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In particular, the term well-defined is used with respect to (binary) operations on cosets. In this case, one can view the operation as a function of two variables, and the property of being well-defined is the same as that for a function. For example, addition on the integers modulo some n can be defined naturally in terms of integer addition.
A probabilistic proof is one in which an example is shown to exist, with certainty, by using methods of probability theory. Probabilistic proof, like proof by construction, is one of many ways to prove existence theorems. In the probabilistic method, one seeks an object having a given property, starting with a large set of candidates.
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 ...
According to Egri, well defined characters will drive the plot themselves, and so the foundation of character is the essential germination of a well crafted story. Central to Egri's argument is his claim that the best stories follow the logical method of thesis, antithesis, synthesis, or dialectic, to prove what he calls a "premise." A premise ...
For example, it quotes one respondent who states, “No matter the level of employee, clearly communicating ideas is critical to the success of initiatives.” Why Style Matters Discusses the importance of writing well to establish credibility in business. For example, “Good communication skills are increasingly viewed as a core competency in ...
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. If A1 intersect A2 is empty, then f is well-defined, but if A1 intersect A2 is not empty, then f is not well-defined since f(a) is ambiguous for a is ...
With five multicolor play shapes, this foam fort building set will give kiddos plenty of ways to play. From a cozy couch to a castle and moat, their imagination is the limit.
The well-definedness of functional calculus now follows as an easy consequence. Let D be an open set containing σ(T). Suppose Γ = {γ i} and Ω = {ω j} are two (finite) collections of Jordan curves satisfying the assumption given for the functional calculus. We wish to show