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

Formalized Mathematics (2008)

- Volume: 16, Issue: 1, page 1-5
- ISSN: 1426-2630

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topJesse Alama. "The Vector Space of Subsets of a Set Based on Symmetric Difference." Formalized Mathematics 16.1 (2008): 1-5. <http://eudml.org/doc/267096>.

@article{JesseAlama2008,

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},

author = {Jesse Alama},

journal = {Formalized Mathematics},

language = {eng},

number = {1},

pages = {1-5},

title = {The Vector Space of Subsets of a Set Based on Symmetric Difference},

url = {http://eudml.org/doc/267096},

volume = {16},

year = {2008},

}

TY - JOUR

AU - Jesse Alama

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

JO - Formalized Mathematics

PY - 2008

VL - 16

IS - 1

SP - 1

EP - 5

AB - 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

LA - eng

UR - http://eudml.org/doc/267096

ER -

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