** Pope Pius X

** for all f in X ′ there exists x in X with ǁxǁ ≤ 1, so that f ( x ) = ǁfǁ.

** Louis X ( 1314 – 1316 )

** Charles X ( 1824 – 1830 )

** Console ( Mac OS X ), a log viewer on OS X

** X register and Y register-They are number stores where numbers are stored temporarily while doing calculations.

** Louis X the Quarreller, 1314 – 1316

** Leather Goddesses of Phobos 2: Gas Pump Girls Meet the Pulsating Inconvenience from Planet X!

** 2007 – 2009 X

** XNU, from the Mac OS X operating systems

** Knuth's Algorithm X

** X PixMap for portable icons

** Mac OS X Calculator

** Planet X < sup > 1 </ sup >

** publickey: a method for public key-based authentication, usually supporting at least DSA or RSA keypairs, with other implementations also supporting X. 509 certificates.

** If O takes center ( best move for him ), X should take the corner opposite the original, and proceed as detailed above.

** If O plays a corner or side-middle first, X is guaranteed to win:

** Ogg ( Vorbis ) vs. Lame ( MP3 )-a comparison at 128 .. 350kbit / s, Vorbis_1. 0beta4 X Lame_3. 88, year 2001

A space X can be embedded into the double dual X ** by

Thus T: X → X ** is an injective linear mapping, though it is not surjective unless X is reflexive.

** 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.

** The Cartesian product of any family of nonempty sets is nonempty.

** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.

** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

** For every non-empty set S there is a binary operation defined on S that makes it a group.

** Tychonoff's theorem stating that every product of compact topological spaces is compact.

** 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.

** Any union of countably many countable sets is itself countable.

** If the set A is infinite, then there exists an injection from the natural numbers N to A ( see Dedekind infinite ).

** Every infinite game in which is a Borel subset of Baire space is determined.

** The Vitali theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.

** The Lebesgue measure of a countable disjoint union of measurable sets is equal to the sum of the measures of the individual sets.

** The Nielsen – Schreier theorem, that every subgroup of a free group is free.

** A reflexive saccade is triggered exogenously by the appearance of a peripheral stimulus, or by the disappearance of a fixation stimulus.

** con sí → consigo = " with yourself / himself / herself / itself " ( reflexive )

** Well-ordering theorem: Every set can be well-ordered.

** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.

** Every surjective function has a right inverse.

** 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.

** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.

** Antichain principle: Every partially ordered set has a maximal antichain.

** Every vector space has a basis.

** Every unital ring other than the trivial ring contains a maximal ideal.

** The closed unit ball of the dual of a normed vector space over the reals has an extreme point.