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Consider multiplication operation $$f(x_1,\dots, x_k)=\prod_{i=1}^kx_i$$ where $x_i\in\{1,\dots, n_i\}$ with $n_1,\dots, n_k\in\{1,\dots,\infty\}$. What is the cardinality of the range? At $k =2$ ...