※ 引述《mqazz1 (無法顯示)》之銘言：
: show that the set of rational numbers between 0 and 1 is countable
: 請問該如何證明呢?
Consider f:N->Q, given by f(n) = n; it's 1-1, hence |N|≦|Q|.
Consider g:ZxZ -> Q, given by g(n,m) = n/m if m≠0
g(n,m) = 0 if m = 0
Then, g is onto, hence |N| = |ZxZ| ≧ |Q|.
So |Q| = |N|.
( Q is the rational numbers, Z is the integers and N is the
natural numbers).
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