes 3.
00:08:523.5, round up, yeah.
00:08:552.4, okay?
00:08:56Yeah, that's that.
00:08:59Now fraction function is defined in Wikipedia.
00:09:02But complement function is not defined in Wikipedia, okay?
00:09:05We defined it.
00:09:06What is it?
00:09:081.7, for example.
00:09:10Yeah, flow of that, 1.
00:09:12That's the integer part.
00:09:140.7, that's the fraction part, okay?
00:09:16That's this curly x, okay?
00:09:19That's 0.7.
00:09:21Now, slash 7, that's a complement of that fraction, 0.3, okay?
00:09:28So 1 minus 0.7, 0.3, that's the slash x, or, yeah.
00:09:39This, we call it, we call it like nearest x, okay?
00:09:49Or near x, whatever.
00:09:51Okay?
00:09:53Yeah.
00:09:54Okay?
00:09:58Mm-hmm.
00:10:06And let's do it.
00:10:10Today we'll look at the distributive property of this fraction function and the complement function, okay?
00:10:17Yeah.
00:10:19Let's go to Wikipedia and let's see if they have something about distributive property, okay?
00:10:23So, I don't think they do.
00:10:28We'll see.
00:10:32I don't remember seeing it, but we'll double check.
00:10:44Yeah.
00:10:48Ugh.
00:10:52These two, yeah, there's nothing about distributive law, okay?
00:11:01How's this fraction in general?
00:11:06They have this, right?
00:11:19Mm-hmm.
00:11:28Still broken, huh?
00:11:34Mm-hmm.
00:11:38Iverson.
00:11:58Mm-hmm.
00:12:17Yep, they don't have it, okay?
00:12:19Yeah.
00:12:23Maybe some textbook has it.
00:12:29I mean, there are so many textbooks in the world, you cannot check all the textbooks, right?
00:12:35So, okay.
00:12:37It could be brand new, yeah?
00:12:45Okay, now.
00:12:48So these days, after work, I take on that, like, 10 to 15 minutes.
00:12:52Oh, that really refreshes my energy level, which is fantastic, yeah.
00:12:57Okay, good idea, right?
00:13:00Taking on that after work.
00:13:07So, let's take five minutes break, okay?
00:13:11Yeah, and I take some terms, and I start to do all of the work.
00:13:22Five minutes, thank you.
00:13:33We'll call it square brackets, okay?
00:13:35Square brackets, sure.
00:13:38Yeah, I forgot what that directly was called.
00:13:41Yeah, square brackets, sure.
00:13:43Five minutes, thank you.
00:15:39Five minutes, thank you.
00:16:03So, yesterday, Instagram Live, yeah, I used the term.
00:16:10When I was, like, cyberbullied in MassTaxStateIsland.com, I used the term devastated.
00:16:17I was devastated.
00:16:18That's an exaggeration, okay?
00:16:21Over-dramatization.
00:16:23I mean, I'm a mentally and physically strong person.
00:16:25I do exercise, martial arts, okay?
00:16:27But still, it was a very unpleasant experience, okay?
00:16:32But I forgive them, okay?
00:16:34People are people.
00:16:37We all make mistakes.
00:16:41No hard feelings, okay?
00:16:42Yeah, it's all right.
00:16:45Yeah.
00:16:49Now, what do I drink?
00:16:56Whiskey, sure.
00:16:57We can start with whiskey.
00:17:13Yeah, we have been doing very firm foundation, going back to the basics, and discovering basic stuff, which is fantastic.
00:17:23Okay.
00:17:27We don't really care about integer cases.
00:17:29We only care about fraction cases, like 1.7, okay?
00:17:33It looks like this.
00:17:34So, let's say X, Y, Z, they're all like fraction cases, okay?
00:17:42One whole number, right?
00:17:44Like 1.7, okay?
00:17:46Let's go.
00:17:47Distributive law here.
00:17:55Curl X plus Y, curl, curly bracket, okay?
00:18:02Is equal to curl X plus curl Y and curl O.
00:18:14It's kind of like lower zebra, right?
00:18:17Yeah.
00:18:21And we can formally prove this.
00:18:27Let's do it, because this will not be a difficult proof, okay?
00:18:31Based on the definitions, right?
00:18:33Yeah.
00:18:38Because nowadays, we're doing like formal proofs, okay?
00:18:43Because these are easy enough to do, formal proof, okay?
00:18:47And let's switch the whiteboard.
00:18:54We need some space here, so.
00:18:57Okay.
00:19:09Right.
00:19:12Yeah, I caught it.
00:19:15Before it fails, before it falls.
00:19:30Space right here.
00:19:41Okay.
00:19:44Cheers.
00:19:54Type as this.
00:19:57Left-hand side.
00:20:09Right-hand side.
00:20:18Paragraph zebra distribution.
00:20:25Okay.
00:20:27This is the right-hand side.
00:20:31Right?
00:20:32No.
00:20:47Cheers.
00:21:01Basically, we start with definition, okay?
00:21:13Flooring of X is equal to X minus flooring of X.
00:21:22Okay, that's what definition, okay?
00:21:28Okay.
00:21:30So.
00:21:33Left-hand side.
00:21:47Okay.
00:21:54Right-hand side.
00:22:23Okay.
00:22:52So, right-hand side is.
00:23:22Okay.
00:23:48So, left-hand side and right-hand side.
00:23:51We have X plus Y, X plus Y, so we can cancel that out, okay?
00:23:55So, now.
00:23:57And let's multiply negative 1, 2.
00:24:02L prime is equal to L minus X minus Y.
00:24:14Negative number, okay?
00:24:16R prime is equal to minus R minus X minus Y.
00:24:25To make it simple, okay?
00:24:26So, yeah.
00:24:31Now.
00:25:01Okay?
00:25:10Now, if we prove that L prime is equal to R prime, then that will be the proof, okay?
00:25:18Okay, yeah.
00:25:44Okay.
00:25:56Bye now.
00:26:26To make it easier, let's say L2 prime is equal to L prime plus.
00:26:55Mm-hmm.
00:27:22Likewise, R prime.
00:27:23R2 prime is equal to.
00:27:27Well, actually, there is more efficient way to do this.
00:27:32As we did in the past, like circle operator.
00:27:36That's like operator, well, relational operator variable, circle.
00:27:40It could be equal to, not equal to, or larger than, smaller than, okay?
00:27:43Yeah, we'll do that too.
00:27:45Well, we're just experimenting with different notation combination, okay?
00:27:49Because we did that very, very many times, so.
00:28:06Okay?
00:28:09Then question boils down to is we're transforming the problem into equivalent problem, okay?
00:28:21Yeah.
00:28:23Equivalent problem transformation.
00:28:39Yeah, it's kind of like interesting.
00:28:44Distributive law a little bit.
00:28:46Okay.
00:28:48Oh, problem function, okay, okay.
00:28:50Five minutes break, okay?
00:28:51Thank you.
00:28:52Yep.
00:28:53How interesting.
00:28:54Yeah.
00:28:57Fractional algebra, brand new mathematics, okay?
00:28:59Nice.
00:29:01Five minutes, thank you.
00:29:10There we go, thank you.
00:29:31Okay.
00:29:33Okay.
00:29:35Okay.
00:29:38Oof.
00:29:43Okay.
00:30:07Okay.
00:30:12Okay.
00:30:17Okay.
00:30:22Okay.
00:30:27Okay.
00:30:32Okay.
00:30:37Okay.
00:30:42Okay.
00:30:47Okay.
00:30:52Okay.
00:30:57Okay.
00:31:02Okay.
00:31:07Okay.
00:31:12Okay.
00:31:17Okay.
00:31:22Okay.
00:31:27Okay.
00:31:32Okay.
00:31:37Okay.
00:31:42Okay.
00:31:47Okay.
00:31:52Okay.
00:31:58Okay.
00:32:03Okay.
00:32:08Well, take a breath from mathematics a little bit.
00:32:11Like some invention idea freely sharing with you for free.
00:32:18Yeah, like manned drone, like flying car, the challenges, they don't fly too high, okay?
00:32:25That's why parachute, when engine fails, parachute may not be, may not work because they're not,
00:32:31they don't fly very high, okay?
00:32:34So manned drone are like, well, the flying car in the future.
00:32:40How about bubble?
00:32:42Like, like an airbag popping off, okay?
00:32:45Surround the entire body, okay?
00:32:49Yeah, so special costumes where this balloon pops everywhere to surround entire person's body so that this person falls,
00:33:01bouncing around, okay, to land safely, okay, when the drone engine fails, okay?
00:33:08Yeah, actually it's possible.
00:33:11Okay.
00:33:13Let's continue.
00:33:17Okay.
00:33:22Okay.
00:33:35Let's make some examples.
00:33:40Like, let's say 1.8 plus 2.5, let's say 2.7, okay?
00:34:01Is equal to 2, 3?
00:34:05No, no, 1, 2, 3.
00:34:13Now, is this equal to?
00:34:20Add them together.
00:34:342.5 plus fraction.
00:34:480.8.
00:34:51Yeah, it's not true, but whatever.
00:35:004 plus 1.
00:35:03So maybe this should be minus, okay?
00:35:06So I must have made mistakes somewhere, okay?
00:35:11So.
00:35:40Okay.
00:36:11Okay.
00:36:23Yeah, yeah, I made a mistake here.
00:36:27This is plus.
00:36:56Okay.
00:37:25Okay.
00:37:56Okay.
00:38:03So, we have found the distributive law of flooring function in terms of audition, okay?
00:38:14So, and we did not prove it yet, but most likely it's true, okay?
00:38:22So it goes like this.
00:38:51Okay?
00:38:58Nice.
00:39:05How do you prove this?
00:39:06I don't know yet.
00:39:08Most likely using definition, okay?
00:39:10So, yeah.
00:39:16Yeah.
00:39:19Very cool stuff.
00:39:21And this and that, yeah, the fraction distributive law and the flooring distributive law, they're equivalent, okay?
00:39:32So we just need to prove one of those two.
00:39:35Okay, yeah, sure.
00:39:54Let's try it.
00:39:56But, well, now we're going to use the definition of the flooring function, okay?
00:40:07Maybe this is easier to prove.
00:40:17Okay?
00:40:21If you want to, prove this hypothesis using this or something else too, okay?
00:40:33Yeah.
00:40:35Five minutes break, thank you.
00:40:38How nice, this is fun.
00:40:40I'm glad we are doing this.
00:40:42Yeah, very cool stuff.
00:40:45Yeah, five minutes, thank you.
00:40:47Yep.
00:40:49Mm-hmm.
00:40:55Okay.
00:41:02Thank you.
00:41:32Thank you.
00:42:02Thank you.
00:42:32Thank you.
00:42:34Thank you.
00:43:02Thank you.
00:43:04Thank you.
00:43:33Okay.
00:43:37Last night I wrote some novel short stories, like hypothetical, like me being U.S. president and interaction with Secret Service.
00:43:49It's kind of like a little bit of horror because Secret Service, like me, Mr. President, saying something weird and strange all of a sudden.
00:43:58It's a little bit of horror.
00:44:03Out of character.
00:44:05It's kind of like magical realism, whatever.
00:44:11Okay.
00:44:14I want some vodka, okay?
00:44:17Yeah, let me grab some.
00:44:34Yeah, I really like this.
00:44:38Rosy vodka, it's just so good.
00:44:46From my backyard.
00:44:54Oh, it is super, really good.
00:45:03Beautiful color, too, and very healthy.
00:45:15Pour this back in.
00:45:24There's that.
00:45:30And half a scrambled egg.
00:45:41Yeah, these fruits drop out of the bottle when I pour it.
00:45:45No problem.
00:45:46I put them back in.
00:45:48It's beautiful to look at, you know?
00:45:55Oh, it's chilly.
00:46:02It's getting cold.
00:46:08Wow.
00:46:19Cheers, happy Tuesday.
00:46:27Okay, let's see what it looks like.
00:46:31So this is L, left-hand side.
00:46:37Right-hand side.
00:46:43And left-hand side is, using the definition.
00:46:56Plug it in.
00:47:02Right-hand side is.
00:47:33Okay.
00:47:42Maybe it's the opposite of that, maybe the reverse of that, but whatever.
00:47:53So L prime.
00:47:59Yeah, this one, this one cancels out.
00:48:03It's good.
00:48:09And.
00:48:16R prime.
00:48:19R prime.
00:48:33Which is what we have over there.
00:48:35So, yeah, it's circling around.
00:48:39Yeah, I'm not quite making progress.
00:48:40Well, we are making progress, because we found the distributive law of a floating function.
00:48:47Okay?
00:48:48And distributive law of fraction function.
00:48:53We just need to prove one of those two.
00:48:58And I don't know how to do it.
00:49:03But we discovered something.
00:49:05Just most likely to be true, okay?
00:49:10Yeah, cheers, yeah.
00:49:16Let's go back to Wikipedia.
00:49:18Do they have something like this?
00:49:22I don't think so.
00:49:41Anything regarding distributive law?
00:49:47No, this is all they have, okay?
00:49:55Yeah, what we are doing here could be brand new, okay?
00:50:12But it's possible that it's published, discovered, and published somewhere.
00:50:18Or maybe somebody discovered it, but never published it.
00:50:22That's another possibility, okay?
00:50:24I don't know.
00:50:25Or it could be brand new, okay?
00:50:26Yeah.
00:50:28I don't know.
00:50:54But it makes perfect sense, though.
00:50:58Kinda.
00:51:17Let's try one more thing, okay?
00:51:20If we take a break.
00:51:28Here.
00:51:37All right.
00:51:49Cheers.
00:52:01It's silly.
00:52:19Left-hand side.
00:52:47Mm-hmm.
00:52:56Oh!
00:52:58Actually, we can use that one.
00:53:00Yeah, it was useful, huh, in the Wikipedia?
00:53:05It's elementary, but still a very useful one, okay?
00:53:08Yeah.
00:53:10Good.
00:53:14There's a primitive elementary distributive law here, okay?
00:53:21Here.
00:53:22When n is an integer, n can crawl out of this floor, okay?
00:53:30Right there.
00:53:31Let's use that.
00:53:33Good, good, good.
00:53:37Then, yeah, that's the proof, then.
00:53:42Okay?
00:53:48Flooring of x, flooring of y, they're integers, okay?
00:53:52So they crawl out.
00:54:16Right?
00:54:18Yeah.
00:54:22Nice.
00:54:24Which is?
00:54:27Right-hand side.
00:54:30Yeah, end of proof.
00:54:32QED.
00:54:34Code as demonstrator, yeah.
00:54:37That was demonstrated.
00:54:39It was demonstrated, okay?
00:54:41Nice.
00:54:43Yeah, we proved it.
00:54:45Okay?
00:54:46Very cool.
00:54:47And because this and that, they're equivalent, yeah, we proved both of them.
00:54:54Good.
00:54:55Fantastic.
00:54:58Booyah!
00:54:59Yeah, so Wikipedia really helped, okay?
00:55:00Yeah.
00:55:01Nice, nice.
00:55:02Good, good, good.
00:55:04Okay, all is good.
00:55:06Yeah, it's been less than one hour, okay?
00:55:25Now we can sit back and relax.
00:55:31Mathematical marathon, yeah.
00:55:33Cheers.
00:55:38That's right, I'm hyperventilating.
00:55:41Brain exercise.
00:55:49Booyah!
00:55:56Yeah.
00:56:01Mm-hmm.
00:56:07Oh.
00:56:12Mm-hmm.
00:56:15Yeah, how nice.
00:56:26Okay.
00:56:34Now, we got to prove that, but before we prove that, okay, what we're going to do is we're
00:56:42going to make distributive law.
00:56:46So far, we have distributive law for flooring function and fraction function, and now we
00:56:57need to find distributive law for ceiling function and the complement function, okay?
00:57:05Which will be similar to this one.
00:57:10Similar.
00:57:11I already know the distributive law for fraction, I don't know, complement function, okay?
00:57:19Yeah.
00:57:20I didn't prove it yet, but maybe tomorrow.
00:57:27Okay.
00:57:32Okay.
00:57:36After all those are done, then we'll tackle on this one, maybe the day after tomorrow,
00:57:42okay?
00:57:43Or tomorrow.
00:57:45Yeah.
00:57:54Okay.
00:57:57I'm tired, yeah.
00:58:02Time to take a quick...
00:58:07Yeah, it's been almost one hour, so let's take five minutes break, and then, yeah, we'll
00:58:17see.
00:58:23All right, very cool, yep.
00:58:30There we go.
00:58:33Thank you.
00:58:40Thank you.
00:58:46Thank you.
00:58:52Thank you.
00:59:22Thank you.
00:59:52Thank you.
01:00:22Thank you.
01:00:52Thank you.
01:01:23Thank you.
01:01:29Thank you.
01:01:35Thank you.
01:01:41Thank you.
01:01:48Thank you.
01:01:54Thank you.
01:02:00Thank you.
01:02:06Thank you.
01:02:13Thank you.
01:02:19Thank you.
01:02:25Thank you.
01:02:31Thank you.
01:02:38That's a signal to those animals, I guess, for opposite purposes.
01:02:44Okay.
01:02:47I would like to do just a little bit more, okay?
01:02:56Well, we ran out of room here.
01:03:01Let's go to the...
01:03:07Why is there another whiteboard?
01:03:11Well, maybe not.
01:03:15I'm kind of wondering.
01:03:19I know distributive law for complement function, okay?
01:03:23Complement A plus B is equal to complement A plus complement B, and then fraction of
01:03:30entire thing, okay?
01:03:32It's quite interesting, okay?
01:03:37Cheers.
01:03:41Well, ceiling function, I don't have it yet, but I have some hypothesis based on this.
01:03:54This has to be true.
01:04:02Why?
01:04:08Okay.
01:04:14Let's prove this.
01:04:22Let's prove this real quick, okay?
01:04:24This is easy.
01:04:25It's same as this.
01:04:26So this is left-hand side, right-hand side.
01:04:36Okay.
01:04:38Ceiling of X is defined as X...
01:04:49Oh, maybe it's not fraction, maybe it's ceiling.
01:04:55I mean, complement.
01:05:03That would make more sense.
01:05:06So that kind of symmetric, okay?
01:05:11Plus complement of X, okay?
01:05:14X is 1.7, complement of X is 0.3 to make it the next bigger integer, okay?
01:05:24Okay?
01:05:26So this is...
01:05:51Oh, okay, okay, okay.
01:06:17X is ceiling of X minus complement of X.
01:06:26Okay.
01:06:44This may be minus then, okay?
01:06:46So we'll see.
01:06:48Okay?
01:06:50I don't know.
01:07:10Let's go to Wikipedia, okay?
01:07:11Okay, okay, okay.
01:07:12Let's check out the primitive distributive law for ceiling.
01:07:18Okay, so n just scrolls out.
01:07:20Okay, okay.
01:07:25Okay.
01:07:37Yeah, we modify our hypothesis, okay? According to the result.
01:07:51Let's make some examples.
01:07:57Let's say 1.2, 2.9.
01:08:275, okay?
01:08:33Ceiling of that, 2.
01:08:40Ceiling of that, 3.
01:08:43So, not a very good example, okay?
01:08:46Okay, so and...
01:08:50Okay.
01:08:53And complement of that, 0.8.
01:09:05And complement of that, 0.1.
01:09:09Okay.
01:09:36Okay.
01:09:56I think this should be still a fraction instead of a complement, okay?
01:10:08Okay.
01:10:19Okay.
01:10:21So, complement of x is equal to 1 minus fraction of x, okay?
01:10:34Okay.
01:10:41Then, x is equal to ceiling of x plus fraction of x minus 1, okay?
01:11:01Alright.
01:11:03Booyah!
01:11:33Okay.
01:11:59Okay.
01:12:07Wait a minute.
01:12:29Wait a minute.
01:12:58Wait a minute.
01:13:28Wait a minute.
01:13:35Ugh.
01:14:01Let's take 5 minutes break.
01:14:05We have more than 30 minutes left, okay?
01:14:07So, we have time and I do want to find this, okay?
01:14:10So, yeah.
01:14:15Well, I took a nap, so I, you know, can't resist.
01:14:17So, let's take 5 minutes break and let's grab a brand new whiteboard and find distributive law for ceiling function.
01:14:26Yeah, sure.
01:14:28Okay.
01:14:295 minutes left.
01:14:30Thank you.
01:14:31Yep.
01:14:33I'm going to turn the heat off.
01:14:35Yeah.
01:14:38There we go.
01:14:40Thank you.
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01:17:58Bye bye.
01:17:59Bye bye.
01:18:00Okay.
01:18:01Yeah we got time and I got energy so let's continue.
01:18:21Okay.
01:18:22Okay
01:18:32Yeah
01:18:45Yeah boards they're very cute very beautiful I love boards and
01:18:50And great singing birds
01:18:54All right, yeah, I love their sounds
01:19:00Yeah
01:19:04And they can fly
01:19:07Great animals
01:19:10Yeah, that's like back in like complex logarithm, yeah stuff
01:19:16You know
01:19:19We make it up to it later on okay, I'm not ready to get back to you yet, so
01:19:31Yeah
01:19:35Yeah
01:19:49You okay, yeah, let's continue
01:20:05Left hand side
01:20:07You
01:20:13So let's run some examples, okay, and then come up with hypothesis, okay, so
01:20:32You
01:20:37Okay, which is the same as turning off
01:20:46All done at the same
01:20:57Three plus two five
01:21:01Okay, so there's one difference, okay
01:21:04You okay now
01:21:22You
01:21:24You
01:21:33And then yeah, let's use this trigger legend operator variable circle, okay
01:21:47You
01:21:54You
01:21:59They are the same
01:22:01Okay, so sometimes they are the same sometimes it is less than okay, okay, okay?
01:22:07So we need to do plus something here. Okay, so and
01:22:15In this case
01:22:21Yeah
01:22:23Complement of 2.7
01:22:280.3
01:22:30Complement of 1.9
01:22:330.1, okay, yeah complement of
01:22:442.2 is 0.8
01:22:49And complement of
01:22:521.1 is
01:22:550.9
01:22:58Okay, and one hypothesis would be
01:23:13What is this fraction?
01:23:22You
01:23:25No, it won't work, okay
01:23:32One possibility is this okay
01:23:40Based on these two examples, okay. Yeah
01:23:52You
01:23:55Okay
01:23:57In this instance it works in these two examples, so we made hypothesis based on two examples, okay
01:24:13Yeah
01:24:21You
01:24:23Yes
01:24:39You
01:24:51You
01:25:04You
01:25:07Let's copy down some more equations over there
01:25:21You
01:25:47Okay, yeah
01:25:52You
01:25:54Rolling function? Sure
01:26:06Yeah, I mean
01:26:07We used to do a lot of formal proof like back in the days, right?
01:26:10But it's been a while, so I guess it's a good time to get back to formal proof, right? Sure, sure
01:26:16Okay, so this number theory is easy enough, right? Actually it involves some fractions, so
01:26:23But still easy enough, okay? Yeah, cheers
01:26:30Yeah, Calculating Mathematics? Kind of like Discrete Mathematics a little bit, but sure, whatever
01:26:36Because we are not doing calculus, okay?
01:26:39Yeah, sure
01:26:41You
01:26:43This, Donald Kruse and his friends wrote that mathematics textbook, Concrete Mathematics
01:26:50It's mentioned in a Wikipedia article
01:26:54Okay
01:26:57Now based on this, if you want to prove this, go for it, okay? Yeah
01:27:08Because we're going to take five minutes, right? Thank you
01:27:12Time check
01:27:17We have more than 30 minutes left, okay, good, good. Yeah
01:27:25Well, we are on fire
01:27:31There we go, fantastic
01:27:41You
01:28:11You
01:28:41You
01:29:11You
01:29:41You
01:30:11You
01:30:41You
01:31:12You
01:31:23Okay, we're back
01:31:28Let's continue
01:31:32Based on this
01:31:35Definitions and yeah
01:31:37Yeah
01:31:41Yeah
01:31:47Okay
01:32:07Let's go
01:32:38You
01:32:48And
01:32:54Okay
01:33:01Fractional weights
01:33:08Okay
01:33:14Cheers
01:33:18Working hard. Well, I took a nap. So yeah, I have energy. Yeah. Cheers. And I ate dinner, okay
01:33:32I ate food and I took a nap. So yeah
01:33:37Fully charged, recharged
01:33:54Run aside
01:34:08You
01:34:18Okay
01:34:20Now X plus Y X plus Y equals left-hand side, right-hand side. Okay, so we can get rid of that. Okay, so L prime
01:34:31Slash, okay
01:34:37You
01:34:44Run aside our prime
01:34:59Flooring
01:35:07You
01:35:34Nice it cancels out
01:35:37You
01:35:44Okay
01:36:03And this
01:36:05This was my hypothesis for distributive law for
01:36:13fraction operator
01:36:16Fraction function, okay
01:36:18Yeah, I came up with this hypothesis yesterday
01:36:23Yeah, like based on some examples, okay
01:36:27Okay
01:36:29Okay
01:36:36You
01:36:38Yeah, so let's prove this tomorrow
01:36:44Why I'm tired
01:36:48Let's not work
01:36:54Yeah, just relax
01:36:58Yeah
01:37:05We came a long way, okay. Yeah, making great progress along the way
01:37:20There we go
01:37:31Yeah
01:37:35Cheers
01:37:56Yeah, we continue tomorrow, okay, yeah, so don't tell whose story
01:38:01I'll send you
01:38:06You
01:38:08Yeah, we're like more than 10 minutes left
01:38:11Yeah, uh my child childhood
01:38:15Or all my life. I'm like this. Okay, very average normal person. Okay. Yeah
01:38:23Not too popular not too unpopular come halfway in the middle where yeah my close friends
01:38:32About
01:38:33Two or three and
01:38:36Then my friends, but not very close friends, maybe ten
01:38:42Yeah
01:38:43around there
01:38:45Yeah, cheers
01:38:51Also
01:38:53balancing between alone time and people time like
01:38:57When I was an elementary school, I spent alone time playing with Lego
01:39:02Building block from Denmark Danish Lego, right? Yeah alone time and
01:39:09then otherwise
01:39:14Play some sports with our my friends like soccer
01:39:21Taekwondo school. Yeah sports or running
01:39:25Yeah with friends
01:39:28Ping-pong
01:39:32Hmm
01:39:36Yeah, so
01:39:55So I'm alone now, but this is not live protest is pretty recorded, right
01:40:02in a daily motion, right?
01:40:04but it's for the benefit of future generation your mathematical education and
01:40:09also
01:40:14It's more fun to film this and then upload it
01:40:20Okay, imagining future audience
01:40:22Okay
01:40:24Kind of imagined moral support
01:40:27Moral support. Okay. Yeah
01:40:30Yeah, thank you for spending time with us, thank you future leaders my proud of you, okay
01:40:36Yeah
01:40:39And something new like
01:40:42Mathematical development in real time. Okay
01:40:46Nobody has ever been here before
01:40:49We are the first in the world as far as I know. Okay. Yeah, the complement notation is brand new
01:40:57As far as I know
01:41:00Cheers
01:41:04Maybe somebody some other mathematician maybe use some different notation to denote the same concept. Okay. I don't know
01:41:16In some of their papers maybe. I don't know
01:41:20Yeah, so
01:41:26Okay
01:41:28Well, I need to save some voice for Instagram live, okay, so let's record for
01:41:33This episode. Okay, and after 5 to 10 minutes break we go to Instagram live together
01:41:38Okay, see you later. Thank you. Yeah, happy Tuesday
01:41:43Yeah