Since every equivalence relation over X corresponds to a partition of X, and vice versa, the number of possible equivalence relations on X equals the number of distinct partitions of X, which is the nth Bell number B < sub > n </ sub >:

Since one cannot logically consider these subjects to be both " at the same moment " and " away in time ", an exclusive choice has to be made that defines these two separate domains, B and C. Our reality or domain B is created by the complex, but consistent transformation of A by our biological and mental makeup.

Since this is what ( B ) itself states, it means that ( B ) must be true.

Since initially ( B ) was not true and is now true, another paradox arises.

Since the 1960s, a theory based on Linear B phonetic values suggests that Linear A language could be an Anatolian language, close to Luwian.

Since 1996, when Avon was abolished, Bath has been the principal centre of the unitary authority of Bath and North East Somerset ( B & NES ).

Since the late 1960s other songwriter's award has been presented for genre-specific categories including Grammy Award for Best Country Song, Grammy Award for Best Rock Song, Grammy Award for Best R & B Song and most recently in Grammy Award for Best Rap Song and Grammy Award for Best Gospel Song.

Since the mid-1960s, Jones has sung nearly every form of popular music – pop, rock, R & B, show tunes, country, dance, soul and gospel – and sold over 100 million records.

Since only the microscopic fields E and B are needed in the derivation of

Since 1947, one speaks of the komitatanoj A ( from the national organizations ), the komitatanoj B ( from the delegates, later members ) and the komitatanoj C ( those by-elected ).

Since 2002, actual Medicare Part B expenditures have exceeded projections.

Since the bulges are now displaced from the A – B axis, A's gravitational pull on the mass in them exerts a torque on B.

Since the Amendment's ratification, the only other President who could clearly have legally served more than eight years was Lyndon B. Johnson.

Since failure probabilities on fault trees tend to be small ( less than. 01 ), P ( A ∩ B ) usually becomes a very small error term, and the output of an OR gate may be conservatively approximated by using an assumption that the inputs are mutually exclusive events:

Since this change, the standard baritone has been the instrument pitched in B.

Since average molecular speed corresponds to temperature, the temperature decreases in A and increases in B, contrary to the second law of thermodynamics.

Since its creation in 1871, El Paso County has typically voted for the Republican presidential candidate in presidential elections ; the last Democratic nominee to win the county was Lyndon B. Johnson in 1964.

Since the closure of Garretts, the town's economy has been dominated by the two nuclear power stations on the coast at Sizewell: the now decommissioned Magnox reactor of Sizewell A and the more modern Pressurised Water Reactor of Sizewell B.

Since det ( A ) and det ( B ) are just numbers and so commute, det ( AB )

Since n grows faster than log < sub > 2 </ sub >( n ), there must exist a value n < sub > 0 </ sub > such that

This subextension is called a separable closure of K. Since a separable extension of a separable extension is again separable, there are no finite separable extensions of K < sup > sep </ sup >, of degree > 1.

Since the 1990s, SO < sub > 2 </ sub > emissions have dropped 40 %, and according to the Pacific Research Institute, acid rain levels have dropped 65 % since 1976.

Since the mass numbers of these are 12, 13 and 14 respectively, the three isotopes of carbon are known as carbon-12, carbon-13, and carbon-14, often abbreviated to < sup > 12 </ sup > C, < sup > 13 </ sup > C, and < sup > 14 </ sup > C.

Since the map d restricts to 0 on I < sub > x </ sub >< sup > 2 </ sup > ( the reader should verify this ), d descends to a map from I < sub > x </ sub > / I < sub > x </ sub >< sup > 2 </ sup > to the dual of the tangent space, ( T < sub > x </ sub > M )< sup >*</ sup >.

Since at this stress the slope of the material's stress-strain curve, E < sub > t </ sub > ( called the tangent modulus ), is smaller than that below the proportional limit, the critical load at inelastic buckling is reduced.

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since < tt > ns1 </ tt > is contained in < tt > example. org </ tt >, this requires resolving < tt > example. org </ tt > first, which presents a circular dependency.

Since all probabilities p < sub > i </ sub > add up to one: p < sub > 1 </ sub > + p < sub > 2 </ sub > + ... + p < sub > k </ sub > = 1, the expected value can be viewed as the weighted average, with p < sub > i </ sub >’ s being the weights:

Since 1983 ,< ref >

During a 1935 – 1942 colonization attempt, the island was most likely on Hawaii time, which was then 10. 5 hours behind UTC .< ref > Since it is uninhabited the island's time zone is unspecified, but it lies within a nautical time zone 12 hours behind UTC.

Since the 2002 civil war in Côte d ' Ivoire, relations between it and Burkina Faso have been filled with accusations of Burkinabé support for rebels on one side and claims of mistreatment of Burkinabé workers on the other .< ref > Blaise Campaoré :<< La crise ivoirienne inquiète le Burkina >>, Le Figaro, December 11, 2005 </ ref > Côte d ' Ivoire remains Burkina Faso's largest regional trading partner in spite of their disputes and tens of thousands of Burkinabés continue to work in the Ivory Coast.

The proof of this fact relies on an algorithm which, given the first n digits of Ω, solves Turing's halting problem for programs of length up to n. Since the halting problem is undecidable, Ω can not be computed.

Since the proving of the theorem, efficient algorithms have been found for 4-coloring maps requiring only O ( n < sup > 2 </ sup >) time, where n is the number of vertices.

Since it is a balanced tree, it guarantees insertion, search and delete to be O ( log n ) in time, where n is the total number of elements in the tree.

Since there are n!

Since the leftmost divisor bit zeroed every input bit it touched, when this process ends the only bits in the input row that can be nonzero are the n bits at the right-hand end of the row.

* Omission of the high-order bit of the divisor polynomial: Since the high-order bit is always 1, and since an n-bit CRC must be defined by an ( n + 1 )- bit divisor which overflows an n-bit register, some writers assume that it is unnecessary to mention the divisor's high-order bit.

Since 1953, " binomi < u > n </ u > al nomenclature " is the technically correct term in zoology.

Since this quantity goes to infinity as n increases, we expect that every large even integer has not just one representation as the sum of two primes, but in fact has very many such representations.

If n is not a prime power, then every Sylow subgroup is proper, and, by Sylow's Third Theorem, we know that the number of Sylow p-subgroups of a group of order n is equal to 1 modulo p and divides n. Since 1 is the only such number, the Sylow p-subgroup is unique, and therefore it is normal.

Since for each n this removes intervals adding up to at most 1 / 2 < sup > n + 1 </ sup >, the nowhere dense set remaining after all such intervals have been removed has measure of at least 1 / 2 ( in fact just over 0. 535 ... because of overlaps ) and so in a sense represents the majority of the ambient space.

The transfer principle states that true first order statements about R are also valid in * R. For example, the commutative law of addition, x + y = y + x, holds for the hyperreals just as it does for the reals ; since R is a real closed field, so is * R. Since for all integers n, one also has for all hyperintegers H. The transfer principle for ultrapowers is a consequence of Łoś ' theorem of 1955.

Since every element of C < sub > n </ sub > generates a cyclic subgroup and the subgroups of C < sub > n </ sub > are of the form C < sub > d </ sub > where d | n, the formula follows.