Am I correct in understanding that there are no non-trivial cases of this? I.e. an uncountable sum will either be infinity, or reducible to a countable sum by removing all the zero summands?
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Yes - if there are uncountably many positive terms, there must be infinitely many greater than some ε>0, so the supremum is ∞.
End of conversation
New conversation -
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What was the initial confusion? Is there anything surprising in this that I'm perhaps not getting?
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