Alternative Definitions
Set-theoretically, one may represent a binary function as a subset of the Cartesian product X × Y × Z, where (x,y,z) belongs to the subset if and only if f(x,y) = z. Conversely, a subset R defines a binary function if and only if, for any x in X and y in Y, there exists a unique z in Z such that (x,y,z) belongs to R. We then define f (x,y) to be this z.
Alternatively, a binary function may be interpreted as simply a function from X × Y to Z. Even when thought of this way, however, one generally writes f (x,y) instead of f((x,y)). (That is, the same pair of parentheses is used to indicate both function application and the formation of an ordered pair.)
Read more about this topic: Binary Function
Famous quotes containing the words alternative and/or definitions:
“Our mother gives us our earliest lessons in love—and its partner, hate. Our father—our “second other”Melaborates on them. Offering us an alternative to the mother-baby relationship . . . presenting a masculine model which can supplement and contrast with the feminine. And providing us with further and perhaps quite different meanings of lovable and loving and being loved.”
—Judith Viorst (20th century)
“Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?
There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”
—Edmond De Goncourt (1822–1896)