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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 ...
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 ...
The definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof. However, outside the field of automated proof assistants, this is rarely done in practice.
Let X be the unit Cartesian square [,] [,], and let ~ be the equivalence relation on X defined by (,) (,) for all [,] and (,) (,) for all [,], Then the quotient space / can be naturally identified (homeomorphism) with a torus: take a square piece of paper, bend and glue together the upper and lower edge to form a cylinder, then bend the ...
The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same probability space, then
Steele said she "wouldn't use an egg that I found cracked in a carton I had bought in the store," as a consumer has no idea how long it has been sitting there broken.
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