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  • Billybob-mario

    Many Googological functions are based on up-arrow notation and related concepts, which stems from using exponents. But wouldn't it be possible to use the same systems with a more powerful base function, even an uncomputably powerful one? For example, you can define a function that is equivalent of up-arrow notation, but for FOOT.

    LEG{1}(a, b) = FOOT^b(a)

    LEG{n}(a, b) = FOOT^(LEG{n-1}(a, b-1)) (a)

    Then, equivalents of functions based in up-arrow notation can be defined using LEG, and so on.

    Hyperrecursion of uncomputable functions seems like a pretty powerful thing.

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  • Billybob-mario

    They say great X is built on the shoulders of giants. That includes big numbers, and Meameamealokkapoowa oompa qualifies. So of course I had to start by making Meameamealokkapoowa oompa loompa, the obvious first step. Then I came up with an idea that would be much bigger and harder to solve, forming Gigoombaverse. Then I turned that into a function. But now I have a new idea, which will have many repeats and be very recursive and very big. (as in Gigoombaverse ~= 1 big).So beware!!!!!!

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