Floor inequality
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Show that Floor(x) < Floor(y) iff there is an integer in the half-open interval (x,y], or Z Intersection (x,y] != Phi.
In particular, note that Z Intersection (Floor(y),y] = Phi.
Please refer to the attachment for problem description with appropriate symbols.
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Solution Summary
Floor inequality is demonstrated.
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Proof:
" ": We consider 4 cases.
Case 1: , then , then the integer .
Case 2: , , then ...
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