Editing Combinatorial species (section)

=== Addition ===
'''Addition''' of species is defined by the [[disjoint union]] of sets, and corresponds to a choice between structures.<ref>{{harvnb|Joyal|1981|loc=§ 2.1.}}</ref> For species ''F'' and ''G'', define (''F'' + ''G'')[''A''] to be the disjoint union (also written "+") of ''F''[''A''] and ''G''[''A'']. It follows that (''F''&nbsp;+&nbsp;''G'')(''x'') =&nbsp;''F''(''x'')&nbsp;+&nbsp;''G''(''x''). As a demonstration, take ''E''<sup>+</sup> to be the species of non-empty sets, whose generating function is ''E''<sup>+</sup>(''x'')&nbsp;=&nbsp;''e''<sup>''x''</sup>&nbsp;−&nbsp;1, and '''1''' the species of the [[empty set]], whose generating function is '''1'''(''x'') = 1. It follows that the sum of the two species ''E''&nbsp;=&nbsp;'''1'''&nbsp;+&nbsp;''E''<sup>+</sup>: in words, "a set is either empty or non-empty". Equations like this can be read as referring to a single structure, as well as to the entire collection of structures.