General properties of the translation relation are of interest to translators, translatologists and machine translation system designers. As translation is somehow related to the intuitive notion “equivalence”, one wonders whether it has the properties of strict mathematical equivalence. Symmetry is one of these. The paper starts out with some definitions, so that the question can be treated in a meaningful way. The answer turns out to be positive for “perfect” but negative for “imperfect” translation; the latter because of a tendency of translators to “weaken” claims made in texts. This asymmetric aspect of imperfect translation is explained by relating it to a “monotonic” view of the organization of discourse. The paper ends with a description of a machine translation system designed to produce perfect translation, and draws conclusions about machine translation design.