What is Cardinality of the set?

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Are there more rational number than irrational numbers?

There are more irrational numbers than rational numbers. The
rationals are countably infinite; the irrationals are uncountably
infinite. Uncountably infinite means that the set of irrational
numbers has a cardinality known as the “cardinality of the
continuum,” which is strictly greater than the cardinality of the
set of natural numbers which is countably infinite. The set of
rational numbers has the same cardinality as the set of natural
numbers, so there are more irrationals than rationals.