※ 引述《young11539 (〝☆小小霈★”)》之銘言：
: 請教一題
: If S is an infinite set , either countable and uncountable
: And B is a countable set .
: Show that S and S∪B has the same cardinal number
: 完全沒有頭緒@@
: 有勞各位強者
S countable or uncountable
=> there exists a 1-1 f: N -> S
=> let a_n = f(n), n=1, 2, 3, ......
=> Split {a_n} into Neven and Nodd, containing a_2k and a_2k-1 respectively
=> Then (S\f(N))∪Neven has the same cardinality as S
=> Then (S\f(N))∪Neven∪Nodd has the same cardinality as S∪B
我猜是這樣
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