** 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 synset contains a group of synonymous words or collocations ( a collocation is a sequence of words that go together to form a specific meaning, such as " car pool "); different senses of a word are in different synsets.

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 real number, whether integer, rational, or irrational, has a unique location on the line.

Every real number has a ( possibly infinite ) decimal representation ; i. e., it can be written as

Every node has a location, which is a number between 0 and 1.

The album's lead single, " She's Every Woman " peaked at number-one on the Billboard Country Chart, however its follow-up single, " The Fever " ( a cover of an Aerosmith song ) only peaked at number 23, becoming Brooks's first released Country single to not chart on the Top 10.

Every rational number has a unique representation as an irreducible fraction.

Every year the International Labour Conference's Committee on the Application of Standards examines a number of alleged breaches of international labour standards.

Every year from 1985 through 1993, the number of attendees tripled.

Every LORAN chain in the world uses a unique Group Repetition Interval, the number of which, when multiplied by ten, gives how many microseconds pass between pulses from a given station in the chain.

Every vector space has a basis, and all bases of a vector space have the same number of elements, called the dimension of the vector space.

Every ketose will have 2 < sup >( n-3 )</ sup > stereoisomers where n > 2 is the number of carbons.

Every aldose will have 2 < sup >( n-2 )</ sup > stereoisomers where n > 2 is the number of carbons.

The second single from the UK release was " With Every Heartbeat ", released in late July and reached number one on the UK singles chart.

Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by, where √ is called the radical sign or radix.

Every positive number a has two square roots:, which is positive, and, which is negative.

Every number is thought of as a decimal fraction with the initial decimal point omitted, which determines the filing order.

Every well-ordered set is uniquely order isomorphic to a unique ordinal number, called the order type of the well-ordered set.

Every twin prime pair except ( 3, 5 ) is of the form ( 6n − 1, 6n + 1 ) for some natural number n, and with the exception of < var > n </ var > = 1, < var > n </ var > must end in 0, 2, 3, 5, 7, or 8.

Every third odd number is divisible by 3, which requires that no three successive odd numbers can be prime unless one of them is 3.

Every dual number has the form z = a + bε with a and b uniquely determined real numbers.

# Every noun belongs to a unique number class.

* Hardy and Littlewood listed as their Conjecture I: " Every large odd number ( n > 5 ) is the sum of a prime and the double of a prime.

Every real number has an additive inverse ( i. e. an inverse with respect to addition ) given by.

Every nonzero real number has a multiplicative inverse ( i. e. an inverse with respect to multiplication ) given by ( or ).

Every real number, rational or not, is equated to one and only one cut of rationals.