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Googol-stack is equal to $$10\uparrow\uparrow(10^{100})$$ in up-arrow notation.[1] It is also known as a googolgoogolplex.[2] It is equal to a power tower of a googol tens.

Sbiis Saibian calls this number googologue, and it's equal to E1#10100 using Hyper-E notation.[3]

Aarex Tiaokhiao and Username5243 call this number googolduex.[4][5] Aarex Tiaokhiao also calls this number Giggolplexin-Googol.[6]

## Etymology

The name "googol-stack" comes from the -stack suffix which, when applied to a number x, turns it into $$10 \uparrow\uparrow x$$.

## Approximations in other notations

Notation Approximation
Up-arrow notation $$10 \uparrow\uparrow(10 \uparrow 100)$$ (exact)
Chained arrow notation $$10 \rightarrow 10^{100} \rightarrow 2$$ (exact)
BEAF $$\{10,\{10,100\},2\}$$ (exact)
Hyper-E Notation $$\textrm{E}100\#1\#2$$
Hyperfactorial Array Notation $$(70!)!1$$
Fast-growing hierarchy $$f_3(f_2(324))$$
Hardy hierarchy $$H_{\omega^3+\omega^2}(324)$$
Slow-growing hierarchy $$g_{\varepsilon_{\omega^\omega}}(100)$$

## Sources

1. Sbiis Saibian's Ultimate Finite Numbers List Part I
2. Saibian, Sbiis. 4.3.2 - Hyper-E Notation - Large Numbers. Retrieved 2016-07-18.
3. Username5243. Part 1 - My Large Numbers. Retrieved 2017-02-25.
4. Tiaokhiao, Aarex. Aarex's Googology - SAN. Retrieved 2021-06-06.