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, 15:42, 22 February 2013→6.36. Irreducibly Triadic Relations: markup
The relations <math>L_0, L_1 \subseteq \mathbb{B}^3\!</math> are defined by the following equations, with algebraic operations taking place as in <math>\text{GF}(2),\!</math> that is, with <math>1 + 1 = 0.\!</math>
The relations <math>L_0, L_1 \subseteq \mathbb{B}^3\!</math> are defined by the following equations, with algebraic operations taking place as in <math>\text{GF}(2),\!</math> that is, with <math>1 + 1 = 0.\!</math>
# The triple <math>(x, y, z)\!</math> in <math>\mathbb{B}^3\!</math> belongs to <math>L_0\!</math> if and only if <math>x + y + z = 0.\!</math> Thus, <math>L_0\!</math> is the set of even-parity bit vectors, with <math>x + y = z.\!</math>
# The triple <math>(x, y, z)\!</math> in <math>\mathbb{B}^3\!</math> belongs to <math>L_1\!</math> if and only if <math>x + y + z = 1.\!</math> Thus, <math>L_1\!</math> is the set of odd-parity bit vectors, with <math>x + y = z + 1.\!</math>
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The corresponding projections of Proj (R0) and Proj (R1) are identical. In fact, all six projections, taken at the level of logical abstraction, constitute precisely the same dyadic relation, isomorphic to the whole of BxB and expressed by the universal constant proposition 1 : BxB > B. In summary:
The corresponding projections of Proj (R0) and Proj (R1) are identical. In fact, all six projections, taken at the level of logical abstraction, constitute precisely the same dyadic relation, isomorphic to the whole of BxB and expressed by the universal constant proposition 1 : BxB > B. In summary:
