Let $X$ be a countably infinite set. Let $\prod$ denote the free abelian semigroup generated by $X.$ Apparently $\prod$ consists of all the 'formal products' of the form $\prod_{P \in X} P^{a_P}$ there $a_P$ are non-negative integers, and 0 for all but finitely many $P.$ Why can't we call these elements as simply products. What distinguishes a product from a formal one?
2026-03-29 22:12:36.1774822356
What is the difference between formal product and product?
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