Source : Webster's Revised Unabridged Dictionary (1913)

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

   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;
      basis.

            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.
                                                  --Macaulay.

   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
      college.

Source : WordNet®

foundation
     n 1: the basis on which something is grounded; "there is little
          foundation for his objections"
     2: an institution supported by an endowment
     3: the fundamental assumptions from which something is begun or
        developed or calculated or explained; "the whole argument
        rested on a basis of conjecture" [syn: {basis}, {base}, {fundament},
         {groundwork}, {cornerstone}]
     4: lowest support 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}, {understructure}]
     5: education or instruction in the fundamentals of a field of
        knowledge; "he lacks the foundation necessary for advanced
        study"; "a good grounding in mathematics" [syn: {grounding}]
     6: a woman's undergarment worn to give shape to the contours of
        the body [syn: {foundation garment}]
     7: the act of starting something for the first time;
        introducing something new; "she looked forward to her
        initiation as an adult"; "the foundation of a new
        scientific society"; "he regards the fork as a modern
        introduction" [syn: {initiation}, {founding}, {institution},
         {origination}, {creation}, {innovation}, {introduction},
        {instauration}]

Source : Free On-Line Dictionary of Computing

foundation
     
        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).