** 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.

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

: Every non-empty set A contains an element B which is disjoint from A.

Every computer contains an internal clock that regulates the rate at which instructions are executed and synchronizes all the various computer components.

Cantor points out that his constructions prove more — namely, they provide a new proof of Liouville's theorem: Every interval contains infinitely many transcendental numbers.

Every organic compound contains at least one atom of carbon.

Every ordered field contains an ordered subfield that is isomorphic to the rational numbers.

The revised edition of Robyn was released in the UK in April 2007, and contains two new tracks —" With Every Heartbeat " ( a collaboration with Kleerup ) and " Cobrastyle " ( a cover of a 2006 single by Swedish rockers Teddybears )— alongside slightly altered versions of two of the original songs.

# Every simple path from a given node to any of its descendant leaves contains the same number of black nodes.

Every altar in every Orthodox church contains relics, usually of martyrs.

Every PostScript printer contains a RIP in its firmware.

* Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.

Every one has higher glucose levels for one or two hours after eating food which contains some types of carbohydrates.

Every bag of blood ( 450 – 500 ml ) contains 200 – 250 milligrams of iron.

Every temple of The Church of Jesus Christ of Latter-day Saints ( LDS Church ) contains a baptismal font on twelve oxen that is modeled after the molten sea.

Every issue of GAMES Magazine contains a large crossword with a double clue list, under the title The World's Most Ornery Crossword ; both lists are straight and arrive at the same solution, but one list is significantly more challenging than the other.

Every gap sequence that contains 1 yields a correct sort ; however, the properties of thus obtained versions of Shellsort may be very different.

Every prostaglandin contains 20 carbon atoms, including a 5-carbon ring.

Every device contains at least one swap chain.

Every living organism contains DNA, RNA, and proteins.

Every game in the Mario Party series contains 50 to 80 mini-games of a few different types.

The offset part of the logical address contains an offset inside the segment, i. e. the physical address can be calculated as ( if the address line A20 is enabled ), respectively ( segment_part × 16 + offset ) mod 2 < sup > 20 </ sup > ( if A20 is off ) Every segment has a size of 2 < sup > 16 </ sup > bytes.

Every chapter contains a comprehensive compilation all of the published examples of the reaction organized in tables according to the structure of the starting material.

Every Riemann surface is a two-dimensional real analytic manifold ( i. e., a surface ), but it contains more structure ( specifically a complex structure ) which is needed for the unambiguous definition of holomorphic functions.

Every finite simple group is isomorphic to one of the following groups:

Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.

* Every group G acts on G, i. e. in two natural but essentially different ways:, or.

Every galaxy of sufficient mass in the Local Group has an associated group of globular clusters, and almost every large galaxy surveyed has been found to possess a system of globular clusters.

* Every Lie group is parallelizable, and hence an orientable manifold ( there is a bundle isomorphism between its tangent bundle and the product of itself with the tangent space at the identity )

Every instrumental group ( or section ) has a principal who is generally responsible for leading the group and playing orchestral solos.

* Every closed subgroup of a profinite group is itself profinite ; the topology arising from the profiniteness agrees with the subspace topology.

While he admits the existence of caste-based discrimination, he writes that " Every social group cannot be regarded as a race simply because we want to protect it against prejudice and discrimination ".

Every local group is required to have a seneschal who reports to the kingdom's seneschal.

Every local group is required to have one.

* Every topological group is completely regular.

Every summer the group gathers in Newport, RI for week long dance training, seaside teas, and evenings enjoying the splendors of the Gilded Age.

* Every finitely generated group with a recursively enumerable presentation and insoluble word problem is a subgroup of a finitely presented group with insoluble word problem

Every group can be trivially made into a topological group by considering it with the discrete topology ; such groups are called discrete groups.

Every topological group can be viewed as a uniform space in two ways ; the left uniformity turns all left multiplications into uniformly continuous maps while the right uniformity turns all right multiplications into uniformly continuous maps.

Every subgroup of a topological group is itself a topological group when given the subspace topology.

:" Every group is naturally isomorphic to its opposite group "

Every ten years, when the general census of population takes place, each citizen has to declare which linguistic group they belong or want to be aggregated to.