List of numbers

This is a list of googolisms in ascending order.

This list contains ill-defined large numbers, e.g. BEAF numbers beyond tetrational arrays, BIG FOOT, Little Bigeddon, Sasquatch, and large numbers whose well-definedness is not known, e.g. large numbers defined by Taranovsky's ordinal notation and Bashicu matrix number with respect to Bashicu matrix system version 2.3.

This page (the main list) lists the more notable googolisms on each class; click the "More..." link at the end of each section to see more googolisms in that class.

Tier 0 (0 >= x < 6)
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Class 1 (7 - 1,000,000)
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Class 2 (1,000,000 - \(10^{1,000,000}\))
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Class 3 (\(10^{1,000,000} - 10^{10^{1,000,000}}\))
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Class 4 (1010 1,000,000 - 103*10 3*10 3,000,000 +3 )
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Class 5 (103*10 3,000,000+3 10↑↑6)
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Tier 6 (10↑↑6 googolplexgoogolplex-1 googolplex-2 ... 4 3 2    )
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Up-arrow notation level (googolplexgoogolplex-1 googolplex-2 ... 4 3 2    \(q(6)\) (lower bound))
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Linear omega level (\(q(6)\) (lower bound) {10,10,10,{10,10,10,10}})
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Quadratic omega level ({10,10,10,{10,10,10,10}} {3,{3,3,3}(1)2})
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Polynomial omega level ({10,10,10,10,{10,10,10,10,10}} {3,{3,3,3}(1)2}
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Exponentiated linear omega level ({3,{3,3,3}(1)2} {10,10,10,10,{10,10,10,10,10}})
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Exponentiated polynomial omega level ({10,xappol (2) 2} {10,10 (gongulus) 2})
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Double exponentiated polynomial omega level ({10,10 (gongulus) 2} s(3,3{1`2}2))
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Triple exponentiated polynomial omega level (s(3,3{1`2}2) E100#^#^#^#^##100)
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Iterated Cantor normal form level (E100#^#^#^#^##100 E100#^^#100#2)
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Epsilon level (E100#^^#100#2 E100(#^^##)^^#100)
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Binary phi level (E100(#^^##)^^#100 E100(#^^^#)^^^#100)
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Bachmann's collapsing level (E100(#^^^#)^^^#100 200![1(1)[2200,200,200,200,200]])
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Higher computable level (200![1(1)[2200,200,200,200,200]] \(\Sigma(1919)\))
Since the comparison (or even the well-definedness) of numbers of this level is unknown, the order of entries does not necessarily imply the order of the sizes. Also, several numbers are defined by an OCF, which is uncomputable, and are not known to be computable.

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Uncomputable numbers (\(\Sigma(1919)\) ∞)
The term "uncomputable number" here refers to the numbers defined in terms of uncomputably fast-growing functions. This table contains large numbers which are known to be ill-defined. For more details on the ill-definedness, click the "More..." link below.

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