I am stuck at this question in my hw. It seems very very
familiar, but sumhow I dunno how to do it.
The fractional part of x is the amount by which it exceeds its
floor, [x]. For
x in R (real number system) and n in N(integer), let
S={x,2x,...,(n-1)x}.
a) Prove that is some pair of numbers in S have fractional parts
that differ by at most 1/n, then some number in S is within 1/n of
an integer.
b) Use part a to prove that some number in S is within 1/n of an
integer.
Any help appreciated 
