If A⊆ B and A is infinite, what follows about B?

Nothing, the size of B does not depend on A

B has exactly the same elements as A

Exercise · ZW-INFINITE-SET-003 · ★★☆ Intermediate

If \(A\subseteq B\) and \(A\) is infinite, what follows about \(B\)?

Choose one option.

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If \(B\) were finite, every subset of it, including \(A\), would be finite. Therefore \(B\) is infinite.

A set \(A\) is infinite if it is not finite, that is, if there is no bijection between \(A\) and \(\{1,\dots,n\}\) for any \(n\in\mathbb{N}\).

\[A\not\sim\{1,\dots,n\}\ \ \forall n\in\mathbb{N}\]