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

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Duplicate?… – Qiaochu Yuan Nov 15 '10 at 1:19
up vote 8 down vote accepted

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?" – Jonas Kibelbek Nov 15 '10 at 1:07
@Jonas Kibelbek: Oops; yes. Thanks – Arturo Magidin Nov 15 '10 at 1:08

Never forget that irrational numbers are the result of our choice of unit length, indicating the inherent limitations of a given number system. An irrational number in one number system can be rational number in other number system.

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