Definition & Betydelse | Engelska ordet EQUIVALENCE

Definition av EQUIVALENCE

1. (matematik) ekvivalens

Exempel på hur man kan använda EQUIVALENCE i en mening

• In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
• The word "class" in the term "equivalence class" may generally be considered as a synonym of "set", although some equivalence classes are not sets but proper classes.
• A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored out").
• Moral equivalence is a term used in political debate, usually to deny that a moral comparison can be made of two sides in a conflict, or in the actions or tactics of two sides.
• The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene).
• Completely regular spaces and Tychonoff spaces are related through the notion of Kolmogorov equivalence.
• Most consist of defining explicitly a vector space that is called a tensor product, and, generally, the equivalence proof results almost immediately from the basic properties of the vector spaces that are so defined.
• The first three of these characterizations can be proven equivalent in Zermelo–Fraenkel set theory without the axiom of choice, but the equivalence of the third and fourth cannot be proved without additional choice principles.
• The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.
• The ringer equivalence number (REN) is a telecommunications measure that represents the electrical loading effect of a telephone ringer on a telephone line.
• In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements.
• This equivalence is a consequence of the facts that compact subsets of Hausdorff spaces are closed, and closed subsets of compact spaces are compact.
• In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories.
• In first-order syntactic unification, variables range over first-order terms and equivalence is syntactic.
• Demonstrates that determining equivalence of regular expressions with exponentiation is EXPSPACE-complete.
• In statistical terms, it underpins the principle of probabilistic equivalence among groups, allowing for the unbiased estimation of treatment effects and the generalizability of conclusions drawn from sample data to the broader population.
• The vanishing of the pseudometric induces an equivalence relation, called the metric identification, that converts the pseudometric space into a full-fledged metric space.
• If we extend the relation by transitivity, we obtain a symmetric relation, which is therefore also an equivalence relation on germs (but not an ordering).
• In music, two written notes have enharmonic equivalence if they produce the same pitch but are notated differently.
• From ancient times, the idea of equivalence has been cherished for all Hindus, in its texts and in early 1st-millennium sculpture with concepts such as Harihara (Half Vishnu, Half Shiva) and Ardhanārīshvara (half Shiva, half Parvati), with myths and temples that feature them together, declaring they are the same.

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