To select an element from countably infinite set (list set of integers) you need to provide finite amount of information. To specify an element in continuum in general case you have to provide infinite amount of information: any real number is specified as countable-infinite number of digits. So here is a pattern:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\aleph_0[/itex] - finite information

[itex]\aleph_{continuum}[/itex] - countably infinite number of digits,

So the amount of information is 1 degree less than the cardinality of set.

Now, lets denycontinuum hypotesisand lets assumecontinuum= [itex]\aleph_2[/itex], so there is 1 cardinality between countable and continuum (I've heard that Goedel believed in it), and that cardinality is obviously [itex]\omega_1[/itex]

What information is required to completely specify an element in [itex]\omega_1[/itex] ?

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# I Information and Cardinality

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