Proximity

Distance is a numerical description of how far apart things lie. In Physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria (e.g. “two counties over”). In Mathematics , distance must meet more rigorous criteria. FORMAL TREATMENT Mathematical analysis General case In M which meets the following criteria: One can find the distance between any two points. That distance is a distinct Real Number . It is Positive Definite . d(''x'',''y'') ≥ 0, and d(''x'',''y'') = 0 If And Only If ''x'' = ''y''. (Distance is always positive, and it is zero precisely when measuring the distance from a point to itself). It is Symmetric . d(''x'',''y'') = d(''y'',''x''). (The distance from ''x'' to ''y'' is the same as that from ''y'' to ''x''). It satisfies the Triangle Inequality , d(''x'',''z'') ≤ d(''x'',''y'') + d(''y'',''z''). (The shortest distance between two points is on a straight line). Such a function is known as a Metric . Together with the set, it makes up a Metric Space .
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