Is an infinite language with an infinite alphabet always recursively enumerable?
isn't it just enumerable?
So.... no? Interesting.
If the language has uncountable alphabet, surely not?
I was thinking that since the alphabet is infinite (countable or not), a Turing machine would need infinitely many states to recognize it, which goes against the definition of a TM.
Isn't everything, should you accept the axiom of choice? I guess you meant it in the constructable sense.
What does the axiom of choice have to do with anything?
Ah, my mistake. See, I was thinking in the lines of the well ordering theorem. But the theorem doesn't state anything about every element of set having a predecessor, so it doesn't necessarily equate denumerability. I knew this was weird.
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