[[PageOutline]] = The Sandbox = This is just a page to practice and learn WikiFormatting. Go ahead, edit it freely. == TEST == Using [http://www.openvest.com/trac/wiki/LatexEquation LatexEquation]: [[LatexEquation(r_n=\sum_{k=1}^K{X_{n,k}\cdot b_k+u_nn)]] {{{ #!LatexEquation \entitytype{Thing\equiv (AbstractObject \sqcup PossibleIndividual)} }}} == Levels == Let [[LatexEquation(U)]] be the set of all individuals and [[LatexEquation(R)]] be the set of all pairs [[LatexEquation(\langle a, b \rangle)]] for all [[LatexEquation(a, b \in ??)]]. (Note that [[LatexEquation(a, b)]] may be any set and not just an individual.) ---- Definition '''Level''': Level_0 is the set of all individuals and relationships: [[LatexEquation(Level_0 = U \cup R)]]. Level_n is the powerset of Level_n-1 for all positive integers n: [[LatexEquation(Level_n = \mathcal{P} (Level_{n-1}), 0 < n \in \mathbb{N})]]. Level_X is the union of all "Level_n sets" for all non-negative integers n: [[LatexEquation(Level_X = \bigcup Level_n, n \in \mathbb{N})]]. ---- Definition '''Type_Individual''': Let [[LatexEquation(I_0 = U)]] and [[LatexEquation(I_{n+1} = \mathcal{P} (I_{n}), n \in \mathbb{N})]], then [[LatexEquation(Type_{Individual} = \bigcup I_n, n \in \mathbb{N})]]. ---- Definition '''Type_Relationship''': Let [[LatexEquation(R_0 = R)]] and [[LatexEquation(R_{n+1} = \mathcal{P} (R_{n}), n \in \mathbb{N})]], then [[LatexEquation(Type_{Relationship} = \bigcup R_n, n \in \mathbb{N})]]. {{{ #!html }}}