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Are there any guidelines for deciding whether an infinite set is countable or not?
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Here is a simple guideline for deciding whether a set is countable or not. As far as applied probability is concerned, this guideline should be sufficient for most cases.

• $\mathbb{N}, \mathbb{Z}, \mathbb{Q}_{1}$ and any of their subsets are countable.
• Any set containing an interval on the real line such as $[a, b],(a, b],[a, b)$, or $(a, b)$, where $a<b$ is uncountable.
by Diamond (74,866 points)

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