Generalized Functions In New Forms(5): New mathematical

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In each case the indivisible in question is infinitesimal in the sense of possessing one fewer dimension than the figure from which it is generated. Beveridge completes his statement above on the importance of intuition and luck in discoveries with emphasis on the role of reason being “the principle agent in most aspects of research and the guide to most of our actions.”18 On the road toward proof, he says: “It [reason] is the main tool in formulating hypotheses, in judging the correctness of ideas conjured up by imagination and intuition, in planning experiments and in deciding what observations to make, in assessing the evidence and interpreting new facts, in making generalizations and finally in finding extensions and applications of a discovery.”19 One novel characteristic of the middle stage of scientific confidence development is that it is here where the investigator makes models and simulations of the reality he or she wishes to better understand.

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