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are these sets countable
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{0,1,2,...,9}^N
N is the set of natural number
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Quote:
Originally Posted by
szpengchao
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Not this is $\displaystyle 2^{\aleph_0}$.
$\displaystyle 10 = {0,1,...,9}$ and $\displaystyle 2\leq 10$ thus $\displaystyle |2^{\mathbb{N}} | \leq |10^{\mathbb{N}}|$.
Thus, it cannot be countable.