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Megafuganine is equal to $$9\uparrow\uparrow9$$ or 9 tetrated to 9 or 9 pentated to 2.[1] It is approximately equal to $$\textrm E369,693,100\#7$$ in Hyper-E notation.

Its exact value can be simplified (sort of) with laws of algebra, just like with Tritet Jr.:

$$9\uparrow\uparrow9 = 9^{9^{9^{9^{9^{9^{9^{9^{9}}}}}}}} = 9^{9^{9^{9^{9^{9^{9^{387,420,489}}}}}}} = 9^{9^{9^{9^{9^{9^{3^{774,840,978}}}}}}} = 9^{9^{9^{9^{9^{3^{2\times3^{774,840,978}}}}}}} = 9^{9^{9^{9^{3^{2\times3^{2\times3^{774,840,978}}}}}}}$$

$$= \ldots = 3^{2\times3^{2\times3^{2\times3^{3^{2\times3^{2\times3^{774,840,978}}}}}}}$$

The name is formed by adding the megafuga- prefix to 9.

## Approximation

Notation Approximation
Arrow notation $$9\uparrow\uparrow9$$
Fast-growing hierarchy $$f_3(9)$$
Hardy hierarchy $$H_{\omega^3}(9)$$
Slow-growing hierarchy $$g_{\varepsilon_0}(9)$$
Steinhaus-Moser Notation $$(9-1)[4]$$ lower bound $$9[4]$$ upper bound
Strong array notation s(9,9,2)
Bowers Exploding Array Function $$\{ 9, 9, 2\}$$
Bird's array notation $$\{ 9, 9, 2\}$$
Hyperfactorial array notation $$9!1$$ lower bound $$(9+1)!1$$ upper bound
Chained arrow notation $$9\rightarrow9\rightarrow 2$$

## Sources

1. Saibian, Sbiis. 3.2.2 - The Fz, The Fuga & The Megafuga - Large Numbers. Retrieved 2017-03-10.