Thus the cofinality of this poset is n choose m.

According to the Christian doctrine of Universal Reconciliation, the Greek New Testament scriptures use the word " eon " to mean a long period ( perhaps 1000 years ) and the word " eonian " to mean " during a long period "; Thus there was a time before the eons, and the eonian period is finite.

Thus a 2 × 2 matrix with determinant − 2, when applied to a region of the plane with finite area, will transform that region into one with twice the area, while reversing its orientation.

Thus, Olbers ' paradox can not decide between a finite ( e. g. some variants of the Big Bang model ) and an infinite ( Steady State theory or static universe ) solution.

Thus meanings are generated on the fly based on finite context.

Thus for finite n, the expression " n-th element " of a well-ordered set requires context to know whether this counts from zero or one.

Thus, while in an ordinary ( finite ) hotel with more than one room, the number of odd-numbered rooms is obviously smaller than the total number of rooms.

Thus, the derivative of f ( x ) becomes for an infinitesimal, where st (·) denotes the standard part function, which associates to every finite hyperreal the unique real infinitely close to it.

Thus there is an infinite list of English phrases ( where each phrase is of finite length, but lengths vary in the list ) that unambiguously define real numbers ; arrange this list by length and then dictionary order, so that the ordering is canonical.

Thus the subcritical phase may be described as finite open islands in an infinite closed ocean.

Thus all geodesics leaving a point will eventually reconverge after a finite time, provided the appropriate energy condition holds, a result also known as the focusing theorem.

Thus it is not always true, for finite domains, that a global maximum ( minimum ) must also be a local maximum ( minimum ).

Thus, a continuous system such as a plate or shell is modeled as a discrete system with a finite number of elements interconnected at finite number of nodes.

Thus it follows, according to Zeno, that motion ( travelling a non-zero distance in finite time ) is a supertask.

Thus, the existence of a finite automaton recognizing L implies that the Myhill – Nerode relation has a finite number of equivalence classes, at most equal to the number of states of the automaton, and the existence of a finite number of equivalence classes implies the existence of an automaton with that many states.

Thus, for any set S of P-smooth numbers, there is a finite subset of S such that every element of S is divisible by one of the numbers in this subset.

Thus the Cayley graph of the abelian group with the set of generators consisting of four elements is the infinite grid on the plane, while for the direct product with similar generators the Cayley graph is the finite grid on a torus.

Thus, he advocated a system very close to that in which Hegel had argued for the ideality of the finite.

Thus, in existentialist discourse, essence can refer to physical aspect or attribute to the ongoing being of a person ( the character or internally determined goals ), or to the infinite inbound within the human ( which can be lost, can atrophy, or can be developed into an equal part with the finite ), depending upon the type of existentialist discourse.

For example an algebraic curve C either meets a given line L in a finite number of points, or possibly contains all of L. Thus a curve intersecting any line in an infinite number of points, while not containing it, must be transcendental.

Thus, the contact between ball and race is of finite size and has finite pressure.

Thus the only member churches of the present Anglican Communion existing by the mid-18th century were the Church of England, its closely linked sister church, the Church of Ireland ( which also separated from Roman Catholicism under Henry VIII ) and the Scottish Episcopal Church which for parts of the 17th and 18th centuries was partially underground ( it was suspected of Jacobite sympathies ).

Thus the conjugated p-orbitals form a one-dimensional electronic band, and the electrons within this band become mobile when it is partially emptied.

Thus, the funds of the Civil List ( la Liste civile ), voted annually by the National Assembly were partially assigned to secret expenses in order to preserve the monarchy.

Thus, partially translated and partially transliterated, the term could be rendered " Praise Jah.

Thus many of Repton's 400 or so designs remained wholly or partially unexecuted and, while Brown became very wealthy, Repton's income was never more than comfortable.

Thus, individuals with little or no direct ancestry from the Arabian Peninsula could identify themselves or be considered as Arabs, partially by virtue of their home language ( see Arab identity ).

Thus, if the perpetrator uses the prybar to pry open the window and then used his hands to lift the partially opened window, an " entry " would have taken place when he grasped the bottom of the window with his hands.

Thus, selecting the pulse waveform together with any other waveform causes every bit on the DAC to partially mix, and the loudness of the waveform is affected by the state of the pulse.

Thus it is the doctors who maybe partially responsible for mortality.

Thus the NHS is partially funded from NI contributions but not from the NI Fund.

Thus, no intermolecular antisymmetrization of the electronic states is included and the Pauli exclusion principle is only partially satisfied.

Thus, the issue was still fresh in voters ' minds when he recommended the Lieutenant Governor call a snap election in 1990, and it was partially responsible for his party's defeat.

Thus began an ignoble aspect to his career partially that culminated in Johnson's advocacy on behalf of Southern slaveowners in the infamous Dred Scott case, and which was only partially redeemed by his support for the Union during 1861-1865 War of the Rebellion.

Thus, the Judiciary Act of 1789 was the first act of Congress to be partially invalidated by the Supreme Court.

Thus, the Central Bank, turning a new page in its history, was vested with a new structure in line with, albeit partially, novelties in the field of the economy and central banking of the time.

Thus, they have only partially webbed paws, which distinguishes them from all other otters.

Thus in a deal partially brokered by Martin Luther, Roman Catholic Teutonic Prussia was transformed into the Duchy of Prussia, the first Protestant state.

Thus, the central edifice of Alba Mons resembles a partially collapsed shield volcano with a smaller, summit dome sitting on top ( pictured right ).

Thus, many non native animals were freed along parts of the community, which partially accounts for the " Belgreen Bear " in some retellings.

Thus a partial isometry is also sometimes defined as a closed partially defined isometric map.

Thus it was at least partially nocturnal.

Thus, when a fully or partially developed stand is bisected by a new road or by a clearcut, the trees on the new edge are less supported by neighbouring trees than they were and may not be capable of withstanding the higher forces which they now experience.