Kronecker's Theorem

Kronecker's Theorem states that if you have real numbers, and their differences are all rational, then the numbers are connected in a way that allows certain patterns to repeat periodically when you look at their multiples. More practically, it tells us that if some numbers are close to rational ratios, then by multiplying them by integers, they can get arbitrarily close to whole numbers. This theorem helps understand how numbers with rational relationships behave when scaled, demonstrating that their fractional parts can be made as small as desired through suitable multiplication.