I'm working on a homework assignment in which I have to find the upper and lower limits of a sequence. I've partitioned the sequence into two subsequences (one consisting of all even terms and another consisting of all odd terms), I've seen the following claim:
If we partition a sequence into a finite number of subsequences then the upper and lower limit of the sequence are equal to the maximum upper limit and minimum lower limit of the subsequences.
But we have never proved this in my class or textbook. How would I go about proving it for my assignment?