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Bombieri, Enrico (2006), "The Riemann Hypothesis", The Millennium Prize Problems, Clay Mathematics Institute Cambridge, MA: 107–124 Moxley, Frederick (2021), "Complete solutions of inverse quantum orthogonal equivalence classes", Examples and Counterexamples , 1 : 100003, doi : 10.1016/j.exco.2021.100003
For functions in certain classes, the problem of determining: whether two functions are equal, known as the zero-equivalence problem (see Richardson's theorem); [4] the zeroes of a function; whether the indefinite integral of a function is also in the class. [5] Of course, some subclasses of these problems are decidable.
Conceptual questions or conceptual problems in science, technology, engineering, and mathematics (STEM) education are questions that can be answered based only on the knowledge of relevant concepts, rather than performing extensive calculations. They contrast with most homework and exam problems in science and engineering that typically require ...
Even a purely surface semantic analysis of accusatory language cannot be performed in the absence of social context, including who is making the accusation and to whom it is being made—often the subject of supposedly accusatory language might well interpret the utterance in question as something that he need not respond to. [1]
A decision problem is a question which, for every input in some infinite set of inputs, answers "yes" or "no". [2] Those inputs can be numbers (for example, the decision problem "is the input a prime number?") or values of some other kind, such as strings of a formal language.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
A typical example is the proof of the proposition "there is no smallest positive rational number": assume there is a smallest positive rational number q and derive a contradiction by observing that q / 2 is even smaller than q and still positive.
A loaded question is a form of complex question that contains a controversial assumption (e.g., a presumption of guilt). [1] Such questions may be used as a rhetorical tool: the question attempts to limit direct replies to be those that serve the questioner's agenda. [2] The traditional example is the question "Have you stopped beating your wife?"
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