Greatest integer sums

Algebra Level 2

For two random positive real numbers x x and y y chosen uniformly and independently from the interval (1,1000)(1,1000), determine the probability that x+y=x+y. \lfloor x+y \rfloor = \lfloor x \rfloor + \lfloor y \rfloor.

Notation: \lfloor \cdot \rfloor denotes the floor function.

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