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The "Real Numbers" are all the "locations" on the number line. IMG:Realnumberline.png [[[>40 Interestingly, between every pair of rational numbers there are infinitely many irrational numbers, and between every pair of irrational numbers there are infinitely many rational numbers. ]]] One way of dividing the real numbers is: * Rational numbers versus irrational numbers, * Algebraic numbers versus transcendental numbers. The real numbers can be counter-intuitive. The reals can be constructed via * Cauchy Sequences * Dedekind Cuts * Infinite decimal expansions * Continued Fractions