I am trying to prove this statement about countability:
Let $a\subset b$, if $b$ is countable then $a$ is countable.
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6$\Bbb N \subset \Bbb R$, and $\Bbb N$ is countable, yet $\Bbb R$ is not. – Kenny Lau May 12 '17 at 06:22
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I apologies for that mistake should correct the question – Bawantha May 12 '17 at 06:27
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Now if a is subset of b, you can always define a inclusion mapping from a to b such that f(x) = x for each x in a. – Li Chun Min May 12 '17 at 06:32
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What definition of countability do you know? – Henrik supports the community May 12 '17 at 06:32
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See Subset of Countable Set is Countable. – Mauro ALLEGRANZA May 12 '17 at 06:33
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Basically, show that an injection from $a$ to $b$ exists (trivial to construct this map by "embedding" $a$ into $b$) which would prove the claim. – Prasun Biswas May 12 '17 at 06:33