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Questions regarding the well-definedness of a function often arise when the defining equation of a function refers not only to the arguments themselves, but also to elements of the arguments, serving as representatives. This is sometimes unavoidable when the arguments are cosets and when the equation refers to coset representatives. The result ...
Depending on the type of singularity in the integrand f, the Cauchy principal value is defined according to the following rules: . For a singularity at a finite number b + [() + + ()] with < < and where b is the difficult point, at which the behavior of the function f is such that = for any < and = for any >.
Today, any formal statement or calculation that exhibits this quality of well-definedness is termed computable, while the statement or calculation itself is referred to as a computation. Turing's definition apportioned "well-definedness" to a very large class of mathematical statements, including all well-formed algebraic statements , and all ...
Dummit and Foote give this example: A = A1 union A2 define f: A --> {1,2} as f(a)=1if a in A1 and f(a)=2 if a in A2. What I like about Dummit/Foote's example is (a) that it is more elementary than most other examples, and (b) that it gives an example where f is well-defined, and an example where f is ambiguous.
Problem discovery is an unconscious process which depends upon knowledge whereby an idea enters one's conscious awareness, problem formulation is the discovery of a goal; problem construction involves modifying a known problem or goal to another one; problem identification represents a problem that exists in reality but needs to be discovered ...
(The Center Square) – While many states expanded and adopted school choice programs in 2024, some advocates are excited about new education options for families in 2025 – made possible because ...
While for the definition via intersection well-definedness hinges only on the property that intersections of fields are themselves fields, here two auxiliary assertion are included. That 1. there exist minimal subfields of K that include E 1 {\displaystyle E_{1}} and E 2 {\displaystyle E_{2}} and 2. that such a minimal subfield is unique and ...
To make this 20-minute vegan curry even faster, buy precut veggies from the salad bar at the grocery store. To make it a full, satisfying dinner, serve over cooked brown rice.