I think that it would be possible to "show a set who's cardinality is between the integers and reals". But it is not done with an equation. It is done with a new description of numbers. If numbers are defined as defined or undefined space and value. And all Reals and Integers exist as defined space and defined value, then there cardinality exists between integers and reals only. All numbers containing a variations of undefined space or undefined value are numbers existing in sets outside of the integers and reals.

 

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Moderator Note

Let me know if you're prepared to discuss this "new description of numbers" in its proper place in its own thread in Speculations, and I will split this post off as an OP. Otherwise, please don't pollute mainstream threads with pet theories that are only going to hijack someone else's thread, and steer genuine interest in the original question off into the weeds.

 

You've been around long enough to know, so here's a warning point piece of coal from Santa. Respond to this via Report This Post if you object to our rules, but not in pengkuan's thread, please.

No objections....my apologies to the forum and pengkuan. To be fair....it was NOT off into the weeds it was right on topic....hijacking none the less I suppose. Again my apologies. No further comments.

Edited December 18, 201510 yr by conway