How can I prove, by applying Rice's theorem, that the language L is undecidable?
$L = \lbrace \alpha : M_{\alpha}(x) =x^2 \,\,\, \forall x \in \lbrace 0,1\rbrace^* \rbrace $
I think this is a direct application but I don't fully understand the theorem, nor how to formally write out the answer.
In my notes I have Rice's theorem written as: Let $R$ be the set of all functions of the form $ f:\lbrace 0,1 \rbrace^* \rightarrow \lbrace 0,1 \rbrace^* \cup \lbrace \perp \rbrace $ where $ \perp $ means that the Turing machine does not halt. Then let $ C $ be a non-empty proper subset of $ R $. Then the language $ \lbrace \alpha : M_{\alpha} $ corresponds to a function $ f \in C \rbrace $ is undecidable.