matt grime

Please reconsider postingin mathematics if you have no intention of asking a question about the subject that makes any sense.

Just install latex. It's free and easy, I'll even send you a latex fine template to edit and you can play around with it to your heart's content, so stop whining about wanting a test pad here (which is called the preview button; I've no idea why that is not sufficient for you, and that is after reading your posts). So, get latex (TeTex for linux, Miktex for windows, forget the names for others), and grab a hold of emacs, also free. C-c C-c b and look at the out put. Or if you must use one of those wisywig things that some people seem to think are useful (they're not). (g)vi(m) is probably better for latex these days but it's a steep learning curve on that one, though probably worth it (`g auto-expands \gamma for instance), where as emacs is newbie tolerant.

Grime, more prevalent in Northern England (also as Grimes) than the south, a corruption from the Scandinivian Grimm, literally meaning masked, referring to Odin's disguised forms in nature. Features in place names such as Grimsby, Grimethorpe, etc, and cognate with Grimm, Grimes, Grimley, Grimbley amongst others. For what it's worth, Matt, short for Matthew, means Gift of Jehovah, so I think I have a reasonable claim on the most 'deific' name around.

Several things spring to mind. 1. What on earth does 'some' mean, as in 'some number theory'. Fermat's Little theorem? Roots of polys over F_P? 2. How is anyone else supposed to know what your *local* education rules are about transcripts in *your* school? Why don't you ask someone who has a chance of actually knowing?

What have you done for one? how have you tried to use the hypothesis?

assuming all things being equal, then the winnner is picked at random from all those who got the most entries. of course the number of entries therefore affects the probability you win. the more who enter, the more who get most right, etc. obviously oscars are more predictable than random, so who can say if you've even got a chance at all; it is eminently likely someone got 9/9, and we can't tell the likelihood of that wihtout some random sampling to predict the answer. we could of course work out some conditional probabilities based upon all this, and some assumptions of randomness, but in any such case with only 700 entries and random chances then you're almost certain to win, and that is unlikely to be an accurate representation of the real odds.

How many combinations of what are there?

so you didn't understand what you read but you felt safe to dismiss it? on what grounds? pray do show us some evidence of a prior prediction of an event. actually don't. at least don't bother in a maths forum. put it where someone might care.

why would we care? we are after all only talking about maths here. what has this to do with anything at all? consistent with what? your opinion of what they *ought* to be? perhaps you ought to reconsider what mathematics is and/or does.

How many minimum observers will be required to make purple porridge? More nonsense....

Unless they mean something as trivial as the integer part of 2.6 plus in the integer part of 2.6 is less than the integer part of (2.6 plus 2.6) but the entire debate is pointless, meaningless and silly unless the OP deigns to tell us what he/she is talking about.

Well, what are you talking about? If you can't at least explain what it is you're talking about then no one esle can even begin help. What forum are you referring to where this discussion takes place? Who are the particpants? In what vein is this discussion taking place?

Well, I'm also not sure that I would label what was called mathematics pre1800 as mathematics as we now know it either.

It is a proof, of the way logs convert mult to addition, based upon the definition of what log is.

Not sure I condone the assertion that Kepler was a mathematician.

That is questionable. I'm not sure a refusal to comply with a demand made instantly after 9/11 without corroborating evidence constitutes a declaration of war. However waiting longer would not have sated the understandable (see end to note that understanding is not the same as condoning) desire for instant justice. There are uncorroborated reports at least as far as I can tell that since the hand over would not have been to an Islamic Court then it would never have happened. I wonder what might have happened if a request to be tried in such a court had been made? since you are later going to ask me for corroboration, perhaps here I can also ask for you to state what 'significant number' is in terms of proprtion, or absolute terms, and what evidence there is that that is correct? and pre 9/11? my enemy's enemy is my friend. the main parties are divided along religious grounds. http://www.peacewomen.org/news/Sept03/fight.html http://www.peacewomen.org/news/Iraq/July04/marked.html for my 'odd opinion', which isn't even mine, that women in Iraq have traditionally been given a relatively large amount of freedom. That is not to say Hussein didn't curtail those freedoms (he certainly did), but that it is entirely conceivable that in the current climate of religiosity that the democratic government may curtail them even more. We can only hope that the groups reported in that link are successful and that the conservatives do not win out here. That is not a very accurate representation of what I said. I said that under Hussein it is conceivable that women had more rights than they might perhaps be allowed in the immediate future. You do notice the conditionals there, right? Well, the first has nothing to do with what I said. Certainly the US in the 80s aided and abetted freedom fighters in Afghanistan (one of whom was Bin Laden) when under soviet occupation. As I was pointing out, it is important to see this in context as more than 'post 9/11'. The second is not necessarily a fact (again, as you ask for corroboration, where is a survey backing this up). and did I say otherwise? Bettina said that public beheadings sickened her, quite rightly, yet I believe she supports the death penalty. I could be wrong there, but that is the impression I get. However, I do not think that the death penalty is remotely justifiable in any circumstances. Yes, i withdraw the Iran comments, though this part: should also apply to you: where is your evidence for the things you've asserted as fact? All I was trying to do was point out that an 'unpopular' pro-US, US installed leader (the shah, who pronounced himself 'king of kings') who was overthrown by what has become the clerical leadership of Iran might be a historical explanation for some of the anti-americanism of that country. The US also supported materially Iraq during the Iran-Iraq war. That would be another factor. And possibly could lead to an entire thread on 'the irony of western diplomatic relations'. 'Unpopular' meaning 'sufficiently to be overthrown' by one of several factions. Excuse me? When did I say Al-Qaeda received support? To repeat myself, the CIA supported freedom fighters in Afghanistan during the Soviet occupation, one of whom was Bin Laden. Hamas won 76 of 132 seats on 77% turnout (bbc news). I don't know if it's a PR system or a first past the post system. in either case it is not a given that the majority of those eligible to vote in Palestine supported Hamas. Nor is it necessarily clear that those who support Hamas support all of their views, or if it were a disenchantment vote with the other parties. It is certainly a myth that the elected officials in any country actually represent the majority of all views. The IRA are part of the power sharing arrangements in Northern Ireland. They were part of a terrorist organization too (and I'm sure that many Unionists would be of the opinion they still are, but that cuts both ways). Margaret Thatcher declared Nelson Mandela to be a terrorist. General Pinochet was allowed to return to Chile after being arrested in the UK for war crimes. Our moral ambiguity in the west is troubling. What time scale are we talking here? The biblical one? Or the one that saw that founding of Isreal by the Balfour treaty? Iran has over the years faced attacks from Iraq (who were supported by the US and the British: supergun scandal and everything), and I don't imagine being labelled as part of the axis of evil helped. Of the other two countries named in the state of the union under that label: Iraq has been invaded; North Korea is under little threat of that. One has nuclear weapons one doesn't. There is no moral justification for anyone having nuclear weapons, but there certainly seems to be a practical rationale (again, see the end note on the difference between understanding and condoning). And given the West's current problems with allegations of torture by our allies (particularly in Uzbekistan I think, where the British ambassador was removed for voicing concerns or having an affair, whichever seems most likely) implying that somehow most Arab countries are worse than us on human rights is disingenuous. We turn a blind eye when it helps us. Again, you're taking this out of context, this is not a moral judgement, or one about what we should do to counteract something. The threat to your life (in the West) from a terrorist attack is not significant; there are fatal incidents that are far far more likely to happen. This was not a moral judgement on anything, merely a statement of likelihood of dying from something. Given the statistics of the last year I am approximately 60 times more likely to die in a car accident than from a terrorist attack in the UK (going with the 52 v 3000 number). Why should I be more afraid that I'm going to be attacked by a terrrorist more than that I will be mown down on the highstreet? It doesn't make sense. I didn't draw one. But, since we condone by acceptance the governments of China, Saudi Arabia, Libya (yes, even they are now 'ok') amongst other countries with questionable human rights, any moral absolutism argument is moot. I don't see what the appellation of 'islamic' has to do with anything. Is a non-islamic dictatorship somehow acceptable? Pakistan is an ally in the war on terror and it has an unelected military leader, too. And nuclear weapons. What are we to do now? Some we support, some we don't. This is far too complicated for such simplistic assessment as 'they are evil'. A lot of the posts in this thread seem to make very simple assertions, sweeping ones, about a very complicated situation with many nuances. Even Bush and Blair go out of their way to pointout the problem is not with Islam, and the Islamic groups in the UK condemn terrorism. Were there many (catholic) Irish-American groups condemning the IRA during the 70s and 80s, and there was plenty of support in parts of America for them. Does that mean we should have labelled all of catholicism and america as you wish to label islam and islamic communities? That is not duplicity. It is a refusal to do something. Blair is now claiming some kind of moral post-event justification for ousting Hussein that is completely at odds with his preinvasion words. He is being duplicitous. He is now saying he was evil and had to be removed (no argument there) but previously said he could stay in power. Had Blair made the moral (and illegal) argument for going to war that Hussein needed to be removed because he was a genocidal maniac then I suspect he would have had the support of many of us who have been long time opponents of dictatorships. Once more someone confuses 'understanding' with 'condoning'. It is perfectly possible to 'understand' what's going on in the sense of see why someone else might hold the opinion that they do without actually supporting that opinion. I would suggest 'they hate us' not for our freedoms to wear skimpy clothing and buy macdonalds, but because our actions, or inactions, our double standards have created feelings that have been exploited by those preaching a credo (that has historically been attractive to people, eg Hitler and the feelings he built upon of 'betrayal of Germany at Versailles') of 'we're the victims, it is their fault' with catalyst of being able to claim (wrongly) a religious justification for their actions. It is a heady and dangerous mixture of power and misinformation. And I do not believe that imprisoning people without trial (for example) is going to convince anyone who thinks that way that we have any moral highground.

then I trust you are actively seeking the overthrow of all non-democracies, including those the western governments ships their prisoners to under extraordinary rendition. I was not saying that there was no threat from terrorism, but that the threat is minimal of you actually being killed. You face bigger risks than this every day and do not unduly concern yourself with them. There is no reason to be afraid of this anymore than anything else. These people are a tiny number. And, if you read the other follow up by aardvark, this is not a claim of morality, merely statistics, cold impartial statistics. That doesn't mean one should not do anything about it, merely that being afraid of their actions is not necessary. Perhaps I can treat the threat lightly because I grew up with the IRA.

You also have the order the wrong way round. You must specify your list first, then I get to pick something not on it, and you can't alter the list after you specify it to take my choice into account.

I don't believe Afghanistan declared war on the US either literally or metaphorically. Nor do I believe that the problem is with the entire religion, though there is apparently evidence that many Americans conflate the two terms terrorist and muslim. But many Americans are alleged to conflate Hussein with 9/11 too. I hope that is just urban myth. Incidentally, Bin Laden would have been opposed to the regime of Hussein too since it was secular. Women in Iraq held positions of power (they still do, though when the new government forms and is strongly theocratic, as it inevitably will be, that might set back some of the rights and freedoms we supposedly support), and benefited from many freedoms that are alien to those in countries in the middle east that are considered partners of the west. They, meaning the pilots, presumably, were principally Saudi Arabian (like Bin Laden), not Afghanistanis. The reasons for the attack are far more complicated than that. The last one, bikini clad women, is clearly not something that all followers of Islam have a problem with. Look at Dubai if you don't believe me. As I said, Bin Laden is Saudi, not from Afghanistan. He was not the mastermind of the Taliban, though they certainly refused to hand him over after repeated requests by the US and in defiance of the UN. It is unclear to whom your pronoun 'they' pertains, it appears to shift continually from being Al-Qaeda, the Taliban, those specifically taking part in the attack on 9/11 and the nation of Afghanistan. Don't you feel that is a little rash to brandish an entire religion based upon the actions of some people who during the 1980s were supported by the US government? From briefly scanning this thread I seem to be under the impression that you condone the death penalty, too. There is no 'moral' way to kill someone, and an 'immoral' one with the death penalty, surely. Ah, Iran, which was (hopefully) going to be a model of democracy in the middle east until in 1953 the US decided to support the installation of a theocratic dictatorship, which led in the late 70s to the overthrow by the Muslim clerics and arguably saw the start of the modern fomenting of anti-American sentiment in the middle east. It cost Carter the election, and led to Reagan taking power and creating the underpinnings of what we now call Al-Qaeda, but was then an anti-soviet freedom fighting group supported by the CIA (Bush Snr of course was head of the CIA, though I don't know if the time scales agree). Ill thought out intervention has a way of biting back. The PLO agreed to support the existence of an Isreali state, currently Hamas is refusing to honour this pledge. So some Palestinians are not committed to wiping Israel off the map. Please try to bear the moderates in mind. Attempts to meddle in the Middle East and impose certain western views by force are one of the things that has led us to this current problem. Plus Isreal has nuclear weapons, something they tried to hide, and even now after 'releasing' him from prison after 18 years (11.5 in solitary confinement) they keep attacking the civil liberties of the man who revealed their existence, Mordechai Vanunu. 52 were killed in the attack. As a comparison, 13 people were killed in the Bloody Sunday shooting [source: freely available information, just one of those things you know]. In 1990 35,000 people died in an earthquake in Iran, 15,000 are estimated to have died in another earthquake in Iran in 2003 [source bbc news]. 3,000 people die per day in motoring accidents, 3,500 people per year in the UK [http://www.roadpeace.org/pr/hollowv.html] Perhaps you are worrying abuot the wrong thing if it is fear of attack that concerns you. 'The West', if that is even a meaningful phrase has a long and checkered history of intervention and double standards in the Middle East. As an example look at the duplcity of Blair in making the case for war with Iraq. As late as Feb 2003 he asserted to the House of Commons that Hussein would be allowed to stay in power if he handed over any WMD and complied with the UN resolution 1441. Now he is making claims of moral necessity to remove him since there are no WMD.

It is hard to begin with, everyone finds that. well, at some level proofs are just manipulating symnbols, but the meaning of the symbol tells you what manipulations are permissible. I think that went withou saying. That is difficult since there is no one way to prove something, or to write its proof out. Experience is the best thing I can suggest. Just keep doing them, practising them. Try writing out some of the proofs from the book and decide what they're doing at each step. Valid assumptions take one of two forms. The hypothesis specifically tells you you are allowed to assume something OR the assumption is clearly true and needs no justification. Example: Show that an integer is a perfect square if and only if all its prime factors occur with an even exponent. So there are two things to do here (if and only if). I must show each condition implies the other. Suppose that all prime factors have an even exponent, ie suppose [math]n=p_1^{2e_1)\ldots p_t^{2e_2}[/math] then [math]n=(p_1^{e_1}\ldots p_t^{e_t})^2[/math] so it is a perfect square. Here I used the assumption given to me by the question. I also used the incredibly important and much over looked fact that the statement: m is an even integer is equivalent to m=2k for some integer. Now, that is only one way in the implication, now I must go the other way. So, suppose that n is a perfect square, ie n=m^2, and if m is the unique product [math]m=p_1^{e_1}\ldots p_t^{e_t}[/math] then n has the required properties of its prime decomposition. Here I am assuming the prime number theorem, that every decomposition of an integer into the product of primes is essentially unique.

The most obvious error is that you do not produce a list of all possible strings of 0s and 1s. All of your strings are ones that are eventually either all 1s or all 0s. The string 10101010101.... will appear no where in your list. (Try to tell me where on the list it is. It must be at some finite position, but at any position in the list so produced all of the digits after some point are either 1 or 0.) What you have here is the fact that the finite power set of N is countable, as is the cofinite power set of N, and that is not surprising, but neither of those, nor their union are the same as the power set of N. This is the standard thing that people get wrong when trying to find a flaw in this proof.

I have no idea what his first proof was. Now, you've twice said you have a problem with this particular proof (I can think of two or three more if you want, well, now i've said that i'm not so sure; there is an analysis proof lurking in the back of my mind) so what is your problem with this proof? "just this particular proof seems wrong" Why? "I'm objecting to the way it was proven above " Again, why? All that is is a nice way of visualizing what the construction of the set: {t in T : t not in f(t)} where f is any injection from T to P(T)

There is/was a tv quiz show called catch phrase in the UK, and possibly elsewhere too. The host's advice was to 'say what you see'.

So what is your counter argument? That is a standard proof for Cantor's argument that there is no bijection between N and P(N), since P(N) is in bijection with the strings of binary digits indexed by N: these are just parametrizations of indicator functions.

that also makes no sense. but nothing you have written meets the requirements of being a logical mathematical argument. the only response is: that makes no sense. erm, no that is no-one's definition of the real numbers. the real numbers have been defined for you several times in this thread, if you choose to ignore that, that is your fault. we can thus see that what is at fault is your understanding of maths, not maths itself. not that there was any doubt about that. the rest of your post makes even less sense, but since you aren't even getting the definition of the real numbers correct it is immaterial.