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.
@article{bwmeta1.element.doi-10_2478_v10037-009-0011-0,
author = {Artur Korni\l owicz},
title = {Collective Operations on Number-Membered Sets},
journal = {Formalized Mathematics},
volume = {17},
year = {2009},
pages = {99-115},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-009-0011-0}
}
Artur Korniłowicz. Collective Operations on Number-Membered Sets. Formalized Mathematics, Tome 17 (2009) pp. 99-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-009-0011-0/
[1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
[2] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.
[3] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.
[4] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.