348:, thought of as a spherical surface busted up into triangles. As far as topology is concerned, it doesn't matter if the triangles are flat or projected out onto the curved surface of the sphere. This is the idea of a simplex and of a chain, to "triangulate" a space. The sphere is an "orientable" surface, which is a concept we can translate into triangles (simplexes). We can order the vertices of each triangle so that a perpendicular to each points outward by the right-hand rule. A simple test is to look at edges; the edge between two vertices of the icosahedron is part of two triangles, and we get a consistent orientation for the two of them if one orders the vertices in the opposite order of the other. The "sum" of all these triangles is the surface, the space of interest. If we wanted to integrate over the surface of the sphere, and if we bust the integral into the sum of the integrals for each of the triangular pieces, we'd be looking at something that smells like a chain — complete with orientation.
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intuitively, a sphere has no boundary, no "edge". A ball has a boundary; let's see it happen algebraically. Put a vertex at the center of the sphere, and convert each triangle to a tetrahedron. For the surface we had 2-simplexes; for the solid we have 3-simplexes. If we get the "orientation" right, each interior face is shared by two tetrahedra with opposite ordering. Now when we take the boundary of this solid, this chain of 3-simplexes, the interior faces cancel, but the exterior faces remain. Thus the boundary of the ball is a sphere (with orientation!), and the boundary of the sphere cancels to nothing.
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host opens. Assuming the player is clever, the player who waits has additional information (by watching the host) that he can use to improve his chances of winning. A stupid player, however, makes up his mind before going in and does not take advantage of the additional information given by the host's faulty behaviour. As such, a stupid player cannot improve his odds above the 2/3 result for the vanilla MH problem, but a clever player CAN improve his odds thanks to the extra information he derives from the host. Is that correct?
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numbers change. If we're figuring out the probability of winning if the host opens door 3 we have only the 1000 players who initially picked a goat (with these rules, for all 1000 who initially picked the car the host will open door 2). This makes the conditional probability of winning for the players who see the host open door 3 100%. In this variant the unconditional probability is still 2/3.
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about only however many have seen the host open one (but not the other) of the remaining doors. In the problem as typically stated, we're interested in the subset who see the host open door 3. This subset includes all of the players who will win by switching because the car is behind door 2 (in which case the host must open door 3) and some fraction of the players who have picked door 1.
360:, a thing can have a zero boundary without that thing being a boundary itself. For example, suppose a chain of 1-simplexes forms a closed and consistently oriented loop. Each vertex is shared by two edges, and is the leading vertex of one edge and the trailing vertex of the other. Thus a loop is a "cycle", a chain with no boundary. Boundaries are always cycles, so they carry no information.
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door 2). This makes the odds of winning by switching 1000/1500 (i.e. 2/3). The "random goat" host constraint makes the problem symmetric with respect to which door the host opens, i.e. the numbers are the same if the host opens door 2, and makes the conditional probability given either door the host opens the same as the unconditional probability (the probability across all players).
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202:." Why continue to explain these things to him, spoon-feeding him information to reward his bad faith? I decided — and I believe Meni decided — to stop responding to his mathematical posts and his insults. Perhaps he'd see lack of response as an admission that he was right all along, but better to have one deluded person than a garbage talk page we spend untold hours updating.
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delete. (Several of them did talk to me since then, and I also participated in a debate-cum-flamewar on
Croshaw's message board.) I do not harbor any resentments toward any of the subjects of pages that I have taken it upon myself to submit to AfD. My deletion proposals are attempts to cleanse Knowledge (XXG) of non-notable, non-encyclopedic content, and nothing more.
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Okay, I think I understand, let's see if I've got it right. We are noticing the difference in results because we have introduced a fault into the host's behaviour that can be exploited by a clever player. In this case, a 'clever' player is one who waits to decide his move until he sees which door the
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lets us say that we expect the host will open door 3 roughly half the time if the player initially picks door 1, so the total number of players we care about (the ones who see the host open door 3) is roughly the 500 who have picked the car plus the 1000 who have picked a goat (when the car is behind
535:
the "community of interest" is the subset of players who have picked a specific door and have seen the host open some door in response. For example, if there are 3000 players all of whom initially pick door #1, in the first case we're talking about all 3000. In the second case we need to be talking
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I have, but I'm still confused. Is the question "Is there a difference between between the cases in which " or is the question "Is there a difference between the probability of winning "? In the latter case I can see there might be differences but in the former case I can't see how "at what stage the
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A boundary is literally what its name implies. For the sphere, there is no boundary. This falls out of the calculations easily as well. Each triangle has three edges. Each edge is shared with another triangle, where it is reversed. Therefore each edge cancels in the sum. So algebraically, as well as
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I have been vaguely following the discussion of the module isomorphism problem at the ref desk. The key reason why the kernel of the action stays the same under the module isomorphism is that these isomorphisms have the property φ(rx) = r φ(x). If you find the action concept hard to work with, you
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As for 0.999..., we can discuss this further if you like, but I get the impression that it wasn't particularly a focus of your message. In a nutshell, I think that it is a particularly egregious violation of the purpose of a talk page, and that it probably provokes more inappropriate discussion just
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These people and their amateur adventure games simply aren't worthy of inclusion in a general purpose reference work. They are not notable; not in the broader view of the term (which would probably exclude quite a few commercial video games, but it's a slippery slope) and not in the narrower sense,
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The answer is that I sincerely feel that notability is an important, even crucial, policy on
Knowledge (XXG), and it is the one that gets stretched and distorted most often. People often lose sight of the fact that Knowledge (XXG) is an encyclopedia, not an indiscriminate collection of information.
258:
I'm not really sure what you want me to say. You open with the claim that you are not merely trying to plead for pet articles and that I should consider carefully what you say, but then proceed to accuse me of being irrational, acting in bad faith, and having some kind of personal antipathy towards
547:
The reason this is an important distinction is because it doesn't have to be the case that the unconditional probability and conditional probabilities are the same. In particular, in the variant where instead of picking between two goat doors randomly the host prefers the lowest numbered door the
363:
Let's look at a solid torus, busted into tetrahedra. When we compute its boundary, we get the (triangulated) surface, which in turn has no boundary. Boring; no information there. But look at 1-cycles, and things get more interesting. A 1-cycle on the surface that loops the short way around is the
599:, and in the usual way the problem is presented the host has already opened the door, so the analysis should be a conditional one (using all we know about how the host decides what door to open) rather than an unconditional one. The fully specific problem description currently in the article at
395:
Good afternoon (although I guess it's G'day at your time in
Australia). I'd just like to say that I was pleased to read your reply on the 0.999... arguments page. It was the first civil and rational thing I'd read on there; I myself being guilty of writing things that were less that civil. I was
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Before I read of them on
Knowledge (XXG), I had not heard of any of the games or game designers I have proposed for deletion. Prior to the actual deletion debates, I had never met or spoken to Ben Croshaw, Dave Gilbert, or any of the designers, creators, or fans of the games I have endeavored to
551:
Reading your comment again - I suppose in the "decide before" case, we could be asking about the conditional probability for players who then go on to see the host open door 3. Is this what you mean? This would make it the same conditional probability question as the "decide after" case. --
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article on the cleanup page. As I mentioned there, you are right, the choice of templates in cases like that is difficult. However, cleanup is a bit of catch-all template, but that also means it gets massively over-used. The thing to remember is to be
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Sort of, but calling this clever/stupid is not quite right. It's just different. For example, if the host happens to open door 2 in the "lowest numbered door" variant the player's chance of winning is now 1/2 rather than 2/3. The point is
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Even an mention on the item's own wikipedia entry was eventually deemed not good enough because people started going and adding the word "steampunk" into their favorite movie's article just so they could add it to the list.
355:
OK, so we need chains to describe triangulations (or to use a fancy term, simplicial decompositions), and boundaries are just what our intuition tells us boundaries should be. Boundary of boundary is zero, now and always.
412:. I've just seen the comment above so I guess you're still working on these things. If there's anything I can do to help then just ask. If you'd like to discuss some things then it will help me with Čech homology too.
724:
The list has had in the past a serious problem with cruft and unrelated additions. To combat this, it's been pretty much agreed upon that any item added to the list without a citation should be eliminated on sight.
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Frankly, articles on non-notable personages like Mr. Croshaw just make
Knowledge (XXG) look bad, and the problem is particularly acute within the computer and video games topic area, under the jurisdiction of the
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408:, and thought I could help. In fact I'm trying to get to grips with Čech homology at the moment and I'm finding it slow going. Knowledge (XXG) doesn't have an article on Čech homology, but does have one on
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forces the numeric answer for the conditional problem to be the same as the unconditional problem, mostly to avoid confusing people (although I think it is this very point that is confusing
Glkanter). --
93:
and try and fix things - templates are useful, but someone fixing an article is more preferable. Some options are to copyedit it to improve it, research the subject and expand it or nominate it for
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Oh, and I prefer to keep my discussions fragmented (in other words, I won't post on my own talk page). If you like, you can delete this from your own talk page, but please don't copy it to mine.
234:
Ok i nominated the article. the discussion for deletion page is up. its been 5 days. i read the page on wikipedia about articles for deletion but still am not sure what to do. what do i do now?
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we have to be talking about all players (or the subset of players who have picked a particular door), not a subset who have picked a door and have seen which door the host opens in response.
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redirect. Also, its a good idea to leave a note on the articles talk pages stating why you have made a change such as redirecting (which, hopefully, isn't "because kcordina told me to!).
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from R to R/I defined by f(r) = r + I = r(1+I). The isomorphism then maps this to r + J, which is the same as the canonical homomorphism from R to R/J. Hope this helps,
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There is much more that could be said, but I hope this gives you a sense that the terms have an easily-understood intuitive meaning, closely related to their names.
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I've fixed it, but in the future, if you're adding something, we'd appreciate it if you'd also cite it so we don't waste time reverting each other.
636:. Nothing is sourced or notable. It is fine on IMDB, but unless the references are sourced and notable, they have no place in these articles.
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to
Knowledge (XXG)! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers:
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boundary of a disk; no information. A 1-cycle on the surface that loops the long way around (circling the hole in the donut) is
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on talk pages using four tildes (~~~~); this will automatically produce your name and the date. If you need help, check out
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has gotten a little out of control. You posted (in response to my question about whether you've read the whole thread):
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The difference is when the decision is made because it changes the population we're interested in. If the sequence is:
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Forgot a couple of things - when redirecting, make sure you don't create any double-redirects. Here you'll notice that
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Perhaps you may be bothered to check yourself and either remove the template or leave criticism at the talk page.
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Hi there! You are cordially invited to a meetup next Sunday (6 January). Details and an attendee list are at
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I thought we should move this away from the Ref Desk. Although I'm trying to concentrate on writing about
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If you have follow-up questions, please ask them here and I will reply when (and if) I can. --
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on your talk page and someone will show up shortly to answer your questions. Again, welcome!
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a boundary (of something that is part of the torus); it tells us something. This is what the
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Oh, thanks! The article looks much better now, I will remove the template immediately.
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Please do not add items to the steampunk list without also adding a citation.
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Sorry, but these sections in almost all of the HIMYM episode articles violate
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on a discussions page. I came here to see if I could help. I'm familiar with
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If both remaining doors have goats behind them, he chooses one randomly
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Thanks for the reply to my query on the 0.999 article talk page.
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No worries now, that article i nominated has been deleted.
97:. In this case free running is actually another name for
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decision is made" can possibly influence the outcome.
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Please vote on attempt to delete new Ref Desk rules
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