The Vector Space of Subsets of a Set Based on Symmetric Difference

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The Vector Space of Subsets of a Set Based on Symmetric Difference

For each set X, the power set of X forms a vector space over the field Z2 (the two-element field {0, 1} with addition and multiplication done modulo 2): vector addition is disjoint union, and scalar multiplication is defined by the two equations (1 · x:= x, 0 · x := ∅ for subsets x of X). See [10], Exercise 2.K, for more information.

MML identifier: BSPACE, version: 7.8.05 4.89.993

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