Collective Operations on Number-Membered Sets

Artur Korniłowicz

Formalized Mathematics (2009)

  • Volume: 17, Issue: 2, page 99-115
  • ISSN: 1426-2630

Abstract

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The article starts with definitions of sets of opposite and inverse numbers of a given number membered set. Next, collective addition, subtraction, multiplication and division of two sets are defined. Complex numbers cases and extended real numbers ones are introduced separately and unified for reals. Shortcuts for singletons cases are also defined.

How to cite

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Artur Korniłowicz. "Collective Operations on Number-Membered Sets." Formalized Mathematics 17.2 (2009): 99-115. <http://eudml.org/doc/266691>.

@article{ArturKorniłowicz2009,
abstract = {The article starts with definitions of sets of opposite and inverse numbers of a given number membered set. Next, collective addition, subtraction, multiplication and division of two sets are defined. Complex numbers cases and extended real numbers ones are introduced separately and unified for reals. Shortcuts for singletons cases are also defined.},
author = {Artur Korniłowicz},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {99-115},
title = {Collective Operations on Number-Membered Sets},
url = {http://eudml.org/doc/266691},
volume = {17},
year = {2009},
}

TY - JOUR
AU - Artur Korniłowicz
TI - Collective Operations on Number-Membered Sets
JO - Formalized Mathematics
PY - 2009
VL - 17
IS - 2
SP - 99
EP - 115
AB - The article starts with definitions of sets of opposite and inverse numbers of a given number membered set. Next, collective addition, subtraction, multiplication and division of two sets are defined. Complex numbers cases and extended real numbers ones are introduced separately and unified for reals. Shortcuts for singletons cases are also defined.
LA - eng
UR - http://eudml.org/doc/266691
ER -

References

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  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. [2] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990. 
  3. [3] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003. 
  4. [4] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 

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