User:Vel!/pu/My BEAF/old

''Note: this is the old version, and will no longer be updated. Go to this page for a new one.'' It is not widely agreed how BEAF should work past tetrational arrays. The trouble is there is no way to progress from X↑↑X to X↑↑(X+1), the same reason ω↑↑(ω+1) is undefined.

Up to X^^^X
This is relatively simple. Let's redefine X↑↑(X+1) = XX↑↑X = (X↑↑X)X. Then exponentiation is defined like normal. We get to X↑↑2X, which has the ordinal ε1.

Then X↑↑(2X+1) = XX↑↑2X = (X↑↑2X)X. In general this happens every time the tower height is a limit ordinal