The Vector Space of Subsets of a Set Based on Symmetric Difference
Jesse Alama
Formalized Mathematics, Tome 16 (2008), p. 1-5 / Harvested from The Polish Digital Mathematics Library
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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

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:267096 
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     volume = {16},
     year = {2008},
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     language = {en},
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Jesse Alama. The Vector Space of Subsets of a Set Based on Symmetric Difference. Formalized Mathematics, Tome 16 (2008) pp. 1-5. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-008-0001-7/

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