From Cantor To Christaller?
نویسندگان
چکیده
منابع مشابه
Set Theory from Cantor to Cohen
Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzing mathematical propositions and gauging their consistency strength. But set theory is also distinguished by having begun intertwined with pronounced metaphysical attitudes, and these have even been regarded as crucial by ...
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Gödel’s incompleteness results apply to formal theories for which syntactic constructs can be given names, in the same language, so that some basic syntactic operations are representable in the theory. It is now customary to derive these results from the fixed point theorem (also known as the reflection theorem), which asserts the existence of sentences that “speak about themselves”. Let T be t...
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We show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution from a single input soliton.
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The Cantor-Schroeder-Bernstein theorem [Can97][Sch98][Ber05] states that any two sets that have injections into each other have the same cardinality, i.e. there is a bijection between them. Another way to phrase this is if two sets A,B have monomorphisms from A to B and B to A, then they are isomorphic in the setting of sets. One naturally wonders if this may be extended to other commonly studi...
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Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzingmathematical propositions cast in set-theoretic terms and gauging their consistency strength. But set theory is also distinguished by having begun intertwined with pronounced metaphysical attitudes, and these have even b...
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ژورنال
عنوان ژورنال: Quaestiones Geographicae
سال: 2015
ISSN: 2081-6383
DOI: 10.1515/quageo-2015-0039