| Property | Value |
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| rdfs:label | |
| rdfs:comment | - Fish number 3 (F3) is a number defined by Japanese googologist Fish in 2002. It is one of the seven Fish numbers. Define s(n) map as: \begin{eqnarray*} s(1)f & := & g; g(x)=f^x(x) \\ s(n)f & := & g; g(x)=[s(n-1)^x]f(x) ( ext{if }n>1) \end{eqnarray*} where s(n) is a functional, and the growth rate in FGH is \begin{eqnarray*} s(x)f(x) \approx f_{\omega^\omega}(x) \end{eqnarray*} ss(n) map is defined as: \begin{eqnarray*} ss(1)f & := & g; g(x)=s(x)f(x) \\ ss(n)f & := & g; g(x)=[ss(n-1)^x]f(x) ( ext{if }n>1) \\ \end{eqnarray*}
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| dcterms:subject | |
| dbkwik:googology/property/wikiPageUsesTemplate | |
| abstract | - Fish number 3 (F3) is a number defined by Japanese googologist Fish in 2002. It is one of the seven Fish numbers. Define s(n) map as: \begin{eqnarray*} s(1)f & := & g; g(x)=f^x(x) \\ s(n)f & := & g; g(x)=[s(n-1)^x]f(x) ( ext{if }n>1) \end{eqnarray*} where s(n) is a functional, and the growth rate in FGH is \begin{eqnarray*} s(x)f(x) \approx f_{\omega^\omega}(x) \end{eqnarray*} ss(n) map is defined as: \begin{eqnarray*} ss(1)f & := & g; g(x)=s(x)f(x) \\ ss(n)f & := & g; g(x)=[ss(n-1)^x]f(x) ( ext{if }n>1) \\ \end{eqnarray*} and the growth rate is \begin{eqnarray*} ss(1)f(x) = s(x)f(x) & \approx & f_{\omega^\omega}(x) \\ ss(n)f(x) & \approx & f_{\omega^{\omega+n-1}}(x) \end{eqnarray*} Definition and growth rate of Fish function 3, \(F_3(x)\), is \begin{eqnarray*} F_3(x) & := & ss(2)^{63}f; f(x)=x+1 \\ F_3(x) & \approx & f_{\omega^{\omega+1} imes63}(x) \end{eqnarray*} Finally, \begin{eqnarray*} F_3 := F_3^{63}(3) \approx f_{\omega^{\omega+1} imes63 + 1}(63) \end{eqnarray*}
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