foundation \Foun*da"tion\, n. [F. fondation, L. fundatio. See
           Found to establish.]
           1. The act of founding, fixing, establishing, or beginning to

           2. That upon which anything is founded; that on which
              anything stands, and by which it is supported; the lowest
              and supporting layer of a superstructure; groundwork;

                    Behold, I lay in Zion, for a foundation, a stone . .
                    . a precious corner stone, a sure foundation. --Is.
                                                          xxviii. 16.

                    The foundation of a free common wealth. --Motley.

           3. (Arch.) The lowest and supporting part or member of a
              wall, including the base course (see Base course
              (a), under Base, n.) and footing courses; in a frame
                  house, the whole substructure of masonry.

           4. A donation or legacy appropriated to support a charitable
              institution, and constituting a permanent fund; endowment.

                    He was entered on the foundation of Westminster.

           5. That which is founded, or established by endowment; an
              endowed institution or charity.

                    Against the canon laws of our foundation. --Milton.

           Foundation course. See Base course, under Base, n.

           Foundation muslin, an open-worked gummed fabric used for
              stiffening dresses, bonnets, etc.

           Foundation school, in England, an endowed school.

           To be on a foundation, to be entitled to a support from the
              proceeds of an endowment, as a scholar or a fellow of a

        Source: WordNet (r) 1.6 [wn] 

             n 1: the basis on which something is grounded; "there is little
                  foundation for his objections"
             2: an institution supported by an endowment
             3: lowest supporting part of a structure; "it was built on a
                base of solid rock"; "he stood at the foot of the tower"
                [syn: base, fundament, foot, groundwork, substructure,
             4: the fundamental assumptions underlying an explanation; "the
                whole argument rested on a basis of conjecture" [syn: basis,
                 base, fundament, groundwork, cornerstone]
             5: a woman's undergarment worn to give shape to the contours of
                the body [syn: foundation garment]
             6: starting something for the first time [syn: initiation, founding,
                 institution, origination, creation, instauration]

        Source: The Free On-line Dictionary of Computing (13Jul98) [foldoc] 


           The axiom of foundation states that the membership relation is
           well founded, i.e. that any non-empty collection Y of sets has
           a member y which is disjoint from Y.  This rules out sets
           which contain themselves (directly or indirectly).