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The aardillion is equal to 0[0,0,1] = 0[0,1000] in the Extensible Illion System[1]. The term was coined by Nirvana Supermind. It is equal to the 1000th tier-999 illion in Bower's system. See also the issue of the difference of the intended values and the actual values of the Extended Illion System.

## Etymology

The name of this number is based on the substitute Omnibase digit root aard, which is derived from the word aardvark, and the suffix -illion. The normal root alf was not used because it could be confused with alphillion.

## Approximations

A reader should be careful that the following table is just the approximation of intended values without a source or a proof, as the creator explains the values of the Extensible Illion System in inconsistent ways.

Notation Expression
Up-arrow notation $$10 \uparrow (1000 \uparrow\uparrow 998 + 3)$$
Chained arrow notation $$10 \rightarrow (1000 \rightarrow\rightarrow 998+3)$$
H* function H999(1000)
BEAF $$\{10,\{1000,998,2\}+3\}$$
Munafo's ASCII-lexicographic ordering p998_e3000_3
Fast-growing hierarchy $$f_{3}(998)$$
Hardy hierarchy $$H_{\omega^3}(998)$$