• Mush9

    First Magnarth

    February 1, 2017 by Mush9

    So, I'm working on a new number - one which will hopefully be large.

    We will assume syntax is clear from the context, context, yet more context and that an amateur googologist will not need to have everything explicitly defined but instead referenced (i.e. mentioning Godel encoding).

    Firstly, we will define a function to Godel encode a sentence in FOST + Magnarth: \(\texttt{en}(\cdot)\). We will define the alphabet \(A\), for the encoding, as so:

    \(A = \{\langle=\rangle,\langle\in\rangle,\langle\forall\rangle,\langle\wedge\rangle,\langle\neg\rangle,\langle(\rangle,\langle)\rangle,\langle\texttt{mg}\rangle,\langle,\rangle,\langle\{\rangle,\langle\}\rangle\} \cup \bigcup_{n

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  • Mush9

    IRC Schedule

    December 23, 2016 by Mush9

    Mention me if you see Mush9.

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  • Mush9

    KING function

    December 19, 2016 by Mush9

    This blog post will define the KING function. Eventually.

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  • Mush9

    NOOP function

    November 11, 2016 by Mush9

    \(\text{NOOP}(n)\) = largest natural number output from either some uncomputable function U, defined in n symbols or less of NOOP notation, for U(n) or n;

    NOOP - No Obvious OutPut

    The difficulty is to ensure as little symbols of possible exist in NOOP notation, which create the most number of meaningful expressions and fast-growing functions. Notably, if someone can construct an expression in NOOP notation equal or stronger than what the FOOT notation details, then the length of that expression, which we can call n, will be the upper bound of the point at which the NOOP function dominates the FOOT function.

    i.e. \(\text{NOOP}(n) ≥ \text{FOOT}(n)\)

    My first impression is that \(\text{n ≈ 1000}\) in this case, but we'll have to see.

    NOOP Notation:

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  • Mush9

    I think it would be good to have a central space for numbers beyond BIG FOOT - or rather, functions which eventually dominate the FOOT function. Specifically - don't use any previously existing functions that are uncomputable to build up i.e. don't say FOOT^1000(10^10^100) your number. Ensure it is well defined, or say that it is not. Make sure that you at least lead to something.

    Current idea:

    See here

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