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Jun 19, 2018 at 0:30 comment added aghostinthefigures Is the first suggestion to try and create the vector space $V$ out of the underlying set of whatever multiset one is working with? If so, that should undoubtedly work if the underlying set can form a vector space but potentially tricky to work with if, for example, the multiplicity function is unknown. For the second, I could potentially say both are true and discard uniqueness; the key is that such an addition of elements is "closed" in the sense that you always produce another element of the multiset.
Jun 19, 2018 at 0:12 history edited Bjørn Kjos-Hanssen CC BY-SA 4.0
color!
Jun 19, 2018 at 0:05 history answered Bjørn Kjos-Hanssen CC BY-SA 4.0