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Disjoint union: Difference between revisions
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The disjoint union of a collection of sets is a set so that each element of the collection injects into the disjoint union, and so that the collection of images of each element of the collection creates a partition of the disjoint union. For example, the disjoint union of disjoint sets is just their union, while, e.g. the disjoint union of \(\{1,2\}\) and \(\{2,3\}\) could be taken to be \(\{(1,1),(1,2),(2,2),(2,3)\}\). Disjoint union is used to define sum of cardinals, which disagrees with [[Ordinal#Ordinal arithmetic|ordinal]] sum.
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