<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>For each set <italic>X</italic>, the power set of <italic>X</italic> forms a vector space over the field <bold>Z</bold>2 (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 · <italic>x</italic>:= <italic>x</italic>, 0 · <italic>x</italic> := ∅ for subsets <italic>x</italic> of <italic>X</italic>). See [10], Exercise 2.K, for more information.</p><p>MML identifier: BSPACE, version: 7.8.05 4.89.993</p></abstract>

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

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

Department of Philosophy, Stanford University, USA

Formalized Mathematics

{"article-title":"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...

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

Publié en ligne: 20 mars 2009

Pages: 1 - 5

DOI: https://doi.org/10.2478/v10037-008-0001-7

This content is open access.