I have a question that came up on one of my assignments to prove that REJ010 is undecidable, it has been also stated by our professor that is undecidable but I exactly didn’t understand his explanation. He just kinda skimmed it over.

`REJ010 ={〈M〉|M is a TM that rejects input 010 } `

My problem understanding it is because I see a possible solution for this, so for example.

`Construct a decider D, L(D) = REJ010. run D(w): switch(w) { case: "010": reject; default: accept; } `

Maybe it is meant that for any **Turing machine** can we predict if that TM rejects input 010.

But I am not sure that is why I am asking here.

Thank you in advance.