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Question Im stuck on this problem: For a positive real number x, the difference x*=x−[x] (floor) is called the fractional part of x. Given arbitrary positive real numbers a and b, state a condition in terms of the fractional parts of a* and b* that is necessary and sufficient for [a+b] (floor) = [a] (floor) + [b] (floor). I’m trying to prove that this equation is true if and only if my condition holds.

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Question

Im stuck on this problem: For a positive real number x, the difference x*=x−[x] (floor) is called 

the fractional part of x. Given arbitrary positive real numbers a and b, state

a condition in terms of the fractional parts of a* and b* that is necessary and sufficient for [a+b] (floor) = [a] (floor) + [b] (floor). I’m trying to prove that this equation is true if and only if my condition holds.

 
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