(adsbygoogle = window.adsbygoogle || []).push({}); "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!

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# There exists versus for all but finitely many

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