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Buddy's Ordinal is well, an ordinal. It can be described with ƒ. So how do we describe it? It would be like the wheel that was on ƒ. Heres a print of the first layer, |

The symbol is a Delta, even though its in math kinda.

The first layer.

The next layer, " has the ƒ and ʆ on the corners and | on the top with -| on the bottom. This continues with every layer (layer 3 would be " on top, | and ʄ would be on the corners, and the ƒ on the sides, with -| and the others would be ) Repeat this ƒ times. You will get Δ.

First 10 Layers with some infinites

Set 0: α, Wuf

Set 1: |, Goq

Set 2: ", Loe

Set 3: §, Eol

Set 4: ⌐, Efr

Set 5: ß, Rfe

Set 6: ╝, Ghe

Set 7: ╣, Ehg

Set 8: ∟, Kiw

Set 9: ¥, Wik

Set 10: |α, Goqwuf

Set : ╠, Ets'wuf

Set : ╘, Ets'goq

The aleph numbers are Ets'[number of set]

(Another way to name it is Dalt)

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