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:
“I see no reason for calling my work poetry except that there is no other category in which to put it.”
—Marianne Moore (1887–1972)
“[Anarchism] is the philosophy of the sovereignty of the individual. It is the theory of social harmony. It is the great, surging, living truth that is reconstructing the world, and that will usher in the Dawn.”
—Emma Goldman (1869–1940)
“There’s a point of poverty at which the spirit isn’t with the body all the time. It finds the body really too unbearable. So it’s almost as if you were talking to the soul itself. And a soul’s not properly responsible.”
—Louis-Ferdinand Céline (1894–1961)
“Let us never accept the point of view that mysteries are written by hacks. The poorest of us shed our blood over every chapter. The best of us start from scratch with every new book.”
—Raymond Chandler (1888–1959)