| dbp:proof |
According to the definition of the remainder , : : : For the left side of the inequality, we select the largest such that : There is always a largest such , because and if , then : but because , , , this is always true. For the right side of the inequality we assume there exists a smallest such that : Since this is the smallest that the inequality holds true, this must mean that for : which is exactly the same as the left side of the inequality. Thus, . As will always exist, so will equal to , and there is only one unique that is valid for the inequality. Thus we have proven the existence and uniqueness of . (en) |
