dichotomy

[dahy-kot-uh-mee]
noun, plural dichotomies.
1.
division into two parts, kinds, etc.; subdivision into halves or pairs.
2.
division into two mutually exclusive, opposed, or contradictory groups: a dichotomy between thought and action.
3.
Botany. a mode of branching by constant forking, as in some stems, in veins of leaves, etc.
4.
Astronomy. the phase of the moon or of an inferior planet when half of its disk is visible.

Origin:
1600–10; < Greek dichotomía. See dicho-, -tomy

dichotomic [dahy-kuh-tom-ik] , adjective
dichotomically, adverb
subdichotomy, noun, plural subdichotomies.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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Collins
World English Dictionary
dichotomy (daɪˈkɒtəmɪ)
 
n , pl -mies
1.  division into two parts or classifications, esp when they are sharply distinguished or opposed: the dichotomy between eastern and western cultures
2.  logic the division of a class into two mutually exclusive subclasses: the dichotomy of married and single people
3.  botany a simple method of branching by repeated division into two equal parts
4.  the phase of the moon, Venus, or Mercury when half of the disc is visible
 
[C17: from Greek dichotomia; see dicho-, -tomy]
 
usage  Dichotomy should always refer to a division of some kind into two groups. It is sometimes used to refer to a puzzling situation which seems to involve a contradiction, but this use is generally thought to be incorrect
 
di'chotomous
 
adj
 
dichotomic
 
adj
 
di'chotomously
 
adv

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Etymonline
Word Origin & History

dichotomy
1610, from Gk. dichotomia "a cutting in half," from dicha "in two" + temnein "to cut" (see tome).
Online Etymology Dictionary, © 2010 Douglas Harper
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Encyclopedia Britannica
Encyclopedia

dichotomy

(from Greek dicha, "apart," and tomos, "cutting"), a form of logical division consisting of the separation of a class into two subclasses, one of which has and the other has not a certain quality or attribute. Men thus may be divided into professional men and men who are not professionals; each of these may be subdivided similarly. On the principle of contradiction this division is both exhaustive and exclusive; there can be no overlapping, and no members of the original genus or the lower groups are omitted. This method of classification, though formally accurate, has slight value in the exact sciences, partly because at every step one of the two groups is merely negatively characterized and is usually an artificial, motley class; but it sets forth clearly the gradual descent from the most inclusive genus (summum genus) through species to the lowest class (infima species), which is divisible only into individual persons or things.

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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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Example sentences
The dichotomy between personal liberties and property rights is a false one.
This dichotomy will not end until mankind frees itself from the bondage of
  fragmented allegiance.
In regard to your larger point, you are positing a false dichotomy.
The dichotomy in their backgrounds made for instant friendship.
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