Given,
$$A=\{B\subset \mathbb{N}: B \text{ is finite} \vee B^c \text{ is finite }\}$$
How can I prove that A is countable.
For me it seems it is uncountable.
2026-04-06 13:26:15.1775481975
Cardinality of given set
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$$A = \{B \subset \mathbb N | B \text{ finite}\} \cup \{B^C \subset \mathbb N | B \text{ is finite}\} = \bigcup_{n=1}^\infty \{B \subset \mathbb N | |B| = n\} \cup \bigcup_{n=1}^\infty \{B^C \subset \mathbb N | |B| = n \}$$ From this, the enumeration can be received by a diagonalisation.