User blog comment:Googleaarex/SGH Functions/@comment-5029411-20130406231045/@comment-1605058-20130407082808

When alpha is limit ordinal (i.e. non-zero, non-succesor), then alpha-1 simply doesn't exist. If we define alpha+1 to be order type corresponding to augmenting order type of alpha by element >alpha, then alpha-1 would be order type with largest element deleted, which for limit structures doesn't exist (by definition).