Rational Numbers are Countable
We prove that the rational numbers are countable in two ways. The first approach is classical: define the height of a rational number and use a result on countable unions of countable sets. The second is a cool proof of Campbell using base 11. #mikedabkowski, #mikethemathematician, #profdabkowski, #realanalysis
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The Real Numbers are Uncountable
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Integers & Rationals are both infinite but is it the SAME infinity?
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Integration by Parts | Calculus | IBDP Math AA HL | Analysis and Approaches | Higher Level
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The Countable Union of Countable Sets
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Countable & Uncountable Infinities
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Russell's Paradox - a simple explanation of a profound problem
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Cantor's Diagonal Argument: The rationals and reals have different sizes?!?!?
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Real Analysis | The countability of the rational numbers.
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Is The Sum Of All Positive Numbers Really -1/12?
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The Oldest Unsolved Problem in Math
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Proof that the rational numbers is a countably infinite set
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