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    Asymptotes as the lines y=x an y=-x

    Thanks for the help guys :D My head of department was so sure you could each of the 4 sections between the said asymptotes filled with a curve. Using what the first two posts said, I drew the graphs of y = sqrt(1+x^2) y = -sqrt(1+x^2) x = sqrt(1+y^2) x = -sqrt(1+y^2) to get what...
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    Asymptotes as the lines y=x an y=-x

    Hi there. I'm a maths teacher and today was having a discussion with my Head of Department about asymptotes (as you do!) She was me if I could think on an equation of a graph(s) which has an asymptotes at the line y=x and another at y=-x. Thinking about it, neither of us could come up...
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    Killing form of a Lie algebra

    Yes, I think it does make it clear now. I sort of got it a few minutes ago as I was making a post on this subjec tover on Science forums and debate. I remeber doing a hell of a lot of work on this sort of thingback in my topology course last year, only I'd some how temporarilly put it out of my...
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    Killing form of a Lie algebra

    I am feeling really dumb here, as I'm sure all this is not too difficult, I'm just sure I am missing something that makes it all fit into place. Why are we ending up with 3x3 matrice to describe the transformation? Is it becasue we have a 3 dimensional Lie algebra? Is it possible to get a...
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    Killing form of a Lie algebra

    OK, firstly I hope this is the rigth place for my question. I'm in a bit of a problem. I need to be able to calucalte the Killing for for a Lie algebra by next wek, but I'm stuck and won't be able to get any help in 'real life' until Friday, not leaving me enough time to sort out my problem. So...
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    News UK election.

    I certainly hope that Labour win the election again and I think that they are the only party who can possible win out right. However, I have no idea what exatly will happen on the day as to how many seats anyone can get. It could turn out that Labour have an even bigger majority, though very...
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    Center of a Lie algebra

    Thanks. :biggrin: I thought it was right, but I just couldn't quite convinse myself...I thought it was quite obvious... :grumpy:
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    Center of a Lie algebra

    OK, can someone please tell if 0 (zero) would belong to the center of a Lie algebra. By center I mean for a Lie algebra L center(L) = { z in L : [z,x]=0 for all x in L} I think it should, but I'm not too sure...I'm surely confusing myself somewhere along the line, as this shouldn't be...
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    What a homeomorphism means

    From my topology course we were given the definition that 2 spaces were homeomorphic if there exists a continuous bijective map with a continuous inverse btween the two spaces. So yuo need a continuous, reversable transfomation from on space to the other, that is, if you can "convert one space...
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    Mathematics and unprovable assumptions

    I wasn't quite sure what I should call this, so I hope the tile is OK. Now over the weekend I've on on a general message board where I saw the ideas of mathematics and religion being discussed. The connection with religion is not what I'm interested here, but rather the following sentence...
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    Where did this formula come from?

    With out working out a fair few calculations analysing the results I don't see any way to work out this formula from scratch (there probably is an easy way without working out examples, maybe I've even seen it, but I don't remeber any :frown:). But proving it is easier. You need to use...
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    7 iso and hom questions

    Unless I'm the one to have missed something, then you are the one that is wrong. In (2) we a function f: Z ---> Z where f(n) = 2n. For this map to be an isomorphism from Z to Z we need it to be surjective. That is fro any integer y in Z we have an x in Z such that f(x) = y. Since f maps only to...
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    7 iso and hom questions

    The second on is not an iso. since it is not surjective. Take, for example, 1 in Z. If (2) was surjective, then we could find an n in Z such that 2n = 1. In otherwords we need n=0.5 which is not in Z. So not surjective and so not an iso. (7) is quite straight forward. Let a, b be in G...
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    News Condoleezza Rice named as Bush's nominee for new Sec. of State. Good god

    I've read this thread and a few people seem to think this isn't possible, but I've heard the Hilary-Rice idea from several places now. They are for a start the 2 most high profile of all the possible candidates I've heard are in the running. Their actions over the next couple of years will se...
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    How to find automorphism?

    I'd have thought f(x)= -x is a automorphism from Z to Z. But given what has been said here I have tried to figure out why it isn't one, but with no sucess.... :confused: