File:Hyperoperation 3 and 3 with real number.svg

DescriptionHyperoperation 3 and 3 with real number.svg	中文（臺灣）：函數 ${\displaystyle f(n)=3[n]3}$ ${\displaystyle =3\uparrow ^{n}3}$ 的繪圖 圖中展示了3與3的各種超運算結果 以及超運算不是整數的結果
Date	9 November 2014, 16:09:13
Source	Own work
Author	A2569875
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圖中展示了一些特定值，例如在:

${\displaystyle f(1)=3\uparrow ^{1}3=3+3=6}$

${\displaystyle f(2)=3\uparrow ^{2}3=3\times 3=9}$

${\displaystyle f(3)=3\uparrow ^{3}3=3^{3}=27}$

${\displaystyle f(4)=3\uparrow ^{4}3={^{3}3}=3^{3^{3}}=7625597484987}$

${\displaystyle f(5)=3\uparrow ^{5}3={^{^{3}3}3}={\begin{matrix}\underbrace {{3^{3}}^{{\cdot }^{{\cdot }^{{\cdot }^{3}}}}} \\3^{3^{3}}\end{matrix}}}$

可以對其他超運算進行估計，例如:

加法為1、乘法為2，則:${\displaystyle f(1.5)=3\uparrow ^{1.5}3\approx 7.3}$為介於加法、乘法之間的運算

乘法為2、冪為3，則:${\displaystyle f(2.5)=3\uparrow ^{2.5}3\approx 11.2}$為介於乘法、次方之間的運算

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