 <p>That's not a stupid question! I believe what is meant by "strings that it cannot handle" is actually, "strings which are not in a valid format", which I take to mean "strings that contain symbols that we don't know." (I'm going off of slide 14 of <a href="http://web.stanford.edu/class/archive/cs/cs103/cs103.1134/lectures/19/Small19.pdf" rel="nofollow noreferrer">this presentation</a>, which I found by just googling <code>Turing 'implicitly reject'</code>).</p> <p>So, if we do use that definition, then we need to simply create a Turing machine that accepts an input if it contains a symbol not in our valid set.</p> <p>Yes, there are other possible interpretations of "strings that it cannot handle", but I'm fairly sure it means this. It obviously could not be a definition without constraints, or else we could define "strings that it cannot handle" as, say, "strings representing programs that halt", and we'd have solved the halting problem! (Or if you're not familiar with the halting problem, you could substitute in any NP-complete problem, really).</p> <p>I think the reason that the idea of rejecting strings the Turing machine cannot handle was introduced in the first place is so that the machine can be well defined on all input. So, say, if you have a Turing machine that accepts a binary number if it's divisible by 3, but you pass in input that is not a bianry number (like, say, "apple sauce"), we can still reason about the output of the program.</p>