Groups, rings and fields are equipped with binary operations. These can be applied repeatedly: $a_1+a_2+a_3+\dots$ to produce a sum of many elements, perhaps countably many. Can this be done also for uncountable sums? That is, is it possible to define the sum of an uncountable set of elements, using the binary operations?
Is it possible to make a sum of uncountable series of elements of a group or a ring?
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abstract-algebra
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4What do you mean with a sum of a countable set of element in a group? I think you need a topology, at least. – 2012-01-09
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0Related: http://math.stackexchange.com/q/106102/ – 2014-08-22