A Note on Feasibility
The concept of feasibility has a long history, although it has long remained implicit, and was not analysed or discussed as such. It is an obvious supposition that the act of counting may be continued indefinitely, one that need not be stated explicitly. Of course everyone was aware that in reality it is not possible to count to infinity and that, therefore, the indefinite continuability of the number sequence is an idealization of reality. This is why the term “potentially infinite” is sometimes used.
KeywordsTravel Salesman Problem Mathematical Induction Natural Deduction Derivation Rule Feasible Number
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- S. Shapiro, editor. Intensional Mathematics. North-Holland, Amsterdam, 1985. Studies in Logic and the Foundations of Mathematics, Vol. 113.Google Scholar
- A. S. Yessenin-Volpin. About infinity, finiteness and finitization (in connection with foundations of mathematics). In Constructive Mathematics, Proceedings of the New Mexico State University Conference held at Las Cruces, New Mexico, August 11-15, 1980, pages 274–313, Springer-Verlag, Berlin, 1981. Lecture Notes in Mathematics, Vol. 873.Google Scholar
- A. S. Yessenin-Volpin. The ultra-intuitionistic criticism and the anti- traditional program for the foundation of mathematics. In Intuitionism and Proof Theory, Proceedings of the Summer Conference at Buffalo N.Y., 1968, pages 3–45, North-Holland Publishing Company, Amsterdam, 1970. Studies in Logic and the foundations of Mathematics.Google Scholar