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The definition for the Rational Number is given as Numbers that can be expressed as a fraction of an integer and a non-zero integer. at http://en.wikipedia.org/wiki/List_of_types_of_numbers#cite_note-1

What does non-zero integer mean?

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    $\begingroup$ It means an integer that's not zero. $\endgroup$ – Qiaochu Yuan Dec 11 '14 at 6:35
  • $\begingroup$ Not equal to zero for rationals we can't divide by zero so it needs to be non zero. $\endgroup$ – dustin Dec 11 '14 at 6:36
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    $\begingroup$ -1, -2, 1, 3, 5, 7 are all examples of non-zero integers. 0 however is zero and not non-zero... $\endgroup$ – Dair Dec 11 '14 at 6:36
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    $\begingroup$ do you know what zero is? do you know what non is? $\endgroup$ – Rustyn Dec 11 '14 at 6:45
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An integer is any whole number or its negative, e.g. ..., -2, -1, 0, 1, 2, ...

A non-zero integer is any of these but 0.

Your definition of a rational number is just a mathematically rigorous way of saying that a rational number is any fraction of whole numbers, possibly with negatives, and you can't have 0 in the denominator.

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Set of all integer is $\mathbb{Z=}${$0,\pm1,\pm2,\pm3, \ldots\ldots,\pm{1000 \ldots}$}. So just remove $0$ from $\mathbb{Z}$. Rest any of these infinite numbers can be used.

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