ETIMOLOGI PERKATAAN CANTOR'S PARADOX
Named after Georg Cantor (1845–1918), German mathematician, born in Russia.
APAKAH MAKSUD CANTOR'S PARADOX dalam CORSICA?
Paradoks Cantor
Dalam teori yang ditetapkan, paradoks Cantor terbit dari teorem bahawa tidak ada nombor kardinal yang paling besar, supaya koleksi "saiz tak terhingga" itu sendiri tidak terhingga. Kesukaran ditangani dalam teori set aksiomatik dengan mengisytiharkan bahawa koleksi ini bukan set tetapi kelas yang tepat; dalam von Neumann-Bernays-Gödel menetapkan teori yang berikut dari ini dan aksioma keterbatasan saiz bahawa kelas yang sepatutnya mestilah sesuai dengan kelas semua set. Oleh itu, bukan sahaja terdapat banyak infiniti, tetapi infiniti ini lebih besar dari mana-mana infiniti yang ia sebutkan. Paradoks ini dinamakan untuk Georg Cantor, yang sering dikreditkan dengan mengenal pasti pertama pada tahun 1899. Seperti beberapa "paradoks" ia tidak benar-benar bercanggah tetapi hanya menandakan intuisi yang salah, dalam kes ini tentang sifat infiniti dan tanggapan set. Berikan cara lain, ia adalah paradoks dalam batasan teori set naif dan oleh itu menunjukkan bahawa axiomatization cuai teori ini tidak konsisten.
Definisi Cantor's paradox dalam kamus Corsica
Takrifan paradoks Cantor dalam kamus adalah paradoks yang diperolehi daripada anggapan set universal yang menyeluruh, kerana setiap set mempunyai subset lebih daripada ahli manakala setiap subset set universal itu akan menjadi ahli daripadanya.
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Ketahui penggunaan
Cantor's paradox dalam pilihan bibliografi berikut. Buku yang berkait dengan
Cantor's paradox dan ekstrak ringkas dari yang sama untuk menyediakan konteks penggunaannya dalam kesusasteraan Corsica.
1
Encyclopaedia of Mathematics (set)
Cantor's paradox (G. Cantor, 1899). Let M be the set of all sets and let P(M) be
the set of all its subsets. It is clear from the definition of M that P(M) is included in
M. On the other hand, in accordance with a well- known theorem of Cantor, the ...
2
Perspectives on the History of Mathematical Logic
484), who fudges by saying that after Cantor's paradox became known to Russell
the latter constructed his own paradox; by Crossley (1973) and Bunn (1980, p.
239), who show how to obtain the Russell paradox from the Cantor paradox; ...
In Cantor's paradox it is argued that there can be no greatest cardinal number,
and yet that the cardinal number of the class of cardinal numbers (or, indeed, of
the class V) must be the greatest. The obstacle to deriving this paradox, in von ...
Willard Van Orman Quine,
1995
4
Diamond: A
Paradox Logic
Chapter. 8. The. Continuum. Cantor's Paradox Dedekind Splice Cantor's Dyadic
The Line Within the Diamond Zeno's Theorem ... Recall the "paradox of the
boundary": What 103 A Cantor's Paradox.
Nathaniel S. Hellerstein,
1997
Then Cantor's paradox is: Theorem: There is no greatest cardinal number. This
fact is a direct consequence of Cantor's theorem on the cardinality of the power
set of a set. Proof: Assume the contrary, and let C be the largest cardinal number.
6
The Blackwell Dictionary of Western Philosophy
Cantor's theorem shows that for any set A, its power set PA contains more sets
than A. The paradox arises because no set can contain more sets than the set of
all sets S, yet the power set of S does contain more sets than S. Cantor's paradox
...
Nicholas Bunnin, Jiyuan Yu,
2008
7
Logical Foundations of Mathematics and Computational ...
Before analyzing Cantor's Paradox, let us prove his theorem on the cardinality of
powersets. Theorem 1 For every set X, there is no one-to-one mapping from 'P(X)
to X. Proof Suppose f is such a mapping. Define Y : {f(Z); Z g X /\ f(Z) gz' Z}.
8
The Incomplete Universe: Totality, Knowledge, and Truth
Within naive set theory one all too quickly encounters the contradictions of
Cantor's paradox regarding a set of all sets and Russell's paradox regarding a
set of all sets not members of themselves. Cantor's theorem states that every set
will be ...
There is a recognizable version of Cantor's paradox in section 344 of Bertrand
Russell, The Principles of Mathematics (London: George Allen & Unwin, 1903;
2nd ed. 1937), 362, and Russell says in a footnote that he discovered his own ...
10
A Companion to Analytic Philosophy
Russell discovered the contradiction when reflecting upon Cantor's “paradox”
that there is no greatest cardinal number. Cantor's paradox rests on the theorem
that the number of subsets of a given set S is always greater than the number of ...
A. P. Martinich, E. David Sosa,
2008
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Ketahui apa yang diterbitkan oleh akhbar nasional dan antarabangsa dan cara istilah
Cantor's paradox digunakan dalam konteks perkara berita berikut.
Wallace's Too-Bright Fire
His 2003 book on infinity, "Everything and More," was an attempt to guide readers through the history of number theory, Cantor's paradox, ... «Wall Street Journal, Sep 08»
Alternative Axioms: NBG Set Theory
... in comments here, and my most recent post is about Cantor's paradox; ... Cantor's paradox indicates (as far as I can see) that classes are a lot ... «ScienceBlogs, Jun 07»