User blog comment:Boboris02/MBOT/@comment-30004975-20161217225325/@comment-30754445-20161219011158

As long as you withdraw the claim of "MBOT can represent any function", there is - indeed - no paradox.

"What I meant is that with given enough symbols Phi systems can create virtualy any finite number"

Are you sure that was the exact claim you meant to make? Because that statement is trivially true for any system that includes addition. Any number can be created as 1+1+1+1+.... with enough 1's.

"Some Phi systems need a lot more symbols to generate the same number that another function would require to generate.So there are functions stronger than NOOP, we just dont know them."

We do know of at least one such function: F(n) maps n to "the largest number definable in MBOT with n symbols or less". :-)