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The goppatothplex is equal to $$10 \uparrow\uparrow \text{goppatoth} \ \&\ 10$$ using the array of operator. The term was coined by Jonathan Bowers. [1] It is Bowers' last well-defined number as tetrational arrays are the last well-defined part of BEAF.

It can also be written as $$\lbrace10,10(((...(((0,1)1)1)...)1)1)2\rbrace$$ with $$\frac{\text{goppatoth}}{2}$$ pairs of parentheses.

### Approximations

Notation Approximation
Bird's array notation $$\{10,\frac{\text{goppatoth}}{2} [1 \backslash 2] 2\}$$
Extended Cascading-E notation $$\textrm{E}10\#\text{^^}\#101\#2$$
Hyperfactorial Array Notation $$(101![1,1,1,1,2])![1,1,1,1,2]$$
Fast-growing hierarchy $$f_{\varepsilon_0}(f_{\varepsilon_0}(100))$$
Hardy hierarchy $$H_{\varepsilon_02}(100)$$
Slow-growing hierarchy $$g_{\vartheta(\varepsilon_{\Omega+\vartheta(\varepsilon_{\Omega+1})})}(100)$$

### Sources

1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.