英和和英

名詞

nonsymmetry (uncountable)

1. (logic, mathematics) The property of a binary relation that is not symmetric; that is, there exist x and y such that Rxy holds but Ryx does not hold.
   • 2005, Steven G. Krantz, Handbook of Logic and Proof Techniques, Springer, page 58:

     A relation is nonsymmetric if it is not symmetric; i.e., there is at least one ordered pair (a,b) such that aRb but not bRa.

使用する際の注意点

Nonsymmetry is not to be confused with asymmetry. A relation is asymmetric if for all x and y, Rxy implies not Ryx. A relation is nonsymmetric if there exists at least one pair where Rxy holds and Ryx does not, but may still have pairs where both Rxy and Ryx hold. e.g. The relation "love" is often nonsymmetric: person A may love person B, but B may not love A, though it is possible for love to be mutual.

反意語

• symmetry

等位語

• asymmetry
• antisymmetry