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The set Q is infinite but countable: we can list all positive rationals in an infinite matrix that holds at position <i, j> the rational i+1/j+1:
1/1 1/2 1/3 1/4 ... / / / 2/1 2/2 2/3 ... ... / / 3/1 3/2 ... ... ... / 4/1 ... ... ... ... ... ... ... ... ...
We can enumerate all elements in this matrix in a sequence f.