Cannot understand solution (Turing Machine & Reduction)

Question

Please click this to see my problem

Hi.

About this question, I just can't understand its solution provided.

We know the complement of Atm = { <M,W> : M is TM and M does not accept W} and Rtm as described in photo = { <M,W> : M is TM that rejects the input string W}

if we put M,epsilon into each of above,

the complement of Atm = M does not accept epsilon
Rtm = M rejects Epsilon

in either case, it makes sense to me, thus my perspective is is in Rtm and complement of Atm. But answer says <M,epsilon> is NOT in Rtm but in complement of Atm

Why is that?

Thank you very much!

Answer 1

i guess they just mean that running forever is not the same as rejecting. rejecting is terminating with a "reject" status – Anton Knyazyev 14 mins ago

我认为这个答案是正确的。