User:Numspan33/sandbox

ListNav This is a list of googolisms in ascending order.


 * 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.
 * Googolisms in bold are numbers with peer-reviewed source.
 * Googolisms in italics are ill-defined and their placement within this page is reflective of their intended value, assuming them to be well-defined. This list contains ill-defined large numbers, e.g. BEAF numbers beyond tetrational arrays, BIG FOOT, Little Bigeddon, Sasquatch, Oblivion, Utter Oblivion, 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.

Class 0 (0 - 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 (\(10^{10^{1,000,000}}\) - \(10^{10^{10^{10^{1,000,000}}}}\))
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Class 5 (\(10^{10^{10^{10^6}}}\) - \(10^{10^{10^{10^{10^6}}}}\))
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Tetration level (\(10^{10^{10^{10^{10^6}}}}\) - \(10 \uparrow\uparrow\uparrow 3\))
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Up-arrow notation level (\(10 \uparrow\uparrow\uparrow 3\) - \(f_\omega(f_3(10))\))
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Linear omega level (\(f_\omega(f_3(10))\) - \(f_{\omega^2}(f_3(10))\))
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Quadratic omega level (\(f_{\omega^2}(f_3(10))\) - \(f_{\omega^3}(f_3(10))\))
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Polynomial omega level (\(f_{\omega^3}(f_3(10))\) - \(f_{\omega^\omega}(f_3(10))\))
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Exponentiated linear omega level (\(f_{\omega^\omega}(f_3(10))\) - \(f_{\omega^{\omega^2}}(f_3(10))\))
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Exponentiated polynomial omega level (\(f_{\omega^{\omega^2}}(f_3(10))\) - \(f_{\omega^{\omega^\omega}}(f_3(10))\))
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Double exponentiated polynomial omega level (\(f_{\omega^{\omega^\omega}}(f_3(10))\) - \(f_{\omega^{\omega^{\omega^\omega}}}(f_3(10))\))
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Triple exponentiated polynomial omega level (\(f_{\omega^{\omega^{\omega^\omega}}}(f_3(10))\) - \(f_{\omega^{\omega^{\omega^{\omega^\omega}}}}(f_3(10))\))
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Iterated Cantor normal form level (\(f_{\omega^{\omega^{\omega^{\omega^\omega}}}}(f_3(10))\) - \(f_{\varepsilon_0}^2(10)\))
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Epsilon level (\(f_{\varphi(1,0)}^2(10)\) aka \(f_{\varepsilon_0}^2(10)\) - \(f_{\varphi(2,0)}^2(10)\) aka \(f_{\zeta_0}^2(10)\))
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Binary phi level (\(f_{\varphi(2,0)}^2(10)\) or \(f_{\zeta_0}^2(10)\) - \(f_{\varphi(1,0,0)}^2(10)\) or \(f_{\Gamma_0}^2(10)\))
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==Bachmann's collapsing level (\(f_{\varphi(1,0,0)}^2(10)\) or \(f_{\Gamma_0}^2(10)\) - \(f_{\psi_0(\varepsilon_{\Omega+1})}^2(10) = f_{\psi_0(\Omega_2)}^2(10)\) with respect to the Buchholz's function)==

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Higher computable level (\(f_{\psi_0(\varepsilon_{\Omega+1})}^2(10) = f_{\psi_0(\psi_2(0))}^2(10)\) with respect to Buchholz's function - ???)
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
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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