[分析] 高微

[suzzdicon (舒玆迪控)]

Let F be the set of all fractions.

(a) Find a one-to-one function f : N -> F that does not map N onto F.

(b) Find a one-to-one function g : F -> N that does not map F onto N.

(c) Is the set F countable? Explain your answer.

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推 zombiea:1. n-> n/1 , 2. consider F as subset of Z^2 ,
→ zombiea:then build up an Z^2 to N which is not surj
→ zombiea:3. yes , why not , card(F) is at most card(N) by b
→ zombiea:also by 1. we have reverse cardinality inquality
→ zombiea:thus equal