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# Mush9

• I live in the world.
• I am Male
• ## 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 Read more > • ## IRC Schedule December 23, 2016 by Mush9 Mention me if you see Mush9. Read more > • ## KING function December 19, 2016 by Mush9 This blog post will define the KING function. Eventually. Read more > • ## 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:

• ## Beyond BIG FOOT (ideas in comments)

November 6, 2016 by 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