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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.
Formal proof provides the main exception, where the criteria for proofhood are ironclad and it is impermissible to defend any step in the reasoning as "obvious" (except for the necessary ability of the one proving and the one being proven to, to correctly identify any symbol used in the proof.); [15] for a well-formed formula to qualify as part ...
The U.S. Postal Service (USPS) will raise shipping prices in early 2025 while keeping the cost of first-class stamps unchanged. The proposed price hikes, which would take effect Jan. 19, include a ...
Editor’s Note: Help is available if you or someone you know is struggling with suicidal thoughts or mental health matters. In the US: Call or text 988, the Suicide & Crisis Lifeline.
Related: Chef Sentenced to 3 Months in Jail After Serving Wedding Guests Food Infected with Norovirus “It only takes a few norovirus particles to make you and other people sick.” The virus ...
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 ...