User blog comment:Kite in rainbow/A weak and clear version of my Bracket-Comma notation ver2,it reaches Γ(0)/@comment-5529393-20160120132153

As far as I can see, the line:

(4)Let X is an element of BS,X≠φ,n=n(X),every X(i) is LBS.

means that every element of BS is in LBS. If A is in BS, then B = [A] is in BS, and so B(1) = A is in LBS, no matter what A is.

I can't parse the line:

If the biggest i s.t. X(n) doesn't belong to S(X(i)) exists and satisfy 0>>X(n) belongs to S(X(i)).

nor the line:

Define Y(0)=X([1,i-1]),Y(1)=X([1,n-1]),Y(i+1)=Y(i),[m+i>>X(n)]X([i+1,n-1]) for any positive integer i.

Also, you talk about an undefined BCS in:

If for any i belongs to N we have Y(i) is LBS,then X is BCS and i>>X=Y(i) for any i belongs to N.

This sounds like it might be interesting but you really need to clean up the article.