"there exists" versus "for all but finitely many" Hallo everybody! Sorry for the stupid question but I have nobody else to ask I am new in the field so please do not be very strict Can anybody explain me the difference between "there exists" and "for all but finitely many"? I deal with total and partial computable functions and finite/infinite sets... I have to prove some statements. Let's imagine that I proved that "there exists some x" which satisfies the task... So does this mean that I proved the same "for all but finitely many x" ? or it is not and I should prove something else? Thank you in advance!