| # Component-wise inequality convention for vectors If are two vectors in , the notation corresponds to the component-wise inequality: that is, With our convention, we can write A similar convention applies to strict inequalities. With the vectors defined above, we can write the stronger statement . Not every pair of vectors can be compared in a component-wise fashion. For example, the vectors do not satisfy , but we cannot write either. 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.