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Question 95255: Are negative whole numbers Rational Numbers?
and What is the easiest way to determine a Ration Number From a Irrational Number?
Answer by kev82(151)   (Show Source):
You can put this solution on YOUR website! Hi,
Yes, negative whole numbers (or the negative integers) are indeed rational. A rational number is any number that can be expressed as the ratio of two integers (except when the second one is 0). If x is a negative integer, I can say  so x is the ratio of itsself to one, and both x and one are integers, so x is rational.
I'm not sure if this is what you want, but for any irrational p, divide it by itsself to get  which is rational.
(Ignore this if you don't understand it - university level)
There definitely isn't a bijection from the irrationals to the rationals, because this would imply the irrationals were countable. If the irrationals were countable, then this would make the reals countable (union of rationals and irrationals), and the reals are definitely not countable.
Kev
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