# If set of TM's is not countable?

I was reading about counting principle related to TOC. I understand that the set of TMs are countable infinity. I couldn't understand the significance of it. What is its not countable?

• This question is incomprehensible. What is TOC? Presumably theory of computation. The title is not a real question. – Andrej Bauer Jan 13 '13 at 11:31
• I agree, it is hard to understand what the actual question is. Please edit your language. – Raphael Jan 14 '13 at 20:36

The number of different Turing machines is infinite, but countable ($\aleph_0$), while the number of different languages is infinite of a larger magnitude ($\aleph$, and not countable). See more details on the wiki page for Cantor's diagonal argument, or search this site for related questions.