Proof:If A ⊆ B and B is countable then A is countable

From CS2800 wiki
If [math]A \href{/cs2800/wiki/index.php/%E2%8A%86}{⊆} B [/math] and [math]B [/math] is countable then [math]A [/math] is countable
Proof:
Suppose [math]A \href{/cs2800/wiki/index.php/%5Csubseteq}{\subseteq} B [/math] and [math]B [/math] is countable. Then [math]|A| \href{/cs2800/wiki/index.php/%5Cleq}{\leq} |B| [/math] (since [math]A \href{/cs2800/wiki/index.php/%5Csubseteq}{\subseteq} B [/math]) and [math]|B| \href{/cs2800/wiki/index.php/%5Cleq}{\leq} |\mathbb{N}| [/math]. Therefore [math]|A| \href{/cs2800/wiki/index.php/%5Cleq}{\leq} |\mathbb{N}| [/math] so [math]A [/math] is countable.