Component-wise inequality convention for vectorsIf ![]() With our convention, we can write ![]() A similar convention applies to strict inequalities. With the vectors Not every pair of vectors can be compared in a component-wise fashion. For example, the vectors ![]() do not satisfy Thus, the component-wise inequality convention induces only a partial order on vectors. This is contrast with real numbers, for which the ordinary inequality induces a total order, in the sense that any pair of real numbers can be compared. |