Summary: This paper presents in the seventh improved and extended edition a deeper understanding of the quantification of mathematical infinity. After eliminating the incorrect usage of bijections, key results based on the concept of cardinality become...
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Summary: This paper presents in the seventh improved and extended edition a deeper understanding of the quantification of mathematical infinity. After eliminating the incorrect usage of bijections, key results based on the concept of cardinality become obsolete. The number of algebraic numbers is counted in general and asymptotically up to a given degree, and a method for counting the elements of infinite sets is specified. The real and complex numbers are re-characterised by extending them to infinity. In the field of linear programming, the well-known exponential simplex algorithm with a perturbation method for overcoming the problem of multiple vertices is confronted with the polynomial intex method. The generalised Riemann hypothesis is disproved and the equalty of the complexity classes P and NP proved.
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