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We introduce an inductive procedure for this purpose.
Moreover, an inductive procedure for constructing such sets Λ in dimension d≥3 is also given.
While they also rely on the representation formula from [3] they require an inductive procedure and careful remainder estimates.
We will heavily rely on the following inductive procedure introduced by Minc and the two authors in [1].
Denote By an inductive procedure, we obtain a sequence of successive approximations for starting from such that, for each, we have Then (3.4).
Is the inductive procedure correct and scientifically reliable, Hume wondered, when it authorises us to pass from many specific cases to one general statement?
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He felt that inductive reasoning provided the general premises upon which deduction had to be based and that deduction resulted in generalizations or laws which then had to be tested by inductive procedures.
Elsewhere, Reichenbach puts more emphasis on finite frequencies and even suggests that limiting frequencies are simply a mathematical device for justifying inductive procedures ('A letter to B. Russell', 1978, vol. II, p. 405 406).
First was a phase from Plato and Aristotle up until the 17th century where the specificity of scientific knowledge was seen in its absolute certainty established by proof from evident axioms; next was a phase up to the mid-19th century in which the means to establish the certainty of scientific knowledge had been generalized to include inductive procedures as well.
Specifically, we used coding and comparative analytic inductive procedures to de-contextualize and re-contextualize individual cases and experiences [ 49].
We conducted the analysis in stages and in accordance with principles of grounded theory [ 18], using systematic, inductive procedures to generate insights grounded in the views expressed by study participants.
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