User blog comment:Boboris02/MBOT/@comment-30004975-20161217225325/@comment-30118230-20161218130506

\(\Delta_x\) means the largest possible Phi system definable in x symbols or less.

\(\Delta_x[n]\) = the largest number definable in n symbols or less in that system.

So you need x symbols to define \(\Delta_x\) and n symbols to define the number.

So you need x+n symbols in total.

NOOP(n) = \(\Delta_n[n]\)

You need 2n symbols to define NOOP(n)