Two elements of the set are considered equivalent ( with respect to the equivalence relation ) if and only if they are elements of the same cell.

Two such functions are deemed equivalent when their respective sets of fixpoints have the same cardinality, corresponding to cycles of length one in a permutation.

Two loops are considered equivalent if one can be deformed into the other without breaking.

Two likelihood functions are equivalent if one is a scalar multiple of the other.

Metals typically consist of close-packed atoms, meaning that the atoms are arranged like sphere Two packing motifs are common, one being body-centered cubic wherein each metal is surrounded by eight equivalent metals.

Two monosaccharides with equivalent molecular graphs ( same chain length and same carbonyl position ) may still be distinct stereoisomers, whose molecules differ in the three-dimensional arrangement of the bonds of certain atoms.

Two sequences were considered equivalent if they differed only in a finite number of elements.

Two equivalent images of the chemical structure of sodium stearate, a typical soap.

Two computers P and Q are called Turing equivalent if P can simulate Q and Q can simulate P. Thus, a Turing-complete system is one that can simulate a Turing machine ; and, per the Church-Turing thesis, that any real-world computer can be simulated by a Turing machine, it is Turing equivalent to a Turing machine.

: Two publications, the Canada Flight Supplement ( CFS ) and the Water Aerodrome Supplement, published by NAV CANADA under the authority of Transport Canada provides equivalent information.

Two triangles and are said to be similar if either of the following equivalent conditions holds:

Two systems for which these parameters coincide are called similar ( as with similar triangles, they differ only in scale ); they are equivalent for the purposes of the equation, and the experimentalist who want to determine the form of the equation can choose the most convenient one.

Two categories may also be considered " equivalent " for purposes of category theory, even if they are not precisely the same.

Two equivalent images of the chemical structure of sodium stearate, a typical soap.

Khayyam, for example, tried to derive it from an equivalent postulate he formulated from " the principles of the Philosopher " ( Aristotle ): " Two convergent straight lines intersect and it is impossible for two convergent straight lines to diverge in the direction in which they converge.

Two related transforms are the discrete sine transform ( DST ), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform ( MDCT ), which is based on a DCT of overlapping data.

Two flexagons are equivalent if one can be transformed to the other by a series of pinches and rotations.

Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R < sup > 3 </ sup > upon itself ( known as an ambient isotopy ); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.

In Finland, the Elämän Sana (" the Word of life ") group, as the most " mainline " of the different branches of Laestadianism, has been prominent within the hierarchy of the Evangelical Lutheran Church of Finland: Two members have been elected bishops of Oulu, and one has served as Chaplain General ( head chaplain of the Finnish Defence Forces and the equivalent of a Major General ).

Two such metrics are considered equivalent if the angles they measure are the same.

Two gyrators in cascade are equivalent to a transformer but the transformer is usually retained for convenience.

Two TEU are equivalent to one forty-foot equivalent unit ( FEU ).

Volumes One and Two, selected from the sound tracks of a television series, contain `` conversations with the elder wise men of our day ''.

* In Allan Cole and Chris Bunch's Sten science fiction series, Book Two, The Wolf Worlds, the Scottish character Alex bemoans their predicament after crash landing ; ' A slackit way f ' r a mon ,' Alex mourned to himself.

Two different animated cartoon series also starred ' Charlie ' a tramp character, the first a series of nine shorts from 1916 by Movca Film Service.

Two decades later, Herbert's son Brian Herbert, along with Kevin J. Anderson, published two sequels – Hunters of Dune ( 2006 ) and Sandworms of Dune ( 2007 ) – based on notes left behind by Frank Herbert for what he referred to as Dune 7, his own planned seventh novel in the Dune series.

Two decades after Frank Herbert's death, his son Brian Herbert, along with Kevin J. Anderson, published two sequels – Hunters of Dune ( 2006 ) and Sandworms of Dune ( 2007 ) – based on notes left behind by Frank Herbert for what he referred to as Dune 7, his own planned seventh novel in the Dune series.

He also appeared in a series of television roles, some of which ( such as A Tale of Two Cities in 1980 ) mirrored his affinity for the classics.

In January 2009, Kane appeared in the TV series Two and a Half Men as the mother of Alan Harper's receptionist.

Two slots & a hole stamped beneath the number allow the tag to be broken in half, and the long bottom portion has both the ID number and a series of holes which allows the tag to be inserted into a dosimeter.

The completed films included the seven-episode Why We Fight series — consisting of Prelude to War ( 1942 ), The Nazis Strike ( 1942 ), Divide and Conquer ( 1943 ), The Battle of Britain ( 1943 ), The Battle of Russia ( 1943 ), The Battle of China ( 1944 ), War Comes to America ( 1945 ) – plus Know Your Enemy: Japan ( 1945 ), Tunisian Victory ( 1945 ), and Two Down and One to Go ( 1945 ) that do not bear the Why We Fight banner ; as well as the African-American related, The Negro Soldier ( 1944 ).

Dallara briefly tried the series before moving up to Formula One, and AGS moved up from Formula Two but never recaptured their occasional success.

Two anime television series, Ghost in the Shell: Stand Alone Complex and Ghost in the Shell: S. A. C.

Two of the series ' three creators, comedy writers Frank Peppiatt and John Aylesworth, were from Canada.

The Tube is a television documentary originally made by ITV in 2002 in October 2011 the director of BBC Two announced announced a " new " TV series called ' The Tube ' which looks into the life of those who work and travel on London Underground.

In 2010, Ferrigno appeared in " My Two Chads ", an episode of Sonny with a Chance, appearing as himself in an episode of the fictional series MacKenzie Falls.

Two rival theories to account for the relationship between change and identity are Perdurantism, which treats the tree as a series of tree-stages, and Endurantism, which maintains that the tree — the same tree — is present at every stage in its history.

Two days later, the Sex Pistols, The Clash, The Damned, and The Heartbreakers set out on the Anarchy Tour, a series of gigs throughout the UK.

Two new series, Greysuit, a super-powered government agent drawn by John Higgins, and Defoe, a 17th century zombie hunter drawn by Leigh Gallagher, began in 2000 AD prog 1540 .< ref >

Two of the most famous U. S. parodies were the series Mary Hartman, Mary Hartman ( 1976 – 77 ) and Soap ( 1977 – 81 ).

* 2001 – Two hijacked aircraft crash into the World Trade Center in New York City, while a third smashes into The Pentagon in Arlington, Virginia, in a series of coordinated suicide attacks.

All the Sontarans depicted in the television series have monosyllabic names, many beginning with an initial ' st ' sound ( e. g. Styre ( The Sontaran Experiment ), Stor ( The Invasion of Time ), Stike ( The Two Doctors ), Staal ( The Sontaran Stratagem ), and Strax ( A Good Man Goes To War ); exceptions are Linx ( The Time Warrior ), Varl ( The Two Doctors ) Skorr ( The Sontaran Stratagem ) and Kaagh ( The Sarah Jane Adventures )).

They appear for the final time in the original series in The Two Doctors.

* The Space Quest 15th Anniversary Collector's Edition ( 1994 ) – Released for Sierra's 15th anniversary, this contained games I-V and Roger Wilco's Spaced Out Game Pack, plus a video featuring the Two Guys from Andromeda and a complete history of the game series.