Let (left(A_{i}ight)_{i in mathbb{N}}) be a sequence of sets of cardinality (mathfrak{c}). Show that (# bigcup_{i in

Question:

 Let \(\left(A_{i}ight)_{i \in \mathbb{N}}\) be a sequence of sets of cardinality (\mathfrak{c}\). Show that \(\# \bigcup_{i \in \mathbb{N}} A_{i}=\mathfrak{c}\).
[map \(A_{i}\) bijectively onto \((i-1, i)\) and use that \((0,1) \subset \bigcup_{i=1}^{\infty}(i-1, i) \subset \mathbb{R}\).]

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question
Question Posted: