Math Help - why is the intersection of these sets empty?

1. why is the intersection of these sets empty?

let A_n = [n, infinity)

why is

empty?

2. Originally Posted by minivan15
let A_n = [n, infinity) why is
empty?
Given any $r>0$ there is a positive integer $K$ such that $K>r$.
Is this true $r\notin A_K?$
So?

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

why is

empty?
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 $\mathbb{R}$.