Except for the trivial case of the partition consisting of the real number $0$ and everything else, is there any other partition of the entire set of real numbers $\mathbb{R}$ into two sets $A$ and $B$ such that $A$ and $B$ are both closed under multiplication?
2026-03-27 13:29:01.1774618141
Can the real numbers be partitioned into two sets which are both closed under multiplication?
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