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Math · Advanced Math
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(5) (Cantor, 1874) Prove that the set Tra of all transcendental real numbers is uncountably infinite and has the cardinality of the real line i.e. |Tral = c. This not only shows that transcendental numbers must exist (why?), but also that there are actually more transcendental numbers than algebraic ones, in fact as many as there are real numbers. Even though it is very hard to actually prove that a real number is transcendental!
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