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Suppose $a, b \in \mathbb{N}$. If $\frac{a}{b} \notin \mathbb{N}$, then $b>1$. Is this statement true? I use contrapositive to show that if $b=1$, then $\frac{a}{b}\in\mathbb{N}$ which seems obviously true but I always make obvious mistake so I'm not sure.

user665125
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    You meant to write $\frac ab$ at the end, but otherwise your argument is fine. Note that, if $b=1$, then $\frac ab=\frac a1=a\in \mathbb N$ by assumption. – lulu Jan 26 '22 at 21:36
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    Yes, since $b\in\Bbb N$, $\frac ab\notin\Bbb N\implies b>1$ is equivalent to $b=1\implies\frac ab\in\Bbb N$. – José Carlos Santos Jan 26 '22 at 21:37

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