Suppose there is only one product, so that X is the positive real number line (for example, X denotes amounts of money you can win). A decision maker makes choices using the following criteria: an amount x is strictly preferred to an amount y if x y + 1. That is, an amount of money x is preferred to an amount of money y only if it is "sufficiently larger" (in this case, larger by 1). For instance, $5 is not preferred to $4.50 but $5 is preferred to 3. Is this "preference" and actual preference? That is, is it asymmetric and negatively transitive?