## UnkleRhaukus $\bigcap^∞_{n=1}A_n=\{x|(∀n)(x\in A_n)\}$ one year ago one year ago

1. estudier

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

2. UnkleRhaukus

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

3. UnkleRhaukus

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

4. satellite73

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

5. satellite73

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

6. UnkleRhaukus

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