[permalink] [id link]
** The Banach – Tarski paradox.
from
Wikipedia
Some Related Sentences
** and Banach
** Banach algebra: an associative algebra A over the real or complex numbers which at the same time is also a Banach space.
** and –
** This is a distinguished work which stands out from, and above, many of the books and articles which have ben written in this century on Avicenna ( Ibn Sīnā ) ( A. D. 980 – 1037 ).
** The numbers and are not algebraic numbers ( see the Lindemann – Weierstrass theorem ); hence they are transcendental.
** Haliotis brazieri f. hargravesi ( Cox, 1869 ) – synonym: Haliotis ethologus, the Mimic abalone, Haliotis hargravesi, the Hargraves ’ s abalone
** Haliotis diversicolor squamata Reeve, 1846 – synonym: Haliotis squamata – the scaly Australian abalone
** and Tarski
** and paradox
** Shaar HaYichud-The Gate of Unity, Dovber Schneuri-A detailed explanation of the paradox of divine simplicity.
** and .
** Eunectes murinus, the green anaconda, the largest species, is found east of the Andes in Colombia, Venezuela, the Guianas, Ecuador, Peru, Bolivia, Brazil and on the island of Trinidad.
** Eunectes notaeus, the yellow anaconda, a smaller species, is found in eastern Bolivia, southern Brazil, Paraguay and northeastern Argentina.
** Eunectes deschauenseei, the dark-spotted anaconda, is a rare species found in northeastern Brazil and coastal French Guiana.
** Eunectes beniensis, the Bolivian anaconda, the most recently defined species, is found in the Departments of Beni and Pando in Bolivia.
** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.
** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.
** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
** In the product topology, the closure of a product of subsets is equal to the product of the closures.
** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.
0.526 seconds.