1)let P={p1,p2....} be the set of all prime numbers for every n natural, present n as a representation of its prime factors, n=product(p_k^a_k)(adsbygoogle = window.adsbygoogle || []).push({});

1<=k< [itex]\infty[/itex] (where a_k=0 besdies to a finite number of ks).

and now define F:N->Q+ by: F:n=product(p_k^a_k)->r=procudt(p_k^f(a_k)), and show that's a bijection from N onto Q+.

2)let X be a set of sequences with the next property: given a sequence (c_n:n>=1), then there exist a sequence (b_n:n>=1) which belongs to X and lim n-> [itex]\infty[/itex] c_n/b_n=0.

prove that the set X isn't countable.

3)find the cardinality of the set of all the straight lines in a plane.

about the last question i got that, that this set is the plane itself, i.e R^2, so |RxR|=|R||R|= [itex]\aleph[/itex]*[itex]\aleph[/itex] is this the right answer?

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# Some quetions about set theory.

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