Express the interval as the union of subintervals.
.
Since there are of the , at least two of them must be in one of the intervals; i.e,
s.t and , for .
Therefore .
Let n be a positive integer and let a1, a2,...,a(n+1) be an real numbers in the interval [0,1). Show that there exists two integers i,j with 1< i, j < (n+1) and i doesn't equal j such that |ai - aj| < (1/n).
Ok. I can come up with an example...ai = .25 and aj = .3 and n = 5, but I'm sure that it's asking for a more general answer...
Anyone have any ideas?