On: How can some infinities be bigger than others?

[hinkley]

As software engineers this is easier to explain I think.

Create a listA with all integers.

Create a listB with all multiples of 3.

Is listA.length > listB.length? No, it is not.

[jcparkyn → hinkley]

That somewhat falls apart when you start comparing infinite sets that actually _do_ have different cardinalities.

[moritzwarhier → jcparkyn]

I 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.