Merriam-Webster Collegiate Dictionary - dichotomy

 noun  (plural -mies)  Etymology: Greek dichotomia, from dichotomos  Date: 1610  1. a division into two especially mutually exclusive or contradictory groups or entities the ~ between theory and practice; also the process or practice of making such a division ~ of the population into two opposed classes  2. the phase of the moon or an inferior planet in which half its disk appears illuminated  3.  a. bifurcation; especially repeated bifurcation (as of a plant's stem)  b. a system of branching in which the main axis forks repeatedly into two branches  c. branching of an ancestral line into two equal diverging branches  4. something with seemingly contradictory qualities it's a ~, this opulent Ritz-style luxury in a place that fronts on a boat harbor — Jean T. Barrett