axiomatically's Usage Examples:

arithmetic, real analysis and complex analysis are often introduced non-axiomatically, but implicitly or explicitly there is generally an assumption that.

Given a projective space defined axiomatically in terms of an incidence structure (a set of points P, lines L, and.

particular, social choice theoretic methods are often used to describe and (axiomatically) analyze the performance of rules or institutions.

Finite geometries can also be defined purely axiomatically.

Lindeberg has derived axiomatically determined models of simple cells in terms of directional derivatives.

projective planes and in 1954 he showed how one can introduce affine spaces axiomatically without constructing them from projective spaces or vector spaces.

More generally, the homology functor is defined axiomatically, as a functor on an abelian category, or, alternately, as a functor.

For the axiomatically more complicated (finite) n-valued Łukasiewicz logics, suitable algebras.

Among various theories, Bayesian DM is broadly accepted axiomatically based theory that solves the design of optimal decision strategy.

Note that unlike the general linear group, which is generally defined axiomatically as "invertible functions preserving the linear (vector space) structure".

An adopted brother who suckled from the mother of the woman is axiomatically a mahram.

The voting system that returns all maximal lotteries is axiomatically characterized as the only one satisfying probabilistic versions of.

existence of ordered pairs and their characteristic property must be axiomatically assumed.

There are many equivalent ways to define a matroid axiomatically, the most significant being in terms of: independent sets; bases or.

The first must be treated axiomatically and in a deductive way (pure sociology); the second, empirically and.

measures, such as time complexity or space complexity, from properties of axiomatically defined measures.

Recent results show that these properties can be derived axiomatically, from the symmetries of the global evolution.

By contrast, non-philosophy axiomatically deploys immanence as being endlessly conceptualizable by the subject.