Category
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GamingTranscript
00:00:00Hello friends, welcome to Humanology 28.4.1.
00:00:07Yeah, I looked up the reference in the Wikipedia to Donald Knudsen and his colleagues wrote
00:00:16a book in mathematics, concrete mathematics, okay.
00:00:19It's kind of like discrete mathematics, right?
00:00:22Yeah.
00:00:24You deal with like number theory, basically, like maybe graph theory, like basically things
00:00:31that have some jumps, like not...
00:00:34Apart from discrete mathematics, concrete mathematics, that's like calculus, which is
00:00:40continuous, right?
00:00:41Discrete mathematics deal with like non-continuous, like number one, like number two, number three,
00:00:47like natural number, whatever.
00:00:49What?
00:00:50Yeah.
00:00:51Okay.
00:00:52Cheers.
00:00:53Yeah.
00:00:54Yeah, I still don't understand why this is the case, okay?
00:00:57Yeah.
00:01:02And my neck is hurting.
00:01:03Okay.
00:01:04Yeah.
00:01:05Nothing for five minutes, right?
00:01:06Yeah, sure.
00:01:08Okay.
00:01:10Yeah.
00:01:11Yeah.
00:01:14Yeah, some power surge, very briefly, so...
00:01:18Inconnected connection, but...
00:01:21So, daily motion is also back in the...
00:01:25Back up and running, and that's great, so...
00:01:29Yeah, I didn't lose any footage, okay?
00:01:31So, Zoom software is very robust.
00:01:33Sure.
00:01:34Yeah.
00:01:35Five minutes, thank you.
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00:06:10So, during the cigarette break, I came up with an idea.
00:06:23Okay.
00:06:24So during the cigarette break, I came up with an idea, let's see if it works, okay, yeah.
00:06:43Alright.
00:06:44Let's prove this thing, okay, yeah.
00:06:48Yeah, I'm not going to buy that book.
00:06:52I'm not going to buy that book, concrete mathematics, okay.
00:06:56Yeah, it's a problem, yeah, it should not be a very difficult proof, okay, so, yeah,
00:07:05cheers, yeah.
00:07:09So, ceiling of X is equal to X plus alpha, where alpha could be zero.
00:07:38Alpha is strictly less than one, okay.
00:07:53Why?
00:07:55If X is integer, well, we'll just do positive numbers only, okay, X is like natural number,
00:08:06non-negative number, then alpha is zero.
00:08:10If X is a fraction, then alpha is ceiling of X minus X, okay, yeah.
00:08:19So X is like, alpha is like random, okay, exceeding the next integer, you know, yeah,
00:08:29so, okay.
00:08:32Now let's prove this, okay, yeah.
00:09:02Okay.
00:09:32Oh, yeah, it is confusing, okay.
00:09:53Let's say X is 0.7, okay, so.
00:10:23Okay.
00:10:36Okay.
00:10:56Hmm.
00:11:12It's not that easy, huh.
00:11:18We are trying to prove this one, okay, yeah.
00:11:49Okay.
00:11:58Yeah.
00:12:18Okay.
00:12:45Yeah, I'm having some difficulty here.
00:12:48Cheers.
00:13:00But not as exciting as when we, like, discover something new, because this is already known.
00:13:06Some people proved it.
00:13:08So it's not as exciting as doing something brand new, but still, yeah.
00:14:06Okay.
00:14:26Okay.
00:14:54Okay.
00:15:08Okay.
00:15:38Okay, let's step back, let's try this.
00:16:07Well, not exactly.
00:16:19When alpha is 0, this is m, when alpha is non-zero, this is m plus 1, okay, so, okay.
00:16:25That one doesn't work.
00:16:27Okay.
00:16:31Hmm.
00:16:53You know what, I guess we need some more inputs.
00:16:56Let's get back to the Wikipedia, okay.
00:16:59Let's study some more.
00:17:29Oh, fraction part.
00:17:52Hmm.
00:18:07Yeah, we're dealing with complement of fraction part, okay.
00:18:10Okay.
00:18:20Integer part, okay, okay.
00:18:25Okay, okay, okay.
00:18:28Yeah.
00:18:39Integer part, fraction part, okay.
00:18:41Well, we have the complement of fraction part, okay, that's another important thing.
00:18:47Doesn't have notation for that, but then we have to come up with our own notation then, okay.
00:18:52Okay, so we have fraction part, integer part, and, okay, okay, okay.
00:19:04Okay.
00:19:28Okay.
00:19:35This is a lot.
00:19:37Cheers.
00:19:44Let's come up with brand new notation, okay.
00:19:51Alpha.
00:20:01Oh.
00:20:10Let's say alpha, that's like complement of fraction, okay, so alpha is equal to, let's call it slash x slash, okay.
00:20:21Yeah.
00:20:22Okay, yeah, sure.
00:20:26Yeah, x is 0.7, then alpha, the complementary fraction, fraction complement is 0.3, okay.
00:20:36Yeah.
00:20:38Okay.
00:20:43Ah.
00:20:44Yeah.
00:20:46Let's take five minutes, all right, I, not an easy question for me, you know.
00:20:53Yeah, five minutes, okay.
00:20:56Wow.
00:20:58How interesting.
00:21:00Oof, normal theory.
00:21:02Wow.
00:21:03Five minutes, thank you.
00:21:04Yep.
00:21:05Oof.
00:21:17Okay.
00:21:28Oof.
00:21:58Oof.
00:21:59Okay.
00:22:00Oof.
00:22:01Oof.
00:22:02Oof.
00:22:03Oof.
00:22:04Oof.
00:22:05Oof.
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00:22:15Oof.
00:22:16Oof.
00:22:17Oof.
00:22:18Oof.
00:22:19Oof.
00:22:20Okay.
00:22:21Oof.
00:22:22Oof.
00:22:23Oof.
00:22:24Oof.
00:22:25Oof.
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00:24:00Oof.
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00:25:00Oof.
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00:25:03Oof.
00:25:04Oof...
00:25:05Oof...
00:25:06Oof...
00:25:07Oof...
00:25:08Oof...
00:25:09Oof...
00:25:10Oof...
00:25:11Oof...
00:25:12I think we got it, okay?
00:25:13So, in the military science, divide and conquer, right?
00:25:14In mathematics?
00:25:15where x is whole number like integer okay natural number and then second case when x
00:25:24is a fraction yeah sure I think it will work.
00:25:31sure sure let's go
00:25:41ah well I have to share this screen with you so I cannot quite get in the way
00:25:55yeah this one
00:26:07x is a non-negative integer okay
00:26:15okay
00:26:19then the ceiling of x is x okay so
00:26:37okay okay now
00:26:42x is not
00:26:48non-negative integer and then x is a positive number okay
00:26:58ah non-negative number okay in that case
00:27:09we just call it alpha okay so
00:27:18okay so
00:27:48you
00:27:59now
00:28:04a
00:28:18from here, can we say, this is what we want to prove
00:28:36M is a non-negative integer
00:28:54Cheers
00:28:55Cheers
00:28:56Cheers
00:28:57Cheers
00:28:58Cheers
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00:32:36Cheers
00:32:37Cheers
00:32:38Cheers
00:32:39Cheers
00:32:40Cheers
00:32:41Cheers
00:32:42Cheers
00:32:43Cheers
00:32:44Cheers
00:32:45Cheers
00:32:46Cheers
00:32:48Cheers
00:32:49Cheers
00:32:50Cheers
00:32:51Cheers
00:32:52Cheers
00:32:53Cheers
00:32:54Cheers
00:32:55Cheers
00:32:56Cheers
00:32:57Very fine
00:32:58Okay let's see if I was broken yeah
00:33:10Time check
00:33:20Yeah, it's been more than 30 minutes, okay
00:33:23Five minutes, okay. Thank you. Ah
00:33:25I am having difficult proving this. Okay. Yeah, it's
00:33:32tricky
00:33:34Yeah
00:33:35But if you can prove it, go for it. Okay. Yeah
00:33:38Five minutes. Thank you
00:34:08You
00:34:38You
00:35:08You
00:35:38You
00:36:08You
00:36:38You
00:37:08You
00:37:10You
00:37:14You
00:37:18You
00:37:21You
00:37:24You
00:37:28You
00:37:31You
00:37:33You
00:37:37Okay, do you celebrate
00:37:47I came up with a different approach. Let's take a step back. Okay, and
00:37:53Let's go back to the basics
00:37:56All right
00:37:58You can see this right? Yeah
00:38:01Let's go back to the basics, okay, so
00:38:09You have X of fraction, okay
00:38:14X is equal to
00:38:17Flooring of X
00:38:20Plus fraction of X. Okay, that's the notation. Okay, and
00:38:26And
00:38:29Also X plus the
00:38:37Additive complement of X. Okay, so
00:38:42Okay, that's the ceiling of X
00:38:48Okay, yeah
00:38:55You
00:38:58And
00:39:03Fraction of X
00:39:06Plus additive complement of X is equal to 1
00:39:14We've been very systematic here, okay
00:39:18For example when X is 0.7
00:39:26Floor well 1.7. Okay, so 1.7
00:39:33Flooring of X, that's 1. Fraction part 0.7
00:39:41And X is 1.7
00:39:45Additive complement is 0.3
00:39:49Okay, and
00:39:52The ceiling of X is 2. Okay, and fraction of X is 0.7
00:40:02Complement of X is 0.3. Okay
00:40:07Okay
00:40:10Yeah
00:40:14Okay
00:40:16You so now next step
00:40:30X plus M
00:40:37M is the integer. Okay X is not an integer. Okay
00:40:40And
00:40:45Fraction of them is same as fraction of X. Fraction part
00:40:52Okay, and also
00:40:56Additive complement part
00:41:10Because M is an integer, right? Well, there were positive integers, okay. It's same as that
00:41:19Okay
00:41:23Good good to know
00:41:29Hmm
00:41:40You
00:41:47Okay
00:42:10You
00:42:15Okay
00:42:21So here we have ceiling of
00:42:27Right
00:42:40Using this
00:43:03Yeah, using the second equation
00:43:07Oof
00:43:10You
00:43:21Oh
00:43:27And because this is their whole numbers, right? Yeah
00:43:37Okay
00:43:40Yeah
00:43:48Now
00:43:50Just a left-hand side, okay
00:43:54This is right-hand side
00:43:57Now right-hand side
00:44:03Just left-hand side
00:44:06Right-hand side
00:44:10You
00:44:12Are using the same equation
00:44:14You
00:44:39Using this
00:44:45Yeah, now X plus
00:44:54Capital on X, the ceiling of X
00:45:05Just same as left-hand side. Yeah, we proved it. Okay
00:45:11QED. Oh
00:45:15Oh
00:45:22We got it
00:45:26Yeah using the same technique then we can do this, okay when the denominator is not 1, okay
00:45:32I'm pretty sure we work out same way. Okay, so whatever my guess. Okay, but that will be done tomorrow
00:45:39Okay, now I'm tired
00:45:42Okay, yeah, we did good job here, okay, yeah cheers well
00:45:52Ran out of whiskey there
00:45:57Wow, oh
00:46:01My neck is sore
00:46:11You
00:46:21Cheers
00:46:30Mm-hmm
00:46:32You
00:46:40Yeah
00:46:47We we just call this couple amount of X, okay, yeah
00:46:53Yeah
00:46:56Oh
00:47:02Cheers
00:47:21Mm-hmm
00:47:32You
00:47:37This is beautiful, yeah
00:47:46Yeah, oh
00:47:55What a challenge
00:48:02You
00:48:23I'm sure you'll click
00:48:33You
00:48:35It's been less than one hour, okay, good good good. Yeah
00:48:40Now let's take five minutes break and let's go to
00:48:43Instagram live. Okay. Sure. Yeah
00:48:46or I
00:48:48Can't feel like doing some more of this, but I'm kind of tired. Okay, we'll see. Okay
00:48:54When denominator is not 1, but it's 2 for example
00:48:59I am very curious. Okay, let's take five minutes break and I could have another whiteboard and then
00:49:06We'll see
00:49:11We'll see what finest thank you. Oh
00:49:18Good progress here. Yeah. Thank you. Wow
00:49:26Look
00:49:28You
00:49:34Okay
00:49:43You
00:49:58You
00:50:28You
00:50:55You
00:50:58You
00:51:18You
00:51:28You
00:51:58You
00:52:28You
00:52:58You
00:53:28You
00:53:58You
00:54:28You
00:54:58You
00:55:28You
00:55:58You
00:56:28You
00:56:58You
00:57:15Okay, yeah, let's continue huh, I guess we can do that
00:57:26Yeah
00:57:28Yeah
00:57:58Okay.
00:57:59Switch out the whiteboards.
00:58:00Yeah, so.
00:58:01Okay.
00:58:02Let's erase this.
00:58:03Okay.
00:58:04All right.
00:58:05Okay.
00:58:06Let's go to the next page.
00:58:24Okay.
00:58:25Let's erase this.
00:58:26Okay.
00:58:27What was this about?
00:58:28I do not remember.
00:58:29Okay.
00:58:30Yeah.
00:58:31Something to do with prime number, composite number, I guess.
00:58:32Yeah.
00:58:33Prime factorization.
00:58:34Yeah.
00:58:35Yeah.
00:58:36Yeah.
00:58:37Yeah.
00:58:38Yeah.
00:58:39Yeah.
00:58:40Yeah.
00:58:41Yeah.
00:58:42Yeah.
00:58:43Yeah.
00:58:44Yeah.
00:58:45Yeah.
00:58:46Yeah.
00:58:47Yeah.
00:58:48Yeah.
00:58:49Yeah.
00:58:50Yeah.
00:58:51Yeah.
00:58:52Yeah.
00:58:53Yeah.
00:58:54Yeah.
00:58:55Yeah.
00:58:56Yeah.
00:58:57Yeah.
00:58:58Okay.
00:58:59Now.
00:59:00x plus m divided by 2
00:59:18Well, how about excelling?
00:59:38Yeah, it's quite interesting, yeah, and surprising as well, it is significant, that's why it's
00:59:59in Wikipedia, okay, so now let me get this bug on the wall, I just flush it in the toilet,
01:00:17I don't want to squeeze it, you know.
01:01:47Yeah, so we are back to the basics, right, I mean, because that itself is a great contribution
01:01:57to mathematics, because in that Wikipedia page they don't have that kind of stuff, okay,
01:02:03so cheers.
01:02:04We came up with a brand new notational convention too, yeah, welcome to Humanology, okay, we
01:02:15are good at this, okay, yeah, okay, now let's look at this, cheers, yeah, mm-hmm,
01:02:44so if, again, divide and conquer, right, let's assume x is natural number, whole number,
01:03:02integer, non-negative integer, okay, then ceiling of x is x, so that's trivial, okay,
01:03:08so now, second case, x is a fraction, okay, okay, mm-hmm, let's continue, this is a fraction,
01:03:36good, this is left-hand side, this is right-hand side, okay, so, okay, all right, left-hand
01:04:35side, right-hand side, mm-hmm, mm-hmm, mm-hmm, mm-hmm, mm-hmm, mm-hmm, mm-hmm, mm-hmm, mm-hmm,
01:05:04okay, we need to step back again, okay, we need to come up with more lemmas, okay, like
01:05:24like we did before, okay?
01:05:26So, building up the groundwork,
01:05:32building blocks, okay?
01:05:33So, and yeah, my neck is sore, but, oh, cheers.
01:05:51Yeah.
01:05:54So, let's do this, okay?
01:05:59So, let's do this, okay?
01:06:23So, let's do this, okay?
01:06:29Let's say, X divided by some positive integer N, okay?
01:06:59Integer part and fraction part.
01:07:29Mm-hmm.
01:07:59All right, I'm making sure I'm not blocking the view, okay?
01:08:15So, yeah, cheers.
01:08:29Cheers.
01:08:44No, there's some fraction part here
01:08:46and fraction part there, all right?
01:08:48Yeah, so it's not very interesting.
01:08:52Okay.
01:08:59So, what about this?
01:09:22I'm angling my torso, my body,
01:09:24so that I don't twist my neck too much, okay?
01:09:27So, X of fraction, M, like 1.7, something like that,
01:09:44non-whole number, okay?
01:09:45So, M and that will, let's say positive integers, okay?
01:09:51So, yeah, cheers.
01:09:55Mm-hmm.
01:09:57Mm-hmm.
01:10:27Mm-hmm.
01:10:40Mm-hmm.
01:10:47Mm-hmm.
01:10:57Mm-hmm.
01:11:02Yeah, the question is this, okay?
01:11:27Mm-hmm.
01:11:32Is this same as?
01:11:46Okay, let's make some example, okay?
01:11:48So, let's say X is 1.7, okay?
01:11:54Yeah.
01:11:56Hypothesis, okay, yeah.
01:12:01M1, M2, okay, yeah, 2.7 divided by 2, 1.35, okay?
01:12:251.35, 1.35, okay?
01:12:31Okay, now, so just like left-hand side,
01:12:42right-hand side, and this is left-hand side.
01:12:46Now, right-hand side, 1.7 divided by 2,
01:12:551.35, 1.35, 1.35, 1.35, 1.35, 1.35, 1.35.
01:13:25Yeah, fraction part, actually, is 3.5, okay, yeah.
01:13:39Well, we just call it 0.35, okay?
01:13:42So, here, 0.85, okay?
01:13:44So, they are not true, okay?
01:13:46Yeah, okay, good to know.
01:13:53Okay.
01:13:54Yeah, so it's a more difficult problem, okay?
01:13:59Yeah.
01:14:03Booyah!
01:14:04Cheers.
01:14:11Time to check your critic.
01:14:19It's been more than one hour, okay?
01:14:20Okay.
01:14:24Okay.
01:14:27Ah.
01:14:45Okay.
01:14:50Okay.
01:15:20Okay.
01:15:25Mm-hmm.
01:15:37Yeah.
01:15:50Yeah.
01:15:54I do not know.
01:15:58Yeah.
01:16:12I think we did enough, okay?
01:16:14So, let's wrap up this episode,
01:16:17and then we'll take five to 10 minutes break,
01:16:20and let's do the exam log, okay?
01:16:22We are making very good progress here, okay?
01:16:24So, yeah.
01:16:27Yeah, we did enough tonight, mathematics of this, so yeah.
01:16:31Okay, let's go to tomorrow, okay?
01:16:33Yeah.
01:16:34Okay, thank you, yeah.