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What is the set $\mathbb{Q} \setminus \mathbb{N}$. It seems like this would simply be {0}. Is there a proof?

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1 Answer

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It's the set of all rational numbers $\Bbb Q$ ("integer fractions") where we remove ($\setminus$ denotes a set difference) all natural numbers $\{1,2,3,\ldots\}$. If $0 \notin \Bbb N$, $0$ is still rational so $0 \in \Bbb Q \setminus \Bbb N$ but many more numbers are in that set: $-1,-2$ for starters and also proper fractions like $\frac12$, $\frac{113}{355}$ (and their negatives) etc.

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