Every regular ordinal is the initial ordinal of a cardinal.

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

Every finite ordinal ( natural number ) is initial, but most infinite ordinals are not initial.

Every winter a kegful of this sauce was made and placed at the end of a row of four other kegs in the cellar, so that when its turn came, it was properly mellowed.

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

Every time a speech sound is produced for a given phoneme, it will be slightly different from other utterances, even for the same speaker.

Four other hits from the album made the Pop top 20: " Every Heartbeat " ( No. 2 ), " That's What Love Is For " ( No. 7 ), " Good For Me " ( No. 8 ), and " I Will Remember You " ( No. 20 ).

According to Every, one example may be " the myth of St. George " and other stories about saints battling dragons, which were " modelled no doubt in many cases on older representations of the creator and preserver of the world in combat with chaos ".

Every other aspect of film making originated in a different medium than film ( photography, art direction, writing, sound recording ), but editing is the one process that is unique to film.

Every two months IMU publishes an electronic newsletter, IMU-Net, that aims to improve communication between IMU and the worldwide mathematical community by reporting on decisions and recommendations of the Union, major international mathematical events and developments, and on other topics of general mathematical interest.

Every other senior diplomat remained at his post.

Every product is perfectly homogeneous and a perfect substitute for any other.

Every reality of the Marvel Universe has numerous interconnected dimensions, with each dimension differing from those of other realities ; for example, the Ultimate Asgard has clearly been shown to be distinct from the Asgard known to Earth-616 characters.

Every host of a news server maintains agreements with other news servers to regularly synchronize.

Every four years, the Cricket World Cup involves all the Test-playing nations and other national sides who qualify through the ICC World Cup Qualifier.

Every device in a WPAN will be able to plug in to any other device in the same WPAN, provided they are within physical range of one another.

Every year, there are growing numbers of regional, national and international wrestling fan conventions, where fans can meet and converse with wrestlers and each other.

Every associative algebra is obviously power-associative, but so are all other alternative algebras ( like the octonions, which are non-associative ) and even some non-alternative algebras like the sedenions.

Every RFC is submitted as plain ASCII text and is published in that form, but may also be available in other formats.

Every patient with a point total of 6 or higher is unequivocally classified as an RA patient, provided he has synovitis in at least one joint and given that there is no other diagnosis better explaining the synovitis.

Every stereogenic center in one has the opposite configuration in the other.

Every quark in the universe does not attract every other quark in the above distance independent manner, since colour-confinement implies that the strong force acts without distance-diminishment only between pairs of single quarks, and that in collections of bound quarks ( i. e., hadrons ), the net colour-charge of the quarks cancels out, as seen from far away.

Every game in the main Zelda series has consisted of three principal areas: an overworld in which movement is multidirectional, allowing the player some degree of freedom of action ; areas of interaction with other characters ( merely caves or hidden rooms in the first game, but expanding to entire towns and cities in subsequent games ) in which the player gains special items or advice ; and dungeons, areas of labyrinthine layout, usually underground, comprising a wide range of difficult enemies, bosses, and items.

Every other producer had already turned down the show, deeming it too dark and depressing.

Every second ( or more often in advanced levels ), a piece comes in from the side and possibly pushes other pieces forward.

Every Saturday morning it hosts a large outdoor market or " mercadillo ", where many gypsies come and sell their wares of fruits and vegetables, clothes and shoes, and other odds and ends.

Every year Haiti's carnival draws visitors from other countries.

The convention details ( amongst other things ) that " Every driver shall keep to the edge of the carriageway appropriate to the direction of traffic ", and the " Drivers overtaking shall do so on the side opposite to that appropriate to the direction of traffic ", notwithstanding the presence or absence of oncoming traffic.

Disraeli wrote a personal letter to Gladstone, asking him to place the good of the party above personal animosity: " Every man performs his office, and there is a Power, greater than ourselves, that disposes of all this ..." In responding to Disraeli Gladstone denied that personal feelings played any role in his decision then and previously to accept office, while acknowledging that there were differences between him and Derby " broader than you may have supposed.

* Every topological space X is a dense subspace of a compact space having at most one point more than X, by the Alexandroff one-point compactification.

Every contraction mapping is Lipschitz continuous and hence uniformly continuous ( for a Lipschitz continuous function, the constant k is no longer necessarily less than 1 ).

This was to be based on utilitarian principles ; he said: " Every man has a right to that, the exclusive possession of which being awarded to him, a greater sum of benefit or pleasure will result than could have arisen from its being otherwise appropriated.

The work is much more accessible than Sana ’ i ’ s for instance ; " Every line of the Rubaiyat has more meaning than almost anything you could read in Sufi literature ".

Every aspect of the collage is moving and will never be the same more than once, which was congruent with society at the time.

In Anime Essentials: Every Thing a Fan Needs to Know, Giles Poitras wrote " More humorous and less serious looking than the characters in the Lodoss War series, the stars of Slayers provide action and laughs ".

Every new emperor after him was honored by the Senate with the wish felicior Augusto, melior Traiano (" luckier than Augustus and better than Trajan ").

Every element s, except a possible greatest element, has a unique successor ( next element ), namely the least element of the subset of all elements greater than s. Every subset which has an upper bound has a least upper bound.

Every day, there are more than one million vehicles travelling within the city.

Every day, doors seem to open, and every day, we interact, perhaps more than ever before, with the world outside.

: Every even integer greater than 2 can be expressed as the sum of two primes.

: Every integer greater than 2 can be written as the sum of three primes.

: Every integer greater than 5 can be written as the sum of three primes.

: Every even integer greater than 2 can be written as the sum of two primes,

In the autumn of 1970 Jurgen Wischnewski of the SPD declared, ‘ Every week more than three plans for reform come up for decision in cabinet and in the Assembly .’ ”

The Body of Liberties adopted in 1641 by the Massachusetts Bay colonists states, “ Every married woman shall be free from bodily correction or stripes by her husband, unless it be in his own defense from her assault .” In the United States, legal decisions in Mississippi ( 1824 ) and North Carolina ( 1868 and 1874 ) make reference to — and reject — an unnamed " old doctrine " or " ancient law " by which a man was allowed to beat his wife with a stick no wider than his thumb.

* Every rule of thumb on earth in one place-A user participation reference project based on Tom Parker's 3 best-selling books and more than 25 years of research.

Every material has its own characteristic resistivity — for example rubber's resistivity is far larger than copper's.