# Why is REJ010 undecidable

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.