Direct Product of Binary Relations
On the Cartesian product of two sets with binary relations R and S, define (a, b) T (c, d) as a R c and b S d. If R and S are both reflexive, irreflexive, transitive, symmetric, or antisymmetric, relation T has the same property. Combining properties it follows that this also applies for being a preorder and being an equivalence relation. However, if R and S are total relations, T is in general not.
Read more about this topic: Direct Product
Famous quotes containing the words direct, product and/or relations:
“Computer mediation seems to bathe action in a more conditional light: perhaps it happened; perhaps it didn’t. Without the layered richness of direct sensory engagement, the symbolic medium seems thin, flat, and fragile.”
—Shoshana Zuboff (b. 1951)
“The UN is not just a product of do-gooders. It is harshly real. The day will come when men will see the UN and what it means clearly. Everything will be all right—you know when? When people, just people, stop thinking of the United Nations as a weird Picasso abstraction, and see it as a drawing they made themselves.”
—Dag Hammarskjöld (1905–1961)
“The land is the appointed remedy for whatever is false and fantastic in our culture. The continent we inhabit is to be physic and food for our mind, as well as our body. The land, with its tranquilizing, sanative influences, is to repair the errors of a scholastic and traditional education, and bring us to just relations with men and things.”
—Ralph Waldo Emerson (1803–1882)