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S-parabolic manifolds
Get PDFA Stein manifold is called S-Parabolic in case there exits a special
plurisubharmonic exhaustion function that is maximal outside a compact set.
If a continuous special plurisubharmonic exits then we will call the manifold
S*-Parabolic: In one dimensional case these notions are equivalent. However
in several variables the question as to weather these notions coincide seems
open. In this note we establish an interrelation between these two notions
Wittgenstein´s Critique of Gödel´s Incompleteness Results
Get PDFIt is often said that Gödel´s famous theorem of 1931 is\ud
equal to the Cretian Liar, who says that everything that he\ud
says is a lie. But Gödel´s result is only similar to this\ud
sophism and not equivalent to it. When mathematicians\ud
deal with Gödel´s theorem, then it is often the case that\ud
they become poetical or even emotional: some of them\ud
show a high esteem of it and others despise it. Wittgenstein\ud
sees the famous Liar as a useless language game\ud
which doesn´t excite anybody. Gödel´s first incompleteness\ud
theorem shows us that in mathematics there are\ud
puzzles which have no solution at all and therefore in\ud
mathematics one should be very careful when one\ud
chooses a puzzle on which one wants to work. Gödel´s\ud
second imcompleteness theorem deals with hidden\ud
contradictions – Wittgenstein shows a paradigmatic\ud
solution: he simply shrugs his shoulders on this problem\ud
and many mathematicians do so today as well. Wittgenstein\ud
says than Gödel´s results should not be treated as\ud
mathematical theorems, but as elements of the humanistic\ud
sciences. Wittgenstein sees them as something which\ud
should be worked on in a creative manner
On the Difference S(Z(n)) - Z(S(n)
Get PDFIn this paper, we prove that there exist infmitely many positive integers
n satisfying S(Z(n))> Z(S(n)) or S(Z(n)) < Z(S(n))
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