This is making me go 1N54N3!!
I already asked the following 2 question but they were not answer thus I shall ask them again.
1)Are the cardinal numbers countable?
2)Are the cadinal numbers dense; meaning, for there exists a such as . For example, the rationals and the reals are dense? (Perhaps this is connected to the continuum hypothesis?)
3)Finally we get to a question to is making me go insane! I was thinking about this when I was falling asleep. Consider the set of all FINITE sets. What is the cardinality of this set?!?! I was able to prove (although not formally but you can consider it to be a proof) with the property of the power set, that I can make the cardinality of this set as large as I like!!!!! Thus, there is no cardinal number for this set!!!! When I was falling asleep a solution entered my mind. Who says that any infinite set must have a cardinal number? Perhaps, that reasoning is not true. And this is such a case. Thus, I decided to this the "super-cardinal number". Just as a cardinal number always excedes any natural number (cardinality of finite sets) so too the supercardinal number excedes any cardinal number (cardinality for SOME infinite sets). What happened?