# why is the intersection of these sets empty?

Printable View

• April 21st 2010, 11:25 AM
minivan15
why is the intersection of these sets empty?
let A_n = [n, infinity)

why is

http://s3.amazonaws.com/answer-board...7650003160.gifempty?
• April 21st 2010, 11:30 AM
Plato
Quote:

Originally Posted by minivan15
let A_n = [n, infinity) why is
http://s3.amazonaws.com/answer-board...7650003160.gifempty?

Given any $r>0$ there is a positive integer $K$ such that $K>r$.
Is this true $r\notin A_K?$
So?
• April 21st 2010, 04:56 PM
Drexel28
Quote:

Originally Posted by minivan15
let A_n = [n, infinity)

why is

http://s3.amazonaws.com/answer-board...7650003160.gifempty?

Another way of thinking about is that $\left[\bigcap_{n\in\mathbb{N}}A_n\right]'=\bigcup_{n\in\mathbb{N}}A_n'=\bigcup_{n\in\mathb b{N}}(-\infty,n)$. Now I surely hope that you recognize that this is $\mathbb{R}$.