Finite questions

Question

Are there a finite number of questions that can be asked regarding a specific language (and or topic), for example - for T-SQL given that there are only so many commands, can there be a limited number of non-repetitive questions? and if so can you use that to determine sizing for a site like stackoverflow and to determine the probability of a new question being a repeat of a prior one? If there is a finite number, how would you determine/calculate it: for instance, T-SQL has x number of commands, each one can have a set of relevant questions (syntax, example of use, etc.) - so could the # of questions = x times potential questions time some relevant variation? or something like that?

Answer 1

A stack overflow question is expressed as a finite length sequence of bytes. One could in principle consider the question body in terms of an integer, expressed lowest digit first, in base 256 (or larger, if you wish to think about it as unicode). This is a bijection between questions and whole numbers. Therefore the set of all stack overflow questions has a countably infinite cardinality (How do i typeset \aleph_0 in SO?).

Answer 2

No, since, theoretically, programs can be of infinite length, and this site is not just about language commands, but programs developed with those languages.

Answer 3

I'm pretty sure Turing says no, and if you don't believe him them Gödel might have something to say about it.