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=== Set theory and category theory === A far-reaching generalization of the addition of natural numbers is the addition of [[ordinal number]]s and [[cardinal number]]s in set theory. These give two different generalizations of the addition of natural numbers to the [[transfinite number|transfinite]]. Unlike most addition operations, the addition of ordinal numbers is not commutative.{{sfnp|Cheng|2017|pp=124β132}} Addition of cardinal numbers, however, is a commutative operation closely related to the [[disjoint union]] operation. In [[category theory]], disjoint union is seen as a particular case of the [[coproduct]] operation,{{sfnp|Riehl|2016|p=100}} and general coproducts are perhaps the most abstract of all the generalizations of addition. Some coproducts, such as [[direct sum]] and [[wedge sum]], are named to evoke their connection with addition.
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