User blog comment:B1mb0w/Fundamental Sequences/@comment-1605058-20151104112933

Few points:


 * 1) You did not specify at all what is meant with $$>>$$.


 * 1) This definition is ambiguous, e.g. it gives two distinct FSs to $$\omega^2+\omega$$. On one hand, $$(\omega^2+\omega)[n]=\omega^2+\omega[n]=\omega^2+n$$. On the other hand, $$(\omega^2+\omega)[n]=((\omega^2+1)+\omega)[n]=\omega^2+1+\omega[n]=\omega^2+1+n$$.