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Is \( ( \mathbb{N} , \le, 1, *) \) a monoidal preorder, where \( * \) is the usual multiplication of natural numbers?
If not, why not? If so, find a monoidal monotone \( ( \mathbb{N} , \le, 0, + ) → ( \mathbb{N} , \le, 1, * ) \).
Comments
\( f(n) = 3^n \)
\\( f(n) = 3^n \\)