Originally posted by 37818
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I don't have to "prove" anything to you. Infinity (sideways 8) is a symbol representing no upper limit to a function or sequence.
Aleph_null is a (cardinal) number representing "how many" integers there are. It's the first order of infinity (or first transfinite cardinal). And you can do arithmetic with transfinite caradinals. E.g., aleph_null + aleph null = aleph_null, aleph_null + aleph_null + aleph_1 = aleph_1.
Arithmetic with "sideways 8" makes no sense.
K54
P.S. 1) I am NOT a troll and 2) why are you arguing so vehemently about things you clearly don't understand? In this thread "infinity" has been explained over and over and over again.
If you want to do some research on transfinite cardinals, look up Cantor's diagonal proof and the Continuum Hypothesis.
Oh, BTW the notion of infinite sets is an axiom of Set Theory.
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