# Definition of Ordinality

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**Ordinality**Definition from Science & Technology Dictionaries & Glossaries

Web Dictionary of Cybernetics and Systems

Having a certain order of complexity or being defined on a certain logical level (

*see*theory of logical types ). A property, being defined within one variable or set is of ordinality one. A relation between two entities is of ordinality two, ..., a relation with n arguments is of ordinality n. A different convention of expressing ordinality is to count: unary relation or property, binary relation, ternary relation, quarternary relation,..., n-ary relation. A system within n variables contains up to n!/(m!(n-m)!) relations of ordinality m, msee structure, organization ). (Krippendorff )**Ordinality**Definition from Encyclopedia Dictionaries & Glossaries

English Wikipedia - The Free Encyclopedia

In mathematics, especially in set theory, two ordered sets

*X,Y*are said to have the same**order type**just when they are order isomorphic, that is, when there exists a bijection (each element matches exactly one in the other set)*f*:*X*→*Y*such that both*f*and its inverse are strictly increasing (order preserving i.e. the matching elements are also in the correct order). In the special case when*X*is totally ordered, monotonicity of*f*implies monotonicity of its inverse.See more at Wikipedia.org... |

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