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• # Artykuł - szczegóły

## Formalized Mathematics

2008 | 16 | 1 | 1-5

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

EN

### Abstrakty

EN
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

1-5

wydano
2008-01-01
online
2009-03-20

### Twórcy

autor
• Department of Philosophy, Stanford University, USA

### Bibliografia

• [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
• [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
• [3] Józef Białas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990.
• [4] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
• [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
• [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
• [7] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
• [8] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
• [9] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
• [10] John L. Kelley. General Topology, volume 27 of Graduate Texts in Mathematics. Springer-Verlag, 1955.
• [11] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
• [12] Christoph Schwarzweller. The ring of integers, euclidean rings and modulo integers. Formalized Mathematics, 8(1):29-34, 1999.
• [13] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
• [14] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
• [15] Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883-885, 1990.
• [16] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
• [17] Wojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1(5):877-882, 1990.
• [18] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
• [19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• [20] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
• [21] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.