Other Meanings
More generally, the solution set to an arbitrary collection E of relations (Ei) (i varying in some index set I) for a collection of unknowns, supposed to take values in respective spaces, is the set S of all solutions to the relations E, where a solution is a family of values such that substituting by in the collection E makes all relations "true".
(Instead of relations depending on unknowns, one should speak more correctly of predicates, the collection E is their logical conjunction, and the solution set is the inverse image of the boolean value true by the associated boolean-valued function.)
The above meaning is a special case of this one, if the set of polynomials fi if interpreted as the set of equations fi(x)=0.
Read more about this topic: Solution Set
Famous quotes containing the word meanings:
“An amoeba is a formless thing which takes many shapes. It moves by thrusting out an arm, and flowing into the arm. It multiplies by pulling itself in two, without permanently diminishing the original. So with words. A meaning may develop on the periphery of the body of meanings associated with a word, and shortly this tentacle-meaning has grown to such proportions that it dwarfs all other meanings.”
—Charlton Laird (b. 1901)
“Well, “slithy” means “lithe and slimy.” “Lithe” is the same as “active.” You see, it’s like a portmanteau—there are two meanings packed up into one word.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)