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estudierBest ResponseYou've already chosen the best response.0
What is it, intersection of an infinite set? (integers?) Empty, I guess...
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
\(A_n=n\) \[\bigcap\limits^\infty_{n=1}n=\{x(\forall n)(x\in n )\} =\{ x1\cap2\cap3\cap\dots\}=\emptyset\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
\(A_n=11\) \[\bigcap\limits^\infty_{n=1}A_n=\{x11\cap11\cap11\cap\dots)\} =\{11\}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
\[\cap_{n=1}^{\infty}A_n=\{x:\forall n,x\in A_n\}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
\[\bigcap\limits^\infty_{n=1}n=\{x(\forall n)(x\in n )\} =\{ x1\cap2\cap3\cap\dots\}=\emptyset\]doesn't make sense. if \(A_n=\{n\}\) the set with one element, then \[\bigcap\limits^\infty_{n=1}n=\{x(\forall n)(x=n )\} =\emptyset\] you cannot take the intersection of numbers, only sets
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
does this make sense then?\[\bigcap\limits^\infty_{n=1}n=\{x(\forall n)(x\in n )\} =\{ 1\}\cap\{2\}\cap\{3\}\cap\dots=\emptyset\]
 one year ago
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