X represent a some set of objects, as a space of consumption bundles, modeled as a subset of R^K. R is the real line and K is the number of commodities (example K=3 apples, oranges, pears). A typical consumption bundle is a three-vector x = (x1, x2, x3) with x1, x2, x3 giving the amount in kilos of the commodities. We take a second vector from the set X, y = (y1, y2, y3) with y1, y2, y3 giving the amount in kilos of the commodities.
Preferences are asymmetric if there is no pair x and y from X such that x>y and y>x