User blog comment:Denis Maksudov/Second M-notation/@comment-24920136-20160610211858/@comment-28606698-20160611135036

Thanks for comment,  Chronolegends,

Yes, but we can slightly enhance notation

During M-notation creation (08.06.16) next idea visited me

Let f_0 (a)=a+1

Let, for example, in the end of first step of i-cycle we reached level

 θ(Ω_(Ω_(Ω_(…a Ω' s…._(Ω_Ω ) .... )

(this is the limit of Chris Bird notation)

What if

〖f_0 (a)〗_1 =f_(θ(Ω_(Ω_(Ω_(…a Ω' s…._(Ω_Ω ) .... )) (a)

and

〖f_0 ( 〖f_0 (a) 〗_1 ) 〗_1 =f_(θ(Ω_(Ω_(Ω_(…〖f_0 (a)〗_1     Ω' s…._(Ω_Ω ) .... )) (a)

I mean to take a function, which was reached at the end of step, and apply  this in  most sensitive place of the function itself.

<p class="MsoNormal" style="margin-bottom:0.0001pt;">And same way do for all other external cycles.