How to Prove the Empty Intersection of Infinite Intervals?

[happybear]

Homework Statement

If X = R with a special metirc, En = [n, infinity) ()
How can I show infinite intersection of En is empty?

Homework Equations

The Attempt at a Solution

 

[yyat]

I am not sure what you mean by "special metric", since the statement you are trying to show has nothing to do with a metric.

To show that the intersection is empty use the fact that for any real number x there exists a positive integer n such that x<n.