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Does it make sense to say that there are more irrational numbers than rational?

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Yes, in the sense of cardinality. In the same sense that one can say that there are more real numbers than there are rationals (or integers; or natural numbers).

The rational numbers are countable, but the irrationals are uncountable.

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    In your second sentence, do you mean "more real numbers than there are rationals?"2010-11-15
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    @Jonas Kibelbek: Oops; yes. Thanks2010-11-15