symmetric difference

WordReference Random House Unabridged Dictionary of American English © 2025

symmet′ric dif′ference, [Math.]

1. Mathematics the union of the relative complements of two sets. Also called Boolean sum. 

WordReference Random House Learner's Dictionary of American English © 2025

dif•fer•ence /ˈdɪfərəns, ˈdɪfrəns/   n. 

1. [uncountable] the state or relation of being different;
   dissimilarity.
2. an instance or point of unlikeness or dissimilarity:
   [countable] the differences in their behavior.
3. a significant change in a situation:
   [uncountable] It made no difference what I said.
4. a distinguishing characteristic;
   distinctive quality, feature, etc.:
   [countable] There was a difference in her face after the ordeal.
5. the degree to which one person or thing differs from another: [countable; usually singular]
   The difference in their ages is about six months.
   [uncountable] There isn't much difference between one politician and another.
6. a disagreement in opinion;
   dispute;
   quarrel:
   [countable] a strong difference of opinion.

WordReference Random House Unabridged Dictionary of American English © 2025

dif•fer•ence  (dif′ər əns, dif′rəns), n., v., -enced, -enc•ing. 
n. 

1. the state or relation of being different;
   dissimilarity:
   There is a great difference between the two.
2. an instance or point of unlikeness or dissimilarity:
   What accounts for the differences in their behavior?
3. a significant change in or effect on a situation:
   His tact makes a difference in the way people accept his suggestions.
4. a distinguishing characteristic;
   distinctive quality, feature, etc.:
   The difference in the two products is quality.
5. the degree to which one person or thing differs from another.
6. the act of distinguishing;
   discrimination;
   distinction.
7. a disagreement in opinion.
8. a dispute or quarrel.
9. Mathematics Also called finite distance. 
   • the amount by which one quantity is greater or less than another.
   • See relative complement. 
   • (of a function f ) an expression of the form f(x + h) - f(x).
10. a differentia.
11. Idioms split the difference:
    • to compromise, esp. to make equal concessions.
    • to divide the remainder equally:
      Let's take half of the cake and let the three of them split the difference.

v.t. 

12. to cause or constitute a difference in or between;
    make different.
13. to perceive the difference in or between;
    discriminate.

• Latin differentia, equivalent. to different- carrying different ways (see different) + -ia -ia; see -ence
• Anglo-French)
• Middle English (1300–50

Synonyms

• 1. inconsistency, variation, diversity, imbalance, inequality, divergence, contrast, contrariety.
  Difference, discrepancy, disparity, dissimilarity imply perceivable unlikeness, variation, or diversity.
  Difference refers to a lack of identity or a degree of unlikeness:
  a difference of opinion; a difference of six inches.
  Discrepancy usually refers to an inconsistency between things that should agree, balance, or harmonize:
  a discrepancy between the statements of two witnesses.
  Disparity implies inequality, often where a greater equality might reasonably be expected:
  a great disparity between the ages of husband and wife.
  Dissimilarity indicates an essential lack of resemblance between things in some respect comparable:
  a dissimilarity between social customs in Asia and America.
• 6. See distinction. 

Antonyms

• 1. similarity, agreement.

Collins Concise English Dictionary © HarperCollins Publishers::

difference / ˈdɪfərəns ˈdɪfrəns/ noun

1. the state or quality of being unlike
2. a specific instance of being unlike
3. a distinguishing mark or feature
4. a significant change in a situation
5. a disagreement or argument
6. a degree of distinctness, as between two people or things
7. the result of the subtraction of one number, quantity, etc, from another
8. another name for differentia
9. symmetric difference ⇒ (of two sets) the set of members of the first that are not members of the second
10. an addition to the arms of a family to represent a younger branch
11. make a difference ⇒ to have an effect
12. to treat differently
13. split the difference ⇒ to settle a dispute by a compromise
14. to divide a remainder equally
15. with a difference ⇒ with some peculiarly distinguishing quality, good or bad