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pro vyhledávání: '"Anand, Bhupinder Singh"'
Autor:
Anand, Bhupinder Singh
We give a pictorial proof that transparently illustrates why four colours suffce to chromatically differentiate any set of contiguous, simply connected and bounded, planar spaces; by showing that there is no minimal planar map. We show, moreover, why
Externí odkaz:
http://arxiv.org/abs/2110.09718
Autor:
Anand, Bhupinder Singh
All the known approximations of the number of primes pi(n) not exceeding any given integer n are derived from real-valued functions that are asymptotic to pi(x), such as x/log x, Li(x) and Riemann's function R(x). The degree of approximation for fini
Externí odkaz:
http://arxiv.org/abs/1510.04225
Autor:
Anand, Bhupinder Singh
We conclude from Goedel's Theorem VII of his seminal 1931 paper that every recursive function f(x_{1}, x_{2}) is representable in the first-order Peano Arithmetic PA by a formula [F(x_{1}, x_{2}, x_{3})] which is algorithmically verifiable, but not a
Externí odkaz:
http://arxiv.org/abs/1108.4597
Autor:
Anand, Bhupinder Singh
We show that the classical interpretations of Tarski's inductive definitions actually allow us to define the satisfaction and truth of the quantified formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two esse
Externí odkaz:
http://arxiv.org/abs/1108.4598
Autor:
Anand, Bhupinder Singh
We assumed that, for every natural number k, there is a natural number u such that the (k-1)th term of G(u) is k^k, and that G(u) terminates finitely. It immediately follows that every Goodstein Sequence G(m) over the natural numbers must terminate f
Externí odkaz:
http://arxiv.org/abs/1104.4111
Autor:
Anand, Bhupinder Singh
I shall argue that a resolution of the PvNP problem requires building an iff bridge between the domain of provability and that of computability. The former concerns how a human intelligence decides the truth of number-theoretic relations, and is form
Externí odkaz:
http://arxiv.org/abs/1003.5602
Autor:
Anand, Bhupinder Singh
I show--contrary to common beliefs tolerated by the 'bosses'--that any interpretation of ZF that admits Aristotle's particularisation is not sound; that the standard interpretation of PA is not sound; that PA is consistent but omega-inconsistent; tha
Externí odkaz:
http://arxiv.org/abs/0902.1064
Autor:
Anand, Bhupinder Singh
Standard expositions of Goedel's 1931 paper on undecidable arithmetical propositions are based on two presumptions in Goedel's 1931 interpretation of his own, formal, reasoning - one each in Theorem VI and in Theorem XI - which do not meet Goedel's,
Externí odkaz:
http://arxiv.org/abs/math/0703723
Autor:
Anand, Bhupinder Singh
The only fault we can fairly lay at Lucas' and Penrose's doors, for continuing to believe in the essential soundness of the Goedelian argument, is their naive faith in, first, non-verifiable assertions in standard expositions of classical theory, and
Externí odkaz:
http://arxiv.org/abs/math/0607333
Autor:
Anand, Bhupinder Singh
We show that, if PA has no non-standard models, then P=/=NP. We then give an elementary proof that PA has no non-standard models.
Comment: 8 pages; major revision; earlier argument replaced by an elementary proof that PA has no non-standard mode
Comment: 8 pages; major revision; earlier argument replaced by an elementary proof that PA has no non-standard mode
Externí odkaz:
http://arxiv.org/abs/math/0603605