Category Theory Point of View
In category theory the disjoint union is defined as a coproduct in the category of sets.
As such, the discrete union is defined up to an isomorphism, and the above definition is just one realization of the coproduct, among others. When the sets are pairwise disjoint, the usual union is another realization of the coproduct. This justifies the second definition in the lead.
This categorical aspect of the discrete union explains why is frequently used, instead of, to denote it.
Read more about this topic: Disjoint Union
Famous quotes containing the words category, theory, point and/or view:
“Despair is typical of those who do not understand the causes of evil, see no way out, and are incapable of struggle. The modern industrial proletariat does not belong to the category of such classes.”
—Vladimir Ilyich Lenin (1870–1924)
“There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.”
—Albert Einstein (1879–1955)
“As for work, without it, without painstaking work, any writer or artist definitely remains a dilettante; there’s no point in waiting for so-called blissful moments, for inspiration; if it comes, so much the better—but you keep working anyway.”
—Ivan Sergeevich Turgenev (1818–1883)
“War-making is one of the few activities that people are not supposed to view “realistically”; that is, with an eye to expense and practical outcome. In all-out war, expenditure is all-out, unprudent—war being defined as an emergency in which no sacrifice is excessive.”
—Susan Sontag (b. 1933)