10,974 Pages

The corporal is equal to $$\{10,100,1,2\} = 10\{\{1\}\}100$$ (10 expanded to 100) in BEAF.[1] It surpasses Graham's number (roughly equal to $$\{3,65,1,2\}$$), and is currently the smallest Bowersism that does so. The term was coined by Jonathan Bowers.

Bowers jokingly says about this number, "lets [sic] just put it this way, you DON'T want the Corporal coming up to you asking for a corporal push ups" on his "Size 4 Arrays" page.[2]

It is equal to $$10[1,1]100$$ in Username5243's Array Notation, and Username5243 calls this number a Kil-Googol (formerly Meg-Googol).[3]

## Computation

Corporal can be computed in the following process:

• $$a_1 = 10$$
• $$a_2 = 10 \uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow\uparrow 10$$ (this is tridecal).
• $$a_3 = 10 \uparrow\uparrow\uparrow\uparrow\cdots\uparrow\uparrow\uparrow\uparrow 10$$ with $$a_2$$ $$\uparrow$$'s.
• $$a_4 = 10 \uparrow\uparrow\uparrow\uparrow\cdots\uparrow\uparrow\uparrow\uparrow 10$$ with $$a_3$$ $$\uparrow$$'s.
• etc.
• Corporal is equal to $$a_{100}$$.

## Approximations

Notation Approximation
Bird's array notation $$\{10,100,1,2\}$$ (exact)
Hyper-E notation $$E10\#\#10\#100$$
Chained arrow notation $$10 \rightarrow 10 \rightarrow 100 \rightarrow 2$$
Notation Array Notation $$(10,10,100\{3,3\}2)$$
Hyperfactorial array notation $$100![2]$$
X-Sequence Hyper-Exponential Notation $$10\{X+1\}100$$ (exact)
Strong array notation $$s(10,100,2,2)$$
Fast-growing hierarchy (using CNF's fundamental sequences) $$f_{\omega+1}(99)$$
Hardy hierarchy $$H_{\omega^{\omega+1}}(99)$$
Slow-growing hierarchy $$g_{\Gamma_0}(99)$$

## Sources

1. Bowers, JonathanInfinity Scrapers. Retrieved January 2013.
2. Size 4 Arrays
3. Username5243. shortened list - My Large Numbers. Retrieved March 2017.