$$\bigcap^∞_{n=1}A_n=\{x|(∀n)(x\in A_n)\}$$

Question

anonymous · Answer

What is it, intersection of an infinite set? (integers?)

Empty, I guess...

unklerhaukus · Answer

$A_n=n$
 $$\bigcap\limits^\infty_{n=1}n=\{x|(\forall n)(x\in n )\} =\{ x|1\cap2\cap3\cap\dots\}=\emptyset$$

unklerhaukus · Answer

$A_n=11$
$$\bigcap\limits^\infty_{n=1}A_n=\{x|11\cap11\cap11\cap\dots)\} =\{11\}$$

anonymous · Answer

$$\cap_{n=1}^{\infty}A_n=\{x:\forall n,x\in A_n\}$$

anonymous · Answer

$$\bigcap\limits^\infty_{n=1}n=\{x|(\forall n)(x\in n )\} =\{ x|1\cap2\cap3\cap\dots\}=\emptyset$$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

unklerhaukus · Answer

does this make sense then?$$\bigcap\limits^\infty_{n=1}n=\{x|(\forall n)(x\in n )\} =\{ 1\}\cap\{2\}\cap\{3\}\cap\dots=\emptyset$$