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bloodhound

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Posts posted by bloodhound

  1. Evidently no continuous function will do as any continuous image of a compact set is compact' date=' and I think that is your problem with trying to figure this out.

     

    Existence proof:

     

    consider the maps i:[0,1'] to R the inclusion and j:R to [0,1] which is the composition of the inverse tan function, which maps R bijectively with (-pi/2,pi/2) followed by adding pi/2 to map it to (0,pi) bijectively, followed by dividing by pi. j is an injection from R to [0,1] thus we have injections between the two sets and hence there exists some bijection by cantor-schroeder bernstein.

     

    writing one directly.

     

    notice that we can easily get a bijection between (0,1) and R using the tan trick. so we just need one from [0,1] to (0,1) and that is the standard trick:

     

    map 0 to 1/3, 1/3 to 1/5, 1/5 to 1/7 etc .....

     

    map 1 to 1/2, 1/2 to 1/4, 1/4 to 1/6...etc

     

    leave x fixed if x has not been mentioned

     

    this is a bijeciton from [0,1] to (0,1)

     

    Thanks a lot! I must warn you that I will probably swamp this board with questions on Algebra and Topological spaces in the coming days. :rolleyes:

    Meanwhile, I'll go read up on the cantor schroeder bernstein theorem. I just hope it's not too complicated.

  2. Define [math]\Lambda(n):=\log(p)[/math] if n is a power of a prime p

    and 0 if n = 1 or n is a composite number

     

    Prove that [math]\Lambda(n)=\sum_{d|n}\mu(\tfrac{n}{d})\log(d)[/math]

     

    The hint says to look at [math]\sum_{d|n}\Lambda(d)[/math] and apply the Mobius inversion formula.

     

    So far I have got [math]\sum_{d|n}\Lambda(d)= \sum_{i=1}^r \log(p_i)= \log(\prod_{i=1}^r p_i)[/math]

    assuming that n has r distinct primes in its expansion.

     

    So help :)

     

    Don't mind the above, I have figured it out. I will post more questions if any in this thread instead.

  3. talking about sp2, it limits the number max number of outbound connections attempts per second from infinity (almost) to 10. You can still use a patch to change it back, cos that might affect the performance of swarm p2p like bittorrent.

  4. yeah. for example. http://www.piratebay.org is one of the biggest trackers around. and they have a special page for the legal threats they have got and their replies. note: in sweden bt trackers are still legal.

     

    http://thepiratebay.org/legal.php

     

    my fav one being

    Dear Mr. Neij:
    >
    > It has been brought to the attention of Electronic Arts Inc. ("EA") that
    > the website http://www.piratebay.org with the IP addresses of
    > 217.75.120.115, 217.75.120.116, 217.75.120.118 is conducting
    > unauthorized activities with respect to EA's copyrighted software, The
    > Sims 2.  The aforementioned website is offering and distributing
    > bittorrent seeds for an unauthorized downloadable version of this EA
    > game.
    >
    > The infringing material may be found at:
    >
    > http://www.piratebay.org/download.php/3238103/Sims%202.torrent
    >
    > http://www.piratebay.org/download.php/3238222/The_Sims2_AlcoholClone-CLO
    > NEGAME_Full.Release_%28exclusive_for_trackerwww.prq.to%29.torrent
    >
    
    Hello and thank you for contacting us. We have shut down the website in
    question.
    
    Oh wait, just kidding. We haven't, since the site in question is fully
    legal. Unlike certain other countries, such as the one you're in, we have
    sane copyright laws here. But we also have polar bears roaming the
    streets and attacking people .
    
    
    > This unauthorized activity with respect to the distribution of EA's
    > software products constitutes infringement of EA's intellectual property
    > rights. EA enforces its intellectual property rights very aggressively
    > by using every legal option available.
    
    Please don't sue us right now, our lawyer is passed out in an alley from
    too much moonshine, so please atleast wait until he's found and doesn't
    have a huge hangover...
    
    >
    > As you are listed as the registrant for this website, EA demands that
    > you immediately and permanently disable access to the aforementioned
    > bittorrent seeds for The Sims 2 and any in the future.
    
    You're free to demand anything you want. So are we. We demand that you
    cease and desist sending letters like this, since they're frivolous and
    meaningless. Where should I send the bill for the consumed diskspace and
    bandwidth?

     

    It's not easy to go after each seeder. And in UK ISP's don't give out customer details that easily.

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