About: Fish number 5   Sponge Permalink

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Fish number 5 (F5) is a number defined by Japanese googologist Fish in 2003. It is one of Fish numbers. Fish function 5 uses m(n) map. Definition and growth rate of Fish function 5, \(F_5(x)\), is \begin{eqnarray*} F_5(x) & := & ((..((m(x)m(x-1))m(x-2))...m(2))m(1))(x) \\ F_5(x) & \approx & f_{\varepsilon_0}(x) \end{eqnarray*} Then Fish number 5 is defined as: \[F_5 := F_5^{63}(3)\] Therefore, Fish number 5 is greater than Fish number 3 and is approximately \(f_{\varepsilon_0+1}(63)\).

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  • Fish number 5
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  • Fish number 5 (F5) is a number defined by Japanese googologist Fish in 2003. It is one of Fish numbers. Fish function 5 uses m(n) map. Definition and growth rate of Fish function 5, \(F_5(x)\), is \begin{eqnarray*} F_5(x) & := & ((..((m(x)m(x-1))m(x-2))...m(2))m(1))(x) \\ F_5(x) & \approx & f_{\varepsilon_0}(x) \end{eqnarray*} Then Fish number 5 is defined as: \[F_5 := F_5^{63}(3)\] Therefore, Fish number 5 is greater than Fish number 3 and is approximately \(f_{\varepsilon_0+1}(63)\).
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abstract
  • Fish number 5 (F5) is a number defined by Japanese googologist Fish in 2003. It is one of Fish numbers. Fish function 5 uses m(n) map. Definition and growth rate of Fish function 5, \(F_5(x)\), is \begin{eqnarray*} F_5(x) & := & ((..((m(x)m(x-1))m(x-2))...m(2))m(1))(x) \\ F_5(x) & \approx & f_{\varepsilon_0}(x) \end{eqnarray*} Then Fish number 5 is defined as: \[F_5 := F_5^{63}(3)\] Therefore, Fish number 5 is greater than Fish number 3 and is approximately \(f_{\varepsilon_0+1}(63)\).
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