Decidability of a language of Turing Machine descriptions [duplicate]

Given the language

$\{ <M> \mid\:$ M is a Turing machine and there is some w ∈ Σ* for which the computation M(w) takes more than 10 transitions$\}$

How can one prove that this language is decidable?

• What language is supposed to be decidable? I cannot understand the statement of your problem. All you have is a single Turing machne M, that takes more than 10 steps to halt at least once. Where is the language? May be you should clarify the question. – babou Oct 5 '14 at 11:51
• If you're referring to the language {<M> | M is a Turing machine and there is some w ∈ Σ* for which the computation M(w) takes more than 10 transitions}, than this language is NOT decidable – Roi Divon Oct 5 '14 at 11:53
• @babou Ah sorry, I made a bad typo. Roi Divon is right, I meant to say {<M> | M ...}. Which is why I'm confused, it looks non-decidable to me, but the question clearly says "show that the language is decidable". – Chad Dingle Oct 5 '14 at 12:29
• cs.stackexchange.com/questions/3101/… – d'alar'cop Oct 5 '14 at 12:40
• @d'alar'cop Thankyou! Very helpful, I'm surprised I couldn't find this. – Chad Dingle Oct 5 '14 at 12:44