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The article is misleading on this point. The Continuum Hypothesis says that it is undecidable in the standard axioms whether there is a cardinality between cou
by clintonc 9y ago
The article is misleading on this point. The Continuum Hypothesis says that it is undecidable in the standard axioms whether there is a cardinality between countable and the continuum (i.e., the cardinality of the real). This work shows that p and t are different, which also means that t is of greater cardinality than the reals.
- samoright 9y agoWhat is p and t? You say that this work shows that p and t are different. What two entities are proven to be equal then in this work?
- clintonc 9y agop and t are implicitly defined cardinalities (i.e., the smallest cardinalities with given properties). See Definition 1.1 of the source article (https://arxiv.org/pdf/1208.5424.pdf https://arxiv.org/pdf/1208.5424.pdf)
- abnry 9y agoOh, thank you. So the article just threw in Continuum Hypothesis because different infinities 'n stuff. But what is confusing to me is that the article suggested p and t are defined as collections of subsets of the natural numbers. The power set of the natural numbers has the same cardinality as the reals, right? Since p and t are both subsets of this power set, they must have cardinalities below the cardinality of the reals.
- cerved 9y agoWait I'm confused. When you say p and t are different, you mean they are cardibalities of different sets but still equal in "size", right? Because I've understood they've proved p to be of equal "size" of t, which I guess means they have a one to one relation? Fuck this is confusing