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Bearbeitet von Peaches Pan Tao: 9/12/2016 5:51:44 PM
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Which Is Bigger: The Infinite Set of Whole Numbers, or The Infinite Set of Prime Numbers

Whole Number Set, There Are More Wholes Than Primes

91

Prime Number Set, Cuz Reasons

14

Does anyone know? I need a Cheeseburger.

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  • Bearbeitet von Shryke: 9/14/2016 1:14:10 PM
    They're both countably infinite, thus they are the same size: ∞. Now, if you were comparing the set of [i]rational[/i] numbers to the set of whole numbers, then you would have a victor, as the set of rational numbers is [u]uncountably[/u] infinite and is thus larger. A good way to think about this intuitively is that you can start with '1' in the set of whole numbers and count onwards, but you can't really "start" anywhere with rational numbers, as there will always be one more decimal place than the one you've put down to catalogue the position. The degree of specificity necessary to catalogue a given position in the set of all rational numbers is infinite, thus this set is a sort of infinity squared.

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