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Tetralogue is equal to E1#4 = EEEE1 = 10101010 using Hyper-E notation.[1][2] The term was coined by Sbiis Saibian. It is equal to a one followed by a trialogue (ten trillitrestrigintatrecentillitrestrigintatrecentilliduotrigintatrecentillion) zeros. It is also equal to 10^^4 in up-arrow notation.

Writing down the full decimal expansion would take 109,999,999,994 books of 400 pages each, with 2,500 digits on each page.

Username5243 calls this number goodcolduplex or dooquol, and it's equal to 10[2]4 = 10[1]10[1]10[1]10 in Username5243's Array Notation.[3]

## Etymology

The name of this number is based on Greek prefix "tetra-" and the suffix "-logue" for "logarithm".

## Names in -illion systems

In the short scale, it is also called:

ten trimilli-3,333,333,332 times-trestrigintatrecenmilli-duotrigintatrecentillion

## Approximations in other notations

Notation Approximation
Up-arrow notation $$10 \uparrow\uparrow 4$$ (exact)
Down-arrow notation $$10 \downarrow\downarrow (10^{10}+1)$$ (exact)
Chained arrow notation $$10 \rightarrow 4 \rightarrow 2$$ (exact)
Steinhaus-Moser Notation $$10[3][3][3]$$
Copy notation $$9[9[9[10]]]$$
Notation Array Notation $$(10\{2,2\}4)$$ (exact)
BEAF $$\{10,4,2\}$$ (exact)
Bashicu matrix system $$(0)(1)(0)(0)[427]$$
Hyperfactorial array notation $$((13!0)!0)!0$$
Nested Factorial Notation $$13!^3$$
Fast-growing hierarchy $$f_2(f_2(f_2(28))))$$
Hardy hierarchy $$H_{(\omega^2) 3}(28)$$
Slow-growing hierarchy $$g_{\omega^{\omega^{\omega^\omega}}}(10)$$ (exact)

## Sources

1. Saibian, Sbiis. Hyper-E Numbers. Retrieved 2014-11-16.
2. Saibian, Sbiis. Ultimate Large Numbers List Part I. Retrieved 2014-11-16.
3. Part 1 - My Large Numbers