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Which is denser Rational numbers or Irrational numbers?

April 26, 2017denser irrational Mathematics Numbers

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Which is denser Rational numbers or Irrational numbers?

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Irrational numbers. Rational numbers are countably infinite, which means we can order them in a way that we can say that some rational is the 1st or 250th. Basically, we can count them. Irrational numbers are uncountably infinite, meaning we cannot order them in any way such that we can count them all. Essentially, this means that there are far more irrational numbers than there are rational. Since they both span the real numbers, it makes sense to consider the irrationals more dense.