User blog comment:Boboris02/MBOT/@comment-30004975-20161217225325/@comment-30118230-20161218175206

No,No and No.

1.This does not start the Berry paradox!

The case is much more different.In the case of

"the smallest number that cannot be defind in one million words",we have a number that supposedly cannot be described in one million words and is somehow described in just eleven.

In my case it's "The largest number describable in a million symbols using Phi systems."

It uses Phi systems,which are independent of words.It cannot be described in less than a million symbols using Phi systems,but it is describable in just eleven words.That does not lead to a contradiction.

2.No,the function NOOP isn't describable in phi systems,because it diagonalises over them.

It's definition is very similar to that of Rayo's number and BIG FOOT,but using phi systems instead of FOST and FOOT.

So asking "Is NOOP function descibable in phi systems?" is like asking "Is Rayo's function describable in FOST?".

The reason why it's not describable in phi systems is because it is the diagonalizer of them and you can't have Phi systems describing phi systems.

3.No it cannot "trump everything else".I do realize I made a mistake saying "Phi systems can represent every possible function" and I will change that in the blog.However you didn't understand me correctly.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 don't know them.What I meant is that with given enough symbols Phi systems can create virtualy any finite number.That sounds very impressive at first but when you think about it,it really isn't.Almost all functions do that.If I told you that using the simplest of functions:f_0(n),I can define a number bigger than Rayo's number,would you believe me?

Well here it is:f_0(BIG FOOT) = BIG FOOT+1 > Rayo's number.

For any function F for which F(n) > n | there exist n for which F(n) > m / for any m

This is really,very simple.