Less formally, the equivalence relation ker on X, takes each function f: X → X to its kernel ker f. Likewise, ker ( ker ) is an equivalence relation on X ^ X.

Likewise, a function is called monotonically decreasing ( also decreasing, or non-increasing ) if, whenever x ≤ y, then f ( x ) ≥ f ( y ), so it reverses the order ( see Figure 2 ).

Likewise, the question of whether " y is in f ( x )" cannot actually be physically computed.

That is, two objects X and X ′ may map to the same object in D ( which is why the range of a full and faithful functor is not necessarily isomorphic to C ), and two morphisms f: X → Y and f ′: X ′ → Y ′ ( with different domains / codomains ) may map to the same morphism in D. Likewise, a full functor need not be surjective on objects or morphisms.

Likewise, ( x, − y ) are the coordinates of its reflection across the first coordinate axis ( the X axis ).

Likewise, if Q ( x, n ) denotes the number of n-free integers ( e. g. 3-free integers being cube-free integers ) between 1 and x, one can show

Likewise, a variable y is logarithmically proportional to a variable x, if y is directly proportional to the logarithm of x, that is if there exist non-zero constants k and a

Likewise, if more than one root is known, a linear factor ( x – r ) in one of them ( r ) can be divided out to obtain Q ( x ), and then a linear term in another root, s, can be divided out of Q ( x ), etc.

Likewise, a loop in X is one that is based at x < sub > 0 </ sub >.

Likewise, if x is greater than x_center, we know that all intervals in S_center must begin before x, so we find those intervals that end after x using the list sorted by interval endings.

Likewise, a change in is not necessary to change y, because a change in y could be caused by something implicit in the error term ( or by some other causative explanatory variable included in the model ).

Likewise, we can also express dx in terms of dy and solve for y in terms of θ:

Likewise, a legend from Pont y Wern says that in the 13th or 14th century, the inhabitants of the town of Corwrion watched fairies dancing in a ring around a glow worm every Sunday after church at a place called Pen y Bonc.

Likewise, a change in is not necessary to change y, because a change in y could be caused by something implicit in the error term ( or by some other causative explanatory variable included in the model ).

Likewise the letters g, w, and y are also pronounced a bit harder as a terminal letter of a word with a grave accent mark.

Likewise, he was President of the Coordinating Committee of Agricultural, Trade, Industry and Financial Associations ( In Spanish, Comité Coordinador de Asociaciones Agrícolas, Comerciales, Industriales y Financieras – CACIF -) Director of the Hemispheric Congress of the Chambers of Commerce of Latin America, President of the Permanent Secretary of Chambers of Commerce and Industries of Latin America ( In Spanish, Secretaría Permanente de Cámaras de Comercio e Industrias Latinas – CAMACOL -) and Vice-president of the Permanent Committee of Expositions ( In Spanish, Comité Permantente de Exposiciones – COPEREX -)

Likewise, in the theory of the firm, the lemma gives a similar formulation for the conditional factor demand for each input factor: the derivative of the cost function c ( w, y ) with respect to the factor price:

Likewise Mahfouz sees the development of society has an important influence on the role of women, so he represents the traditional, obedient women who do not go to school such as Amina, Abd al-Jawad's wife, and her daughters in the first novel, women as students in the university such as Aida, Kamal's beloved, in the second novel, and women as students in the university, members of the Marxist party and editors of the journal of the party in the third novel.

Likewise, the icon of the blindfold can symbolize the dichotomy of the conscious and the unconscious, as wearing a blindfold represents a stasis or a lesser state of consciousness, whereas taking off one's blindfold represents a form of awakening or rebirth.

Likewise, Melinda is fascinated by Cubism, because it represents what is beyond the surface.

Likewise, Locrinus represents the medieval Welsh word Loegria ( England ) ( modern Welsh Lloegr ), and Camber represents the Latin word Cambria or the Welsh word Cymru ( Wales ).

( P ̸) Likewise, points are represented with number of points before a lower-case " p ", for example, 5p represents “ 5 points ”, and 6P2p represents “ 6 picas and 2 points ”, and 1P1 represents “ 13 points ”, which is converted to a mixed fraction of 1 pica and 1 point.

Likewise, the Logrus seeks to destroy Corwin's Pattern, since it represents an additional artifact of Order against Chaos ( although not in accord with the Order of Amber's Pattern ) — but equally cannot do so without the risk of a counter-stroke from Amber's Pattern.

Likewise, according to the plot the " health " meter represents the Chex Warrior's ability to move, with 0 % representing being completely covered in slime and unable to move.

Likewise the judge, Thomas Yeotis, discredited the psychiatrists view on the grounds that " you make a nice appearance, and yet, there's something about you that disturbs me.

Likewise, their succession was not hereditary, something that would become the custom after them, beginning with the subsequent Umayyad Caliphate.

Likewise, the West Ukrainian troops were more disciplined while those of Kiev's Ukrainian People's Army were more chaotic and prone to committing pogroms, something actively opposed by the western Ukrainians.

Likewise, images of the sideline may suggest that the highlighted player had done something of interest outside of the confines of play.

Likewise, the common practice to without discrimination, publish " Average Joe's " highly opinionated opinion on the cause of something, ( such as a flood ) simply because he's standing by the side of the flood observing it.

Likewise, it was assumed that societies start out primitive, perhaps in a Hobbesian state of nature, and naturally progress toward something resembling industrial Europe.

Likewise, W. J. T. Mitchell explicitly distinguishes the two fields in his claim that visual culture studies “ helps us to see that even something as broad as the image does not exhaust the field of visuality ; that visual studies is not the same thing as image studies, and that the study of the visual image is just one component of the larger field .”

Likewise, it was assumed that societies start out primitive, perhaps in a Hobbesian state of nature, and naturally progress toward something resembling industrial Europe.

Likewise, a group of atoms can remain bound to each other, forming a molecule.

Likewise, there is a formula for combining the covariances of two sets that can be used to parallelize the computation:

Likewise, a baserunner can attempt to steal a base, or the batter can choose to swing at an intentional ball ; however, these rarely occur since taking these risks is rarely more beneficial to the offensive team than allowing the walk.

Likewise, bony fish can release the ammonia into the water where it is quickly diluted.

Likewise, the angular momentum can be measured from far away using frame dragging by the gravitomagnetic field.

Likewise, if a substance can form crystals, it can also form polycrystals.

Likewise, spheres are compact, but a sphere missing a point is not since a sequence of points can tend to the missing point without tending to any point within the space.

Likewise, the menstrual cycle in women with epilepsy can influence patterns of seizure recurrence.

Likewise, a functor from G to the category of vector spaces, Vect < sub > K </ sub >, is a linear representation of G. In general, a functor G → C can be considered as an " action " of G on an object in the category C. If C is a group, then this action is a group homomorphism.

Likewise, graph theory is useful in biology and conservation efforts where a vertex can represent regions where certain species exist ( or habitats ) and the edges represent migration paths, or movement between the regions.

Likewise, grappling sports have been devised so that their participants can compete using full physical effort without injuring their opponents.

Likewise, the tradename Hycodan points to its relationship with oxycodone ( Percodan ) hy-for hydrogen, per-for oxygen ( as in potassium permanganate ) -- this can also be seen with other trade names for other drugs, like Permonid ( desomorphine ) and Hydal ( hydromorphone ).

Likewise, a below favorable oxygen content can make life just as difficult.

Likewise, one can construe semantic internalism in two ways, as a denial of either of these two theses.

Likewise, every use of modus ponens can be converted to a use of modus tollens and transposition.

Likewise, a player with can use his 5-5 to play the full house.

Likewise, it can never have zero energy, meaning that the particle can never " sit still ".

Likewise, these components that aid in insertion of the photo, referred to as slip agents, can break down and transfer from the plastic to the photograph, where they deposit as an oily film, attracting further lint and dust.

Likewise, two sets of one-sided tetrominos can be fit to a rectangle in more than one way.

Likewise, the number for " K " in Europe can refer to the weight of an equivalent quantity of K < sub > 2 </ sub > O, whereas in Australia it refers to elemental potassium.

Likewise, catalase has one of the highest turnover numbers of all enzymes ; one catalase molecule can convert millions of molecules of hydrogen peroxide to water and oxygen each second.