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Super K is equal to $$10 \uparrow\uparrow\uparrow\uparrow 3$$ with arrow notation defined by Donald Knuth in his lecture "God and Computer Science", which is part 6 in the "God and Computers" lecture series, which is transcribed in the book Things a Computer Scientist Rarely Talks About.[1][2] Knuth's point with showing Super K is that "infinity is a red herring", since natural language can't describe the difference between infinity and a large finite number like Super K. Super K is equal to $$10 \uparrow\uparrow\uparrow$$ by using fancy K.

Sbiis Saibian calls this number tria-petaxis (formerly tria-petaksys, also called dekataxia-taxis), and it is equal to E1#1#1#3 = E1#1#(E1#1#10) in Hyper-E Notation.[3]

Username5243 calls this number toodcolplex or tetootol, and it's equal to 10[3]10[3]10 = 10[4]3 in Username5243's Array Notation.[4]

BlankEntity calls this number taupillion.[5]

## Approximations in other notations

Notation Approximation
Hyper-E notation E1#1#1#3 (exact)
Chained arrow notation $$10 \rightarrow 3 \rightarrow 4$$ (exact)
BEAF $$\{10,4,3\}$$ (exact)
Hyperfactorial array notation $$5!3$$
Fast-growing hierarchy $$f_4^2(10) \approx f_5(3)$$
Hardy hierarchy $$H_{(\omega^4) 2}(10)$$
Slow-growing hierarchy $$g_{\zeta_{\zeta_0}}(9)$$

## Sources

1. Donald Knuth. Things a Computer Scientist Rarely Talks About Center for the Study of Language and Inf. 2001. pp.171-176, 188, 192, 202. ISBN 1-57586-326-X
2. 3Suns's post at everything2 2002-03-05.
3. Saibian, Sbiis. Hyper-E Numbers. Retrieved 2015-03-25.
4. Part 1 - My Large Numbers
5. BlankEntity's Googology - Up-arrow notation level Retrieved 2024-09-07.

Note: The readers should be careful that numbers defined by Username5243's Array Notation are ill-defined as explained in Username5243's Array Notation#Issues. So, when an article refers to a number defined by the notation, it actually refers to an intended value, not an actual value itself (for example, a[c]b = $$a \uparrow^c b$$ in arrow notation). In addition, even if the notation is ill-defined, a class category should be based on an intended value when listed, not an actual value itself, as it is not hard to fix all the issues from the original definition, hence it should not be removed.