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punk

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  1. Okay then here is the solution: 1. We let the kid play 2. Every other team forfeits their games with the kid's team 3. Before the season even start we give the kid's team the first place trophy 4. Everyone else has a really fun time playing to see who comes in second Problem solved. Well except for those other kids on the kid's team who wanted to have some fun playing the game. ... The fact is you can't force all the other kids to play against this really good kid. If they all want to forfeit their games with him that is their own business.
  2. The alternative is that no other team is ever going to play that team. Okay they win every one of their games by forfeit. Kudos. They win every game. If their goal in the league is to win every game, they've got it. No, I think that since no other team appears to want to play that team that he isn't going to play even if he is pitcher. I mean, if it is about a perfect record, they'll get it by forfeits. There, they won. Look at it this way - if a master chess player wants to play chess with me, I'm going to say "no". Why? Because I wouldnt' have a chance. If he wants to take some pieces off the board I'll play him. Is it wrong of him to not play the full game (with all the pieces) because someone else demands he do so?
  3. Look at it this way - Suppose you let him play. Then every team knows they aren't going to win so whenever they are going to play this team they just forfeit. Well that's nice, this team ends up with a perfect record, and never plays a game. However, since we are talking about a league for 9 year olds, I think it is about more than winning every game. This probably has something to do with playing, having a good time, being out in the Sun. You know - fun. So they told him he couldn't pitch so everyone could have fun. It seems pretty reasonable to me.
  4. Yes, formally one typically takes Ex ('there exists') as a basic thing from which Ax ('for all') is defined by: Ax := ~Ex~ ('it is not the case that there exists something such that not...'). Again this is going to come up if one wants the system to be Boolean.
  5. I'm sorry, It has been ages since I've done this stuff at an introductory or intermediate level. Yes, "just in case" is the same as "if and only if". Not really. If I say that every egg in an empty basket is red, that is a true statement. All of the eggs (of which there are none) are read. It gets at the way this is written formally: Ax (E(x)&B(x)) -> R(x) ('every egg in the basket is red') So what is being said is that for any x (which can be anything in the universe, say the star alpha proxima) you ask is it an egg? (no), is it in the basket (no), then it would be red if it were an egg and in the basket. If there were anything in the universe that were an egg and in the basket and were not red then you'd have a problem. Effectively all the expressions are defined in such away that you can test every object in the universe to see if it holds. The fact that no object in the universe satisfies the expression isn't a problem, the statement is still true by virtue of the fact that no object in the universe makes it false. The alternative is to say "well no object in the universe makes it false, so it isn't false, but yet no object in the universe satisfies it, so it must be neither true nor false". But the minute you start doing this you have given up the Law of the Excluded Middle (which requires every expression be either true or false). No, as above, if we require the Law of the Excluded Middle then every expression must be either true or false. You are saying that since the empty set is empty we can't ascribe properties to it. So for a given set A it is neither true that the empty set is a subset of A nor false that the empty set is a subset of A (as there are no properties to make the comparison). Again, you've denied the Law of the Excluded Middle. No, you really need some way of reasoning with the empty set per what I said above, or else you drop the Law of the Excluded Middle. Which is fine, there is a logic without that Law, namely Intuitionistic logic. But I don't think you really want to go there. For any expression A the Law of the Excluded Middle states A v ~A. So every expression must be true or false. Otherwise you must assign some other truth value (neither true nor false) to some expressions (such as those involving the empty set, since every expression should be able to have some assignment, you could call the third state "vacuous"), but now you have three truth values (true, false, vacuous) and you've dropped the law of Excluded Middle since vacuous expressions don't satisfy A v ~A. The Law of the Excluded Middle requires a truth value be assigned to every expression in itself. This is how deduction works. If I give you the expression "{} is a subset of A", the Law of the Excluded Middle says I can say "either {} is a subset of A or {} is not a subset of A" and that this statement is true. But with a third truth value (vacuous) it isn't true any longer. The point of deductive logic is to create a system where every expression is either true or false and that there are methods of deduction that always reason from true expressions to true expressions. But, again, you are proposing a non-Boolean system. You can do it if you want to, but you are no longer doing classical logic. Okay you have the expression "either the light is on or the light is off", but there is no light. If you are in a Boolean system with the Law of the Excluded Middle, then the expression must be either true or false. If you don't want to work in a Boolean system with the Law of the Excluded Middle you can get the result you want. Again, you are proposing using a non-classical logic. This doesn't express the Law of the Excluded Middle. The Law of the Excluded Middle states that for any given property and any given object either the object has the property OR it doesn't have the property. The expression you gave would be derivable from the Law of the Excluded Middle in a Boolean system.
  6. Like I said, one really shouldn't use that notation for this sort of thing. It is too prone to misleading the user. It is better to go with a more typical formal notation like: Ax ~0(x) for the empty set. The real thing to use for a subset is what I gave: S' is a subset of S just in case Ax S'(x) -> S(x) That isn't exactly an easy sort of thing to express purely in the other notation. I guess in the other notation you'd have to say: given a set {x1,x2,x3,...} another set {y1,y2,y3,...} is a subset of the first just in case for every yn in the second there exists and xn in the first such that yn = xn. so if the second is not a subset of the first then there exists an yn, call it y, such that there is no xn such that y = xn. Now take the first and {}, then {} is not a subset of the first just in case there exists an element in {} which is not in the first. However there is no element in the {} that is not in the first (by virtue of the fact that there is no element in {}), so {} is a subset of the first. It really gets back to how a subset is defined. If one doesn't like that {} is the subset of any other set then one needs to redefine the notion of subset somehow. The result really follows from the definition. Hey, as long as we are at it, I could use an even simpler (and equivalent) definition of subset: B is a subset of A just in case A u B = A (think about it) So since we all agree A u 0 = A, then 0 is a subset of A. I thought this begged the result too much though. Unfortunately all the nonsense that has gone on has distracted from this simple (and interesting) fact. The question is can one come up with another definition of subset which doesn't lead to other (worse) problems than saying that {} is a subset of every set. I suspect that any other definition of subset is going to force one to have to give up the Law of the Excluded Middle. So you have a choice, the Law of the Excluded Middle or {} is a subset of every set. I needed it for a reference on a particular topic once. I only really used that one section though. It was for a graduate seminar on logic a decade ago, and I remember it had something to do with some result about some kind of "tree". I was probably using it to try to figure out something that wasn't clear in the assigned course readings. I remember finding it an awful reference though.
  7. We used Enderton for mathematical logic, Devlin for set theory, Boolos and Jeffrey for computation theory, and probably a lot of things I've long since forgotten about. I rather like Goldblatt for topos theory as it comes from a logician's view rather than that of an algebraic topologist. But I'm more the mathematician type and mathematicians assume a knowledgeable audience that can fill in the obvious blanks (it makes papers and books much easier to read). Anyway as you seem to be having problems with undergraduate logic: ~(Ax P1x -> P2x) Ex ~(P1x -> P2x) (i.e. ~Ax Px <=> Ex ~Px) Ex ~(~(P1x & ~P2x)) (i.e. ( a -> B ) <=> (~( a & ~B ))) Ex P1x & ~P2x (i.e. ~~a <=> a) This struck me as obvious. Well, being generous, you aren't as familiar with this all as you suppose, even if you can name drop Kleene. As I stated in my second proof the empty set is simply the set for which nothing is a member Ax ~0(x) I think you are confused by the straight set theoretic notation. It isn't too amenable to usage when nothing is denoted by a blank. Let us denote nothing by @ for lack of a better symbol. Then we can say {1} is equivalent to {1 @}. I mean after all just writing down a symbol for nothing doesn't do much of anything. However it is obvious that from {1 @} we can get subsets {1} and {@}. I mean formally {1}u{@} is just {1 @}. So {@} is a subset (that is {} is a subset). But this is confusing. It is better to go the way I did in my second proof and define the empty set by: Ax ~0(x) So it is just the set for which the statement "x is a member of 0" is always false. I'll use my psychic powers better next time around. And as indicated above, while I haven't read Kleene, I've read newer and better books.
  8. What I gave was a formal proof, schoolteacher. That was the typical sort of proof a working mathematican gives. Every word corresponds to an obvious symbol (assuming one has experience in higher mathematics that is). Do you want to argue about the issue at hand or do you want to play petty games? If there is a part of it you find unclear, then please specify which part that is. ... Well I had time so here is something more formal: using Ax for "for all x" Ex for "there exists x", and S(x) for "x is an element of S" - 1. We define a set S' to be a subset of a set S iff Ax S'(x) -> S(x) 2. So a set S'' is not a subset of S iff Ex ~(S''(x) -> S(x)) 3. That is S'' is not a subset of S iff Ex S''(x) & ~ S(x) 4. We define the empty set 0 to be the set with no elements, ie Ax ~0(x) 5. Suppose 0 is not a subset of a nonempty set S 6. Then Ex 0(x) & ~S(x), call this x 'y' 7. So 0(y) 8. But by 4 we have ~0(y) 9. =><= 10. Therefore 0 is a subset of S
  9. I'm fully aware of that. Given a set A we define a subset B of A by the usual convention as: B is a subset of A if and only if for every x in B x is in A. Suppose 0 is not a subset of A, then there exists an x such that x is in 0 but x is not in A. However by definition 0 has no members thus there is a contradiction. So 0 is a subset of A.
  10. On the contrary, I said what I said. That if you want to say that adding the empty set to a given set and get the original set back then you have to say that the empty set is a subset of the original set. Otherwise you will have a contradiction. I think you have given us a nice example of why people who don't understand what formal proofs are trying to achieve for the system taken as whole mistrust what they fail to understand. The point is to make sure that the entire system is consistent. The whole notion of the "empty set" is something that only makes sense within a formal system, and it only has meaning by virtue of that system. The fact is if you want to have a consistent system which also says that the union of any set with the empty set is the original set itself you are also going to have to say that the empty set is the subset of any set. Either one is going to imply the other. If you want to say that 0 is not a subset of any other set, then you have to say that A u 0 = A1 which is distinct from A, which goes against the entire notion of the empty set. If you say this you are saying that adding nothing to a given set somehow generates some member which isn't nothing. What you are proposing will lead to contradictions within the system. The fact is the statement that every set has the empty set as a subset is effectively a dual to the statement that the union of any set with the empty set yields the original set. ... Anyway this is all necessary if you want to work in some Boolean topos like Set (i.e. set theory). If you don't like it, you can always move to some non-Boolean topos that makes you happier, of course then you'll have to work with Heyting Algebras and Intuitionist logic. This will mean dropping the Law of the Excluded Middle though.
  11. You need to say the empty set is a subset of every set for consistency's sake. Now given two sets A,B take the union and call it C = A u B, so A is a subset of C and B is a subset of C. Let's use 0 for the empty set then C = A u 0 and A is a subset of C and 0 is a subset of C. But in this case C = A (as C and A have exactly the same elements), so A = A u 0. So the empty set must be a subset of A.
  12. Setting aside the question of whether acupuncture works, the fact is there are particular spots that must be used, and one must be trained to put the needle (or pressure if using acupressure) on the correct spot. The spots do correspond to clusters of nerves and a needle being put incorrectly into an acupuncture point will hurt a lot more than a needle being put incorrectly into a non-acupuncture point. Also, if you've ever had a sore and/or knotted muscle you will find that rubbing some points alleviates the soreness and helps undo the knot more than rubbing other points. These points are acupuncture points. So, no, a person can't just be sticking needles anywhere.
  13. I was talking with my friend who is an energy analyst, and he says there is a big debate among the analyst community as to whether it is a bubble. The feeling is that it would be due to the large amount of liquid capital that is floating around looking for places to make profits. For recent history the simplified view of events that effected the US would go like this: 1. In the late '90s there was the dot-com bubble driven by this liquid capital, the big shots were able to pull out before and during the collapse and had money on their hands to invest in ... 2. The real estate bubble of the '00s, and again the big shots were able to pull out before and during the collapse and had money on their hands to invest in... 3. The oil bubble. So it is all to say the price of oil is being driven by a large quantity of liquid capital looking for the highest rate of return, and finding that return by buying barrels of oil instead of real estate or dot-com stock. At least that is one side of the debate. Anyway, if this scenario is true one ought to be looking for the likely next bubble and get in on the ground floor.
  14. I'm not sure about the "deadly meme", but I do understand that the Mongols had quite a bit to do with the decline of Islamic civilization.
  15. All I said was that if one doesn't like a book one shouldn't read it. If one persists in reading a book they don't like, they should ask themselves why they are bothering to plod through. Is it simply to say they read it? Is it to impress people at cocktail parties? I mean why waste one's time doing something unpleasant? There is nothing in that about the intelligence of the reader, or the clarity of the writer. All that is going on here is Nietzsche wrote what he wanted to write, some people enjoy it and some people don't, and the people that don't enjoy it are making out like the people that enjoy Nietzsche (and Nietzsche) are engaged in some elaborate insult against them and their intelligence. Why?
  16. Why would you continue to read a book you aren't enjoying? If you don't like it, toss it aside and move on. It is what Nietzsche would want...and that wouldn't be an expression of contempt on his part. His attitude would be "look I wrote what I wanted to write and that is good enough for me...if you like it great, if you don't...pass on by and find what resonates with you". To some degree his whole corpus of writings can be summed up by the secondary title to "Ecce Homo" -> Become who you are We are who we are and we all spend too much of our lives trying to be someone else (part of the herd), and as a result we are unhappy. The problem is we are all hemmed in by social pressures and try to become this and that for all sorts of reason that have nothing to do with whether that is the person we really are. The superman is simply the person that has overcome all of this and lives for him or herself and ignores all those outside pressures. Nietzsche would basically say "look if you are reading me simply for the sake of being able to say you have read me, well, that is simply herd animal behavior" (although he'd say it better than that).
  17. Oh, I agree that there is all kinds of reasonable doubt. I think though that the post giving the case which characterized the situation as a guy sitting innocently by his car in a parking lot with keys in his pocket and waiting for a cab is unlikely to have been the actual entire situation. If this were the entire situation, then he'd have little to worry about as just about any lawyer could get a jury to acquit him (assuming he could afford a lawyer, but I think even a court appointed lawyer would have no problems with such a case either). I've noted though that when people are telling you about the time they got arrested, they tend to leave things out. My money would be with either the guy blabbed about driving, or someone reported his car to the cops.
  18. ยป It is my ambition to say in ten sentences what others say in a whole book. -Friedrich Nietzsche One should bear in mind that Nietzsche is compact and that he expects the reader to put the work into understanding him. He isn't going to spoonfeed the reader and has only contempt for readers that would expect to be spoonfed.
  19. I think the question in this case was whether the hood/engine was warm. If he was the only person near the car, had keys, and the hood/engine was warm, they have probable cause that he had been driving it recently. Even worse, if someone reported they saw the car driving poorly just a little earlier. What your post doesn't tell us is if he drove for a while and then decided he was too drunk, or never drove the car. Most DUI laws have provisions for cases where they can establish you were drunk now, and have driven the car in the recent past (I read about a case where people reported a car for wreckless driving, they went to the owner's house, found the car and found her drunk in the house...which was enough to bring charges). If he started to drive, changed his mind, parked the car and called a cab, they still have the case that he was driving before he changed his mind.
  20. Actually, having checked a grammar book, I can state that the only correct choices are "who" and "that", since the word "population" refers to people rather than things. "the tree which grew in the courtyard" "the man who gave the boy a book" "the population who/that would be at odds with each other" "Who" and "which" as relative pronouns may always be replaced by "that". That, and I was referring to former colonies in the Middle East as well as Africa, so your correction isn't quite right. The British and the French deliberately created territories with populations that didn't get along with each other to make it less likely they could try to throw off the colonial governments. Divide and rule.
  21. Yeah, Hegel suffers from the problem that most of the things people "know" about what he said, they get through Hegel's self-proclaimed followers. All too often then what people "know" about Hegel is what some follower of his said but that Hegel never asserted. But most famous thinkers suffer from the same problem (although Hegel's bad style makes it worse in his case).
  22. It occurs to me (unless I am mistaken) that "zero tolerance" DUI laws are applied to only people that are under the legal drinking age and are found to be driving. So you have the case that the individual has already violated the law by drinking at all and is compounding that by then driving. A quick search of the net seems to confirm that Arizona's "zero tolerance" law is one of these.
  23. First of all, remember that 0.08 BAC isn't even a legal limit in most places. Even in places that claim that is a limit they can charge you even if you have a lower BAC if the officer thinks you are "impaired". In Oregon you can't even get an arrest for DUI off your record even if you have end up having a BAC of 0.00 (and this has in fact happened to people). This is all really just neo-prohibitionism, and 0.08 is really a low number anyway. In fact, when it was lowered to 0.08 in states, they noticed that there was a bump in your typical responsible women getting arrested after long lunches.
  24. We should keep in mind that none of the countries that were originally arranged as European colonies and later gained independence make much sense at all. They were deliberately designed to contain a non-homogenous population that would be at odds with each other. Iraq, as with all these countries, is little more than a geographic designation, created without any reference to the human population. Iraq only worked when it was ruled by a dictator with an iron fist.
  25. Ah, my confusion, I thought that was what was being discussed here.
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