The Collaborative International Dictionary of English v.0.48:

Foundation \Foun*da"tion\, n. [F. fondation, L. fundatio. See
   Found to establish.]
   1. The act of founding, fixing, establishing, or beginning to
      erect.
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   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.
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            Behold, I lay in Zion, for a foundation, a stone . .
            . a precious corner stone, a sure foundation. --Is.
                                                  xxviii. 16.
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            The foundation of a free common wealth. --Motley.
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   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.
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   4. A donation or legacy appropriated to support a charitable
      institution, and constituting a permanent fund; endowment.
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            He was entered on the foundation of Westminster.
                                                  --Macaulay.
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   5. That which is founded, or established by endowment; an
      endowed institution or charity; as, the Ford Foundation.
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            Against the canon laws of our foundation. --Milton.
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   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.
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WordNet (r) 3.0 (2006):

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: lowest support of a structure; "it was built on a base of
       solid rock"; "he stood at the foot of the tower" [syn:
       foundation, base, fundament, foot, groundwork,
       substructure, understructure]
    4: 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: foundation,
       grounding]
    5: 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,
       foundation, fundament, groundwork, cornerstone]
    6: a woman's undergarment worn to give shape to the contours of
       the body [syn: foundation garment, foundation]
    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" [syn:
       initiation, founding, foundation, institution,
       origination, creation, innovation, introduction,
       instauration]

The Free On-line Dictionary of Computing (19 January 2023):

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).