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That somewhat falls apart when you start comparing infinite sets that actually _do_ have different cardinalities.
by jcparkyn 3y ago
That somewhat falls apart when you start comparing infinite sets that actually _do_ have different cardinalities.
- moritzwarhier 3y agoI think the pseudocode might just be hard to write here const N = [1,2,3 ... ]; const countableSet = N.map(n => getEnumeratedFraction(n)); e.g. here the lambda function maps the natural numbers to all fractions (cantor showed how to easily implement getEnumeratedFraction). For all sets of equal cardinality, a pure function exists that transforms N (or another set of the cardinality you wish) when mapping the set members. And conversely, if such a function exists, the sets are of same size. Since the pseudocode is JS-like, you could also write it using Set. The sets are represented in pseudocode as arrays because enumeration is the point here.