User blog comment:Ikosarakt1/Extensions of Catching function/@comment-25418284-20131119195520/@comment-1605058-20131119201156

I think getting-off-the-ground can be defined by this: if a>b then, for suffiscently large n, f_a(n)>f_b(n). This ensures us that f_1 will eventually be at least 1, f_2 at least 2, etc., so f_w will be unbounded, f_w+1 eventually larger etc., just like in SGH.