Utter Oblivion

Utter Oblivion is allegedly the largest googologism coined by Jonathan Bowers. It is defined as "the largest finite number that can be uniquely defined using no more than an Oblivion symbols in some K(oblivion) system in some K2(oblivion) 2-system in some K3(oblivion) 3-system in some K4(oblivion) 4-system in some .........KOblivion(Oblivion) Oblivion-system where the number oblivion can be represented with one symbol (byte).", where a Km(n) m-system is an arbitrary well-defined system of mathematics that can generate K(m-1)(n) (m-1)-systems and which can be uniquely described in at most n symbols and a K1(n) system is an arbitrary well-defined system of mathematics which can be uniquely described in n symbols.

It was created to be absolutely larger than BIG FOOT, as Bowers (allegedly) feared that the 10 in its definition (which simply means recursion) may have referred to something like "start with a K(10,000) system then find a maximum number MK(10,000) then use a K(MK(10,000)) system and repeat it 10 times", which would have made BIG FOOT larger than Oblivion. On the other hand, BIG FOOT turned out to be ill-defined, and hence this comparison does not make sense.

As with its smaller counterpart, it is doubtlessly ill-defined because it is not formalised.

See also

• Busy beaver function
• Rayo's number
• BIG FOOT
• Xi function
• Bowers Exploding Array Function
• Oblivion
• Jonathan Bowers

Sources

Uncomputable numbers

Busy beaver numbers (based on Turing theories): \(\Sigma(1919)\) (1919th busy beaver number) · Fish number 4 · \(\Xi(10^6)\) · \(\Sigma_{\infty}(10^9)\)
Rayo's numbers (based on Set theories): Rayo's number (Rayo(10¹⁰⁰)) · Fish number 7 · BIG FOOT (FOOT¹⁰(10¹⁰⁰)) · Little Bigeddon · Sasquatch · Large Number Garden Number
Miscellany: Hollom's number · Oblivion · Utter Oblivion · (Ultimate Oblivion)