i need to show that there exists a class of sets A which is a subset of P(Q) such that it satisfies:(adsbygoogle = window.adsbygoogle || []).push({});

1) |A|=c (c is the cardinality of the reals)

2) for every A1,A2 which are different their intersection is finite (or empty).

basically i think that i need to use something else iv'e proven: which for every a in R, let s(a) in Q^N is an increasing sequence which converges to a, then |{s(a)|a in R}|=c

i think that such a class could be: A={P(A')||A'|<alephnull} where A' is a subset of Q, A is the union of all P(A') where A' is Q.

im not sure if A's cardinality is c, but other than this example i dont see how to show it.

i think it's related to what i typed in the second paragraph, perhaps i need to find a subset to {s(a)|a in R} which is still uncountable, but i dont see how.

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# Question on cardinality of sequences.

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