12/01/2014, 11:55 PM
2^^w = the first inaccessible ordinal.
This is because 2^x = x is not accessible and 2^^w is the smallest such x.
w^^w = 2^(ln(w) 2^^w) = 2^^w = the first inaccessible ordinal.
2^^(2^^w) = the second inaccessible ordinal.
2^^(2^^w) = 2^^(w^^w) = w^^(w^^w).
Pentation
w^^^w = the w th inaccessible ordinal.
Simple.
regards
tommy1729
the master
This is because 2^x = x is not accessible and 2^^w is the smallest such x.
w^^w = 2^(ln(w) 2^^w) = 2^^w = the first inaccessible ordinal.
2^^(2^^w) = the second inaccessible ordinal.
2^^(2^^w) = 2^^(w^^w) = w^^(w^^w).
Pentation
w^^^w = the w th inaccessible ordinal.
Simple.
regards
tommy1729
the master
