A Problem about perfect set...

[AbelAkil]

Is there any nonempty perfect set in R which contains no rational number?
I cannot figure it out...:frown:
I appreciate your solutions!

PS: A set E is perfect iff E is closed and every point of E is a limit point of E

[micromass]

This thread already exists: http://www.physicsforums.com/showthread.php?p=3640257