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In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems that do not explicitly axiomatize that hypothesis, i.e. to prove an implication A → B, it is sufficient to assume A as a hypothesis and then proceed to derive B.
Whether it is justifiable to reject a hypothesis based on a low probability without knowing the probability of an alternative; Whether a hypothesis could ever be accepted based solely on data In mathematics, deduction proves, while counter-examples disprove. In the Popperian philosophy of science, progress is made when theories are disproven.
The expression "statistical proof" may be used technically or colloquially in areas of pure mathematics, such as involving cryptography, chaotic series, and probabilistic number theory or analytic number theory. [23] [24] [25] It is less commonly used to refer to a mathematical proof in the branch of mathematics known as mathematical statistics.
This is a list of axioms as that term is understood in mathematics. In epistemology, the word axiom is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system.
The p-value is not the probability that the null hypothesis is true, or the probability that the alternative hypothesis is false; it is the probability of obtaining results at least as extreme as the results actually observed under the assumption that the null hypothesis was correct, which can indicate the incompatibility of results with the ...
The Riemann hypothesis is one of the most important conjectures in mathematics.It is a statement about the zeros of the Riemann zeta function.Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar to the Riemann zeta-function.
Asking kids thought-provoking questions is a great way to engage their critical-thinking skills, according to Laura Linn Knight, the author of “Break Free from Reactive Parenting.”
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. [1] [2] [3] Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to ...
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