I want to show that
$\qquad L = \{\langle M \rangle \mid \text{TM $M$ will write a $z$ to the tape at some point for some input}\}$
is undecidable.
I'm really not sure how to show this is undecidable. I know that a language is undecidable if M would not be able to determine if 'z' is or is not in the language.
