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Countable or uncountable?
(a) $x\in\Bbb Q:|x|>4$
(b) $x^2 :x\in\Bbb Q$

I understand that $\Bbb Q$ itself is countable but what I am confused about is that $x\in\Bbb Q$. Is this saying $x$ is an element of $\Bbb Q$? Is $x$ not just a single element of $\Bbb Q$ such as 30/7 for example how can it have a cardinality? Can an element of a set have its own cardinality? I don't see how you can tell if it's greater than 4. I'm aware that my reasoning is greatly flawed here its just I can't find any information anywhere to guide me in the direction to solve this question.

Quantum Chill
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Rian
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    Welcome to stackexchange. Please [edit] the question to tell us what you think the answer is, and why, What do you know about the cardinality of $\mathbb{Q}$? – Ethan Bolker Mar 13 '19 at 13:14
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    Yes. It is true that both sets are either countable or uncountable. – 5xum Mar 13 '19 at 13:14

1 Answers1

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Cardinality is defined for a set, and not for each element. Both (a) and (b) are set defined in set builder form and subsets of a countable set $\Bbb(Q)$, and hence countable. Check Subset of a countable set is itself countable

M. Kumar
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