 The image of "n" under the fundamental sequence for α will be indicated by α["n"].A variation of Cantor normal form used in connection with the Veblen hierarchy is — every nonzero ordinal number α can be uniquely written as formula_10, where "k">0 is a natural number and each term after the first is less than or equal to the previous term, formula_11 and each formula_12 If a fundamental sequence can be provided for the last term, then that term can be replaced by such a sequence to get formula_13

For any β, if γ is a limit with formula_14 then let formula_15

No such sequence can be provided for formula_16 = ω0 = 1 because it does not have cofinality ω.For formula_17 we choose formula_18

For formula_19 we use formula_20 and formula_21 i.e.