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List of googologisms/Uncomputable numbers

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Smaller numbers

The term "uncomputable number" here refers to the numbers defined in terms of uncomputably fast-growing functions.

Note: The special cases of Oblivion, Utter Oblivion, the Iota function, and Hollom's number are not listed due to questionable well-definedness.

Busy beaver numbersEdit

These numbers arise from functions that eventually dominate all computable functions, and are based on the unsolvability of the halting problem. They exploit the maximum scores of a particular Turing machine given the condition that they will halt. They have growth rates of at least \(\omega_1^\text{CK}\) of the Fast-growing hierarchy.

Rayo numbersEdit

These numbers diagonalize over nth-order mathematical theories: Rayo's function diagonalizes over first-order set theory, and the derived FOOT function diagonalizes over nth-order set theory. They are currently the largest well-defined named numbers in professional mathematics.

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