Cantor's completeness principle
Cantor's completeness principle states that the intersection of a nest of closed intervals is non empty and is a point. Now let us consider a nest of open intervals. I1 contains I2 contains in I3........ Now The intersection of I1 and I2 is nothing but the interval I2 so is I3 for I1,I2 and I3. So if N tends to infinity then is the intersection not going to be a point? Can anyone show me with rigor and reason why is does cantor principle fail in case of open intervals,i.e. the intersection is empty.?