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Let me know about this two examples.

1) set of all polynomials with rational coefficients.

2) set of all polynomials whose coefficients belongs to set ${\{1, 2\}}$

I know the first one is countable set. Because we can write first set as union of countable sets $P_n$ which is set of polynomial with rational coefficients having degree at most n"

But, I am stuck at second one, as I see in the first one coefficient belongs to countable set $Q$ so the given set is countable and in second one also, coefficient belongs to set $\{1, 2\}$ which is also countable set and hence set given in 2) is also countable? Is am I right?

Asaf Karagila
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Akash Patalwanshi
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  • Lol read the full question. It is not duplicate! I am not asking about proof of first one! – Akash Patalwanshi Apr 02 '17 at 06:27
  • If $A$ is countable and $B\subset A$ then $B$ is countable because there exists an injective $ f:A\to \mathbb N ,$ so $ f|_B:B\to \mathbb N$ is injective.... The set named in 2) is a subset of the countable set named in 1). – DanielWainfleet Apr 02 '17 at 10:33

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