My intuition is telling me that this is untrue. But I am having trouble formulating a proof for this. Can anyone point me in the right direction? I've seen a proof by contradiction involving the union of all singletons in an infinite language but I am needing a to look at this from a different angle. 

Related question:
Is the infinite union of computably enumerable sets also computably enumerable?
I also believe this to be untrue.