Afternoon talk / Part 1

0:00 The evolution is the part that I think is classed as actual slides. C, in the case C, is... The general case, the general Cs are underlined from that. The thing was that this, what happens to this new prudence in the case when you replace K by the category set, the coefficients seem to have an actual new prudence. I mean, that's the... That's the point you want to make. There's a very strong condition in this category that there are not just a finite number of binary decompositions, but ternary ones, but all told, there's only a finite number of decompositions. So, composition power, you're not getting anything. The degree of melatonin is sort of the longest possible decomposition of that count. Right, one of the, besides being objective, he says, so if it's not really good, then you do that, I would say. This is an equivalent, I guess, in the algebra case.

2:30 No, well, in the Mervius case, for any ring, yeah, the kernel of this homomorphism consists of local developments, and anything that maps to a convertible is therefore, you know, a different decimal distance from... This power series, the geometric series that is near to an invertible, where near means you'll put the difference. In the same place, near things would end up in the same place under this reduction. But that means that there are different slides in the panel. The panel consists of both of the elements. It's also a calculation of an entomological, an invertible element than the other elements that are close to it in the sense of a metric. It doesn't terminate, but it does converge. It's a very general theory. Don't be aware of the information. Well, that's why it's true. You know, it's said it's a local map. It doesn't mean going to one applies to terrible. This is much stronger. There's a reason why it's local. Conversions are good.

5:00 Universal, Mebius, algebra. Taking the category Big M, the subjects are Mebius carriers with each of them turning an object around a small distance. You take the convolution of factors from that M to an objective rating. I'll take the slide, the slide, the slide. And done. That's Mebius inversion in this form. The basic argument about no-cognizance applies also to that one big M. I don't know, but you're dealing with the object, so this issue sort of doesn't come up.

7:30 You want to force it to be a classical quantity. It's all objective conflict. Yeah, don't be able to open it up slightly. Eventually it appears here, right? The powers correspond to the length of the element. Locally, I mean, it's a, it's kind of a locally fixed end, but it's bound on the end, but the truncation of the sum, when you evaluate it in a particular element of C, the place where that happens is related to the length of that element.

10:00 According to the usual, yeah, the Nervius category can be infinite, and so there's no kicks in, so it's just a string through all L and a 7. Yeah. That depends on evaluating it. It's all the way the functional reality of the others. And any C, the Q, the L, the Q, the L, the C, the Nervius category is based on 2. The algebra is based on 2. The inner function, like the Nervius, that's smaller than the muscle.

12:30 I mean that you can relate it with two instead of a ring. Do I get it right? Am I getting it right? You're replacing K by... No, no. You're replacing C by two. Oh, right. You know, because you don't want to calculate a particular function. You want to evaluate it at alpha. Because that will actually live in the much smaller algorithm than you do by... There's a comment about the calculation for alpha here. Let's see. Let's see. And the next function I'd like to see is extra. It's a weird minus one. The average in English is, I guess, three. It's five times zero. It seems that objects can't be teleported, even in that category, in the form of minus one.

15:00 You're not going to have any actual, actual inviolable or actual notebook, but still there could be some sense in which these approximately equal as to the formal, the difference in virtual view. Exactly. The actual difference in view. That's certainly a property of the pair. An object of, well, this extension, you know, virtual minus one, virtually nil if it is a platform. That's exactly what you're thinking about. Virtually now. We didn't make any progress that day. Exactly. That's right, of course. And then the notation, roughly equal. If there's a virtually now, oh, okay. That's a very simple part. But usually, not a very notational trick. Everyone in the office worked hard that day, but they just didn't add up to anything. There was no actual gain. Good, good. Are you, you might be interested in this one. Yes, I am extremely interested in it. So, are you familiar with it? You say that it was an earlier paper where I talked about this. No, you sent me an email. I sent you an email, right. You can explain. Sure. Yeah, thanks. I think I wrote it down there today briefly because I didn't do much with it.

17:30 This, uh, Eurotica is an extension of something you mentioned the other day. Yeah. I've copied that, if you have any extensive categories, or write it like this, as agreeing that the minus one that's not satisfying is a ring. It's a ring, you can factor the construction by adding the minus one and then force it to be an actual minus one. To satisfy this equation I just wrote down. You get the ring recollection of the ring. Either the elements of the ring or the category are played by performing the same construction at the end of categories.

20:00 It looks like this, plus an object in the base category multiplied by. Among this, there are those ones that are multiplied to zero when you put them on the structure. We find, you can say, that it's roughly equal to y. As you've actually written there, it's a partial order, it's not a full-length relation. It's okay, I mean, the order is also significant. You know, one firm was more active, but it didn't make any more profit.

22:30 Because it says, you know, the one on the right, X, has got... Some extra in-go and out-go, which cancelled out, which is why it didn't have. So it's an ordering, and then of course you can make the ordering to the equivalent relation in the usual way. That's virtual equality. Once you have this rough similarity, then you can also speak about imperturbability. It's searchable, and that's why. For example... You've got to know which way you interpret the adding of the virtually nil, right? So you could say xy is less than or equal to 1, or maybe the other one is less than or equal to 1, and it's the greatest y for which that's true, for example. Something more general than the variability is inherent in the fact that you have this partial order, in which case, you know, you just say less than or equal or greater than or equal to 1.

25:00 There are obviously going to be lots of whys, but you could ask for an extremal one, a simple case that might actually satisfy virtual training. So that seems to be an interesting refinement of it. Well, it's not treated there, but I guess one could put it in the end, spiritually. The thing that becomes eventually plus and minus, the two sides become eventually equal. What does that mean, say, for you?

27:30 I should always take this as whole numbers because that would be the first approximation to the standard category of finite sets. Can this hold true for positive energy? Because this is defining it, the curve and the plane, the quadratic section. Does it have any integral points? For integers this is twice the speed of it. Is there any difference for cubes? Nothing the same. A nice example is a curve that has no integer point.

30:00 I could probably make some tea for it. I could make some tea for it. I could make some tea for it. I could make some tea for it. I could make some tea for it. I could make some tea for it. I could make some tea for it. I could make some tea for it.

32:30 So, you can cancel the b-a assuming that a is not b, then a squared plus a b is a positive, the other side of the equation is minus three a b, a squared plus b squared is minus three, so you can calculate that there's something negative.

35:00 We don't get, we do get sometimes virtual work done. Yes, that's the, that happens with the set of lines, the reading, based on the equation. Same words, even and odd, right? Even and odd, yeah.

37:30 Input and output fraction, gain and kind, theta. Theta, what was theta? Theta was... What I did was to use this iso to replace this one here. Yeah. O is literally the function whose value is minus one. No, it simply gives you the number of autocompositions. Right. Number of autocompositions. But that's why it's an element of the algebra. The element has a specific significance. It's just an example of how this serves. Or in such a point, why it's an inverse formula. Or they're the same values. They're invariant, but inverses are not invariant. Yeah, presumably up to a virtual.

40:00 It doesn't matter how badly we did it last year, it's next year, we can make as much money as we lose. Right. So, President, in the particular case that we have in mind, when you apply Zeta, sorry, U, to a... maybe it's a category with an initial and final object, what you do is you apply it to the unique map going from... So, in the case of my noticum procedure of his life, I'm one of all things. Yeah, good authority. There might be a lot of elements other than Veda itself for which this question is true.

42:30 It's involved with the even number of the odd number differs from one. In any such case, it would have a spiritual meaning. What do you say that a map is a platform? Well, here it's not a map, it's a... Well, in this ring structure. In this ring structure, exactly. Well, this ring structure is... Well, anyway, with respect to the tensor product we're talking about... Yeah, it's a refined notion. It's the same notion as in vector models. What we're writing as juxtaposition is really a tensor product. We're hoping that that could come out to be the unit object of the... But you can't in this case, but it can be virtually. Yeah, so it's not virtually, yeah. Triviality, the first thing to write down, what does it mean to be virtually equal to the unit? So it means that the two entries, that they differ by one, because the unit is still a terminal object of the original convention.

45:00 And it seems that E and O are the two basic quantities in some way. You get together with Zeta, Zeta, E, and O, and then U comes out automatically. You know what I'm saying? Even though the algebra is non-communicative, it's a little piece of it, but it's just anything. So, in fact, you might be getting the same result. That's right. Suppose you had two different Mervius categories with the property that the functions E and O were numerically the same. Multiplication laws. Let's say two different monoids are of the same sex and give the same E and O, then they won't be the same monoids, but they're probably giving the same numerical answers to the commute. It depends on this part which seems to be discommitted, isn't it? E times O? What if E times O?

47:30 It's just that the cases you take, you go up or you go down. Yeah, just by string, you adjust it in the middle. Yeah, thank you, or the last thing you do, depending on the case, you go up.

50:00 Yeah, I really checked out. You were saying for each given object C, the number of such pairs could be the same, whether you do EO or OE. I don't know, but if you change the C, I hope. Yes, you're changing the C. Well, what if we do it in it? Not in a global thing, but in a local, in a Hispanic way. Again, the same, roughly the same calculations, at a given value, at a given map. Every decomposition into pairs, and then decompositions of those ingredients. It's a long time coming.

52:30 Yeah, it's a long time coming. We'll see what will happen. We'll take it down. This needs careful thought, it seems to me. I'm a little bit dubious to this idea of moving along one arrow. I'm troubled at the end point or something. So the commutativity of these two particular elements. Well, in any case, if it's not true, it's an interesting condition on the batting record. It's very combinatorial. The two-sided invertibility of Zeta, you see, looks like probably it gives two sides of different proofs in the sense of different virtual elements, like the mu times Zeta, a very similar expansion, I think, but the trivial part will be Zeta E.

55:00 No, it will be OZ, not Zeta O. Oh, okay, OZ, OZ. Oh, I see, right, right. Still O rather than E on the other side. Right, so that could easily come up, and probably that seems to be in this case. If you say that you have a two-sided virtual inverse, then you have to get a proof for the two sides. The proof means the virtual element. Are you on the computer, Mike? Yes, just for a minute. Well, I was just going to say. Why don't you ask what Wiki thinks double-entry bookkeeping is? Oh, okay. I was going to say, if you want me to go into this category, it might be okay. It might be something... As a matter of fact, I've just been pulling up all the photographs of you talking in Cambridge. You can have a look at them in a minute. Oh, dear. Talking in Cambridge. Uh-oh. Including my declaration that...

57:30 Well, maybe it has to be almost a graph. No, we don't have a picture, so we'll pick a graph. The graph is, the graph is restriction. Yeah. You restrict the function, the remote function that you get. Hotline. Hotline. Yeah. And that would somehow give you this. That would be nice, an actual combinatorial. The number of even decompositions depends on the number of even decompositions. It depends on the category to find the same kind of way of expression. They work it out.

1:00:00 But decomposition is a kind of singular figure. I mean, it's a map from the category developed at the end into a given category. Any map is not... But not any map. It has two... Well, the endpoints have to... I mean, it has to compose out to be a given map, a condition of repetition. I think it's just the same as any functor. I can see that the functor is like a composition of any functor like that. No, it has to be non-singular so to speak. You cannot map something non-trivial to identity. The compositions don't have identities in the composition. No, it does sound negative.