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

Jesse Alama

Formalized Mathematics (2008)

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

Abstract

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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

How to cite

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Jesse 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
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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 -

References

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