Definition, Betydelse, Synonymer & Anagram | Engelska ordet BIJECTION

Definition av BIJECTION

1. (matematik) bijektion

Exempel på hur man kan använda BIJECTION i en mening

• A bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain).
• Two sets have the same cardinality if, and only if, there is a one-to-one correspondence (bijection) between the elements of the two sets.
• Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).
• In abstract algebra, a group isomorphism is a function between two groups that sets up a bijection between the elements of the groups in a way that respects the given group operations.
• Specifically, they are a transcendental bijection of the spacetime continuum, an asymptotic projection of the Calabi–Yau manifold manifesting itself in anti-de Sitter space.
• Logical biconditional becomes the equality binary relation, and negation becomes a bijection which permutes true and false.
• If a continuous bijection has as its domain a compact space and its codomain is Hausdorff, then it is a homeomorphism.
• In category theory, the disjoint union is the coproduct of the category of sets, and thus defined up to a bijection.
• With the delta operator defined by a power series in D as above, the natural bijection between delta operators and polynomial sequences of binomial type, also defined above, is a group isomorphism, in which the group operation on power series is formal composition of formal power series.
• Because these mappings merely reinterpret the same numbers, they define a bijection between the elements of the two groups.
• By introducing these transcendental functions and noting the bijection property that implies an inverse function, some facility was provided for algebraic manipulations of the natural logarithm even if it is not an algebraic function.
• The equivalence classes of quadratic irrationalities are then in bijection with the equivalence classes of binary quadratic forms, and Lagrange showed that there are finitely many equivalence classes of binary quadratic forms of given discriminant.
• Hume's principle or HP says that the number of Fs is equal to the number of Gs if and only if there is a one-to-one correspondence (a bijection) between the Fs and the Gs.
• It follows that, if free objects exist in , the functor , called the free functor is a left adjoint to the faithful functor ; that is, there is a bijection.
• In mathematics, two sets or classes A and B are equinumerous if there exists a one-to-one correspondence (or bijection) between them, that is, if there exists a function from A to B such that for every element y of B, there is exactly one element x of A with f(x) = y.
• A fundamental result shows that any two uncountable Polish spaces X and Y are Borel isomorphic: there is a bijection from X to Y such that the preimage of any Borel set is Borel, and the image of any Borel set is Borel.
• An alternative bijective proof, given by Aigner and Ziegler and credited by them to André Joyal, involves a bijection between, on the one hand, n-node trees with two designated nodes (that may be the same as each other), and on the other hand, n-node directed pseudoforests.
• In mathematics, the Schreier refinement theorem of group theory states that any two subnormal series of subgroups of a given group have equivalent refinements, where two series are equivalent if there is a bijection between their factor groups that sends each factor group to an isomorphic one.
• In particular, if the map is a continuous bijection (a homeomorphism), so that the two spaces have the same topology, then their -th homotopy groups are isomorphic for all.
• For the group algebra of a finite group, the (isomorphism types of) projective indecomposable modules are in a one-to-one correspondence with the (isomorphism types of) simple modules: the socle of each projective indecomposable is simple (and isomorphic to the top), and this affords the bijection, as non-isomorphic projective indecomposables have.

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