List of googolisms/Uncomputable numbers

Smaller numbers

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

Note: The special cases of the iota function and Hollom's number are not listed due to ill-definedness.

Busy beaver numbers
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, or related systems, given the condition that they will halt. They have growth rates of at least \(\omega_1^\text{CK}\) of the fast-growing hierarchy.


 * \(\Sigma(1,919)\)
 * \(\Xi(10^6)\)
 * Fish number 4, \(F_4^{63}(3)\)

Rayo numbers
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.


 * Rayo's number, \(\text{Rayo} (10^{100})\)
 * Fish number 7, \(F_{7}^{63}(10^{100})\)
 * BIG FOOT, \(\text{FOOT}^{10}(10^{100})\)
 * Little Bigeddon
 * Sasquatch / Big Bigeddon

Little Bigeddon is considered the largest valid googologism as of October 2017. Sasquatch is even bigger but the community currently cannot understand it.

Oblivion
Jonathan Bowers defined a number called "Oblivion", but the well-definedness is debatable, but if it was well-defined, it would be greater than all the previous numbers. Even larger is "Utter Oblivion".

Sam's Number
A user by the name SammySpore created a page called "Sam's Number", but the "number" described isn't defined, only "described". It is obviously not well-defined, but it remains as an in-joke among googologists.

Infinity
Infinity is not a number. It is not considered a googologism of any sort, and googologists don't like people messing with it in googology. However, transfinite ordinals (a set-theoretic type of "infinity"), are sometimes used to index functions.

Eternity
Eternity is not a number. It is not considered a googologism of any sort, and googologists don't like people messing with it in googology. However, transfinite ordinals (a set-theoretic type of "eternity"), are sometimes used to index functions.

Tranquility
the quality or state of being tranquil; calm.

Zillion
an extremely large number of people or things.

"we had zillions of customers"

Limited
restricted in size, amount, or extent; few, small, or short.

Unlimited
not limited or restricted in terms of number, quantity, or extent.

"the range of possible adaptations was unlimited"

Infinite
limitless or endless in space, extent, or size; impossible to measure or calculate.

Indefinitely
for an unlimited or unspecified period of time.
 * to an unlimited or unspecified degree or extent.