[baddox]

That doesn’t sound right, because “BB(k) plus 1” is larger than BB(k) and has fewer than k characters for sufficiently large k.

[dandanua]

What you say is a Berry paradox. To be consistent we fix a programming language before any such definitions. So you have to count all characters in the BB(k) subprogram. Hence the total program for “BB(k) plus 1” definitely will have more than k characters.

[baddox]

I don't think my example (for example, "BB(11111) + 1") demonstrates the Berry paradox. The original comment "the biggest non-infinity namable number in k characters" is the Berry paradox, which is what I was pointing out.

[shouyatf]

That's why I say 'roughly'. Natural language is very vague and easy to be used to create illogical self-referential statements.