Wedge of Cheese

Wedge of Cheese

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  • cultr1
    ...I have tried to decipher your signature for half an hour, with no result.
    It sounds like a spambot on drugs.
    Care to elaborate?
    Lace
    A girl's finger got ripped off today in school.
    furthermore, if g(x) = f(x) - f'''(x), how can I define f(x) in terms of g(x)?
    Lace
    SO:
    f(x) = f(0)x^0/0! + f'(0)x^1/1! + f''(0)x^2/2! + f'''(0)x^3/3! + ...
    if f(x) = f'(x), this is [;\sum_{i=0}^{\infty}\frac{x^{i}}{i!};] = e^x.
    Where f(x) = f'(x), it means that this is equal to two separate summations, one with all the even values of i (2i) and one with all the odd values of i (2i+1). due to the nature of the series, these summations will be each others derivatives, AND e^x - one of the summations will be the other summation.

    So g(x) (one of the summations) = e^x-g'(x)
    You can algebra this down to ae^x + (b-1)g'(x). As ye pointed out earlier, g(x) is prettily equal to sinh(x) (or cosh(x)), so any function that is its own second derivative is of the form:

    s(x) = ae^x + (b-1)cosh(x)
    or in this case: asinh(x) + bcosh(x)

    Getteth?
    GIRakaCHEEZER
    It was originally planned to be the final boss theme WAY back, but now that perfecta has taken that spot no, it won't be featured in any mod I'm making.
    Lace
    g(x) = e^x-g'(x)

    f(x) = ag(x) + bg'(x)
    f(x) = a(e^x-g'(x)) + bg'(x)
    f(x) = ae^x - ag'(x) +bg'(x)
    f(x) = ae^x + (b-a)g'(x)

    g'(x) = x^0/0! + x^2/2! + x^4/4! + x^6/6! ...
    so basically a way to rewrite g'(x). IT should be able to be in terms of e^x or sin(x) methinks.


    prettymode:
    [; f(x) = ae^x+(b-a)\sum_{i=0}^{\infty}\frac{x^{2i}}{(2i)!};]
    Lace
    It be LaTeX.
    :P

    Get the extension and it makes maths pretty.


    Anyways, it means that f(x) is its own nth derivative. I gived it unto ye cause I can't find a way to write it not in sums. There are n+1 constants that determine the shape of the function, but the simplest case (all constants equal to one) is [;e^x;] for all values n.
    Lace
    not if and is merely a concatenator.

    Also, looky.
    [;f(x) = \sum_{i=0}^{n}(c_i \sum_{m = 0}^{\infty}(\frac{x^{nm+i} }{(nm+i)!}));]
    Lace
    MAC stands for MAC and CHEESE.
    Therefore, it can be expanded to MAC and CHEESE and CHEESE, MAC and CHEESE and CHEESE and CHEESE, MAC and CHEESE and CHEESE and CHEESE and CHEESE, etc.

    When infinitely expanded, it would be one MAC and infinite cheeses, rationally, this means that MAC is one infinith of the whole, and CHEESE is the rest.
    MAC = (1/∞)MAC + (1-1/∞)CHEESE
    1/∞ = 0

    MAC = CHEESE

    We are the same person.
    QED.
    sexplosive
    fan art
    WoC.png
    Noxid
    Good luck with that. I've been collecting music from that site from time to time on account of I like pretty much all their stuff, would you like me to hook you up with a pack of about 144 songs?
    Lace
    Wictory!
    Comps back working. Still on my mom's tho cause its only half assembled.
    As for storyline, I dunno. As far as my game development binges go, I usually approach it from one of two directions. Either I focus on gameplay, or focus on story. On this one, I obviously had a gameplay idea first, but I love storylines, so when you came up with a concept that could fit them, I sprung for it. I really won't know till I work on it tho, will I?

    as far as working-on-it timeline goes, who knows. I really need to finish the album art, I got some homeworks, etc, (and I might program it in something > gm) so no idea, which stinks. I'll definitely be able to do it the day I get my wisdom teeth out, where I'm on vikanen the whole day. might make some interesting levels, too. mmmm.

    yeh, 45 second timer.
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