Similarly, the subset order ⊆ on the subsets of any given set is antisymmetric: given two sets A and B, if every element in A also is in B and every element in B is also in A, then A and B must contain all the same elements and therefore be equal:

Similarly, P is said to satisfy the descending chain condition ( DCC ) if every descending chain of elements eventually terminates, or equivalently if any descending sequence

" The first, another word for " angry ," is " fuming ," which ends in " g ." The second, " hungry ," at least when personified, is " eager " which ends in " r ." Similarly, the third word is " every ," which ends in " y " and is clearly used by the word " everyone.

Similarly, in the Hebrew calendar ( a lunisolar calendar ), Adar Aleph, a 13th lunar month is added seven times every 19 years to the twelve lunar months in its common years to keep its calendar year from drifting through the seasons too rapidly.

" Similarly, Irenaeus wrote that the Christian " will not be commanded to leave idle one day of rest, who is constantly keeping sabbath ", and Tertullian argued " that we still more ought to observe a sabbath from all servile work always, and not only every seventh-day, but through all time ".

Similarly the set of all vectors in which is rational for all i is a countable dense subset of ; so for every the-dimensional Euclidean space is separable.

Similarly, for every hidden argument that completely or partially justifies observed evils it is equally likely that there is a hidden argument that actually makes the observed evils worse than they appear without hidden arguments.

Similarly, for every point below 9 possessed in each of these attributes, the character receives a one-point penalty.

Similarly, they were, at one time or another, at war with virtually every other Native American group living in the Great Plains, leaving opportunities for political maneuvering by European colonial powers and the United States.

Similarly, if every preimage of a base element of Y is open in X, then f is continuous.

* Similarly, the empty space is the unique initial object in the category of topological spaces ; every one-point space is a terminal object in this category.

Similarly, in the category of pointed topological spaces, every singleton is a zero object.

Similarly, a flood level expected to be equaled or exceeded every 10 years on average is known as a ten-year flood.

Similarly, an integral domain is a Dedekind domain if and only if every divisible module over it is injective.

Similarly, Fairburn et al .’ s cognitive behavioral model of bulimia nervosa is not necessarily applicable to every individual and is certainly reductionist.

Similarly, every set is closed and the sets are sometimes called effectively closed.

Similarly, every United States employee was given a paid six-week sabbatical every four years, beyond generous regular vacation accruals.

Similarly, Kilpatrick, Resnick, Ruggiero, Conoscenti, & McCauley ( 2007 ) found in a study of 2, 000 college women nationwide that 5. 2 % experienced rape every year.

Similarly, the film Mr. Deeds shows the main character Adam Sandler purchasing a Chevrolet Corvette for every resident of his town.

Similarly, the authors quote a 1985 lecture by Eliyahu Rips, in which he describes the appellation selection process as taking " every possible variant that we considered reasonable ", and makes no mention of Havlin or an independent expert.

Similarly, private stations sprung up throughout the country, in every city and region and most towns.

Similarly, for every point on the radical axis of circles 2 and 3, the powers must be equal, h < sub > 2 </ sub > = h < sub > 3 </ sub >.

Similarly, Fermat's last theorem is stated in term of elementary arithmetic, which is a part of commutative algebra, but its proof involves deep results of both algebraic number theory and algebraic geometry.

Similarly, we can define a weight space V < sub > λ </ sub > for any representation of a Lie group or an associative algebra.

Similarly we can define a highest-weight module for representation of a Lie group or an associative algebra.

A Hopf subalgebra A is said to be right normal in a Hopf algebra H if it satisfies the condition of stability, for all h in H, where the right adjoint mapping is defined by for all a in A, h in H. Similarly, a Hopf subalgebra A is left normal in H if it is stable under the left adjoint mapping defined by.

Similarly, the quantum group U < sub > q </ sub >( G ) can be regarded as an algebra over the field Q ( q ), the field of all rational functions of an indeterminate q over Q ( see below in the section on quantum groups at q

Similarly, an affine representation of a Lie algebra g on A is a Lie algebra homomorphism from g to the Lie algebra aff ( A ) of the affine group of A.

* Similarly, if F is a finite dimensional extension field of k, then every k-algebra A gives rise naturally to a F algebra, F ⊗< sub > k </ sub > A, and A is a Frobenius k-algebra if and only if F ⊗< sub > k </ sub > A is a Frobenius F-algebra.

Similarly, the normal strain in the-direction, and-direction, becomes

Similarly, the latter expression becomes

Similarly, The South town line is not fully bordered by Hall Rd., because it becomes a dead end West of Bowen Rd.

Similarly, the district was also the setting of the 1996 film Mongkok Story ( 旺角風雲 ) directed by Wilson Yip which depicts a young man who becomes involved in a Triad gang.

Similarly, if the labyrinth chambers are correctly designed, any liquid that has escaped the main chamber, becomes entrapped in a labyrinth chamber, where it is forced into a vortex-like motion.

Similarly, when copper is inserted into a flame, the flame becomes green.

Similarly, economic production becomes more bureaucratic and rationally goal-oriented.

Similarly, becomes in ' laugh ( noun )', but in ' to be sick '.

Similarly, if a candidate gets " added " to an election, it becomes possible for the new candidate to win.

Similarly, When Zhongxiao West Road intersects with Zhongshan Road, it becomes Zhongxiao East Road.

Similarly, Vivekananda's teacher Ramakrishna Paramahansa, using an analogy said that man is like a cow tied to a pole with a rope — the karmic debts and human nature bind him and the amount of free will he has is analogous to the amount of freedom the rope allows ; as one progresses spiritually, the rope becomes longer.

Similarly, the definition of the vector projection becomes

Similarly, a new anus forms on the right side, which becomes the upper, or aboral, surface.

Similarly, when a name beginning with Dž is reduced to initial, the entire letter is initial, not just D. For example, Dženan Ljubović becomes Dž.

Similarly, if port 1 is terminated in the system impedance then becomes zero, giving