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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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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