-In general, the elements need be merely less than comparable to establish this order: so that, given any two elements, it may be determined either that they are equivalent (in the sense that neither is less than the other) or that one is less than the other. This results in an ordering between the non-equivalent elements. On a more technical note, the comparison function is a binary predicate that induces a strict weak ordering in the standard mathematical sense. A binary predicate f(x, y) is a function object that has two argument objects `x` and `y` and a return value of `true` or `false`. An ordering imposed on a hash_multimap is a strict weak ordering if the binary predicate is irreflexive, antisymmetric, and transitive and if equivalence is transitive, where two objects `x` and `y` are defined to be equivalent when both f(x, y) and f(y, x) are `false`. If the stronger condition of equality between keys replaces that of equivalence, then the ordering becomes total (in the sense that all the elements are ordered with respect to each other) and the keys matched will be indiscernible from each other.
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