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We claim that, as a field, the quotient is isomorphic to the complex numbers, C. A general complex number is of the form, where a and b are real numbers and Addition and multiplication are given by
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We and claim
Leslie Newbiggin reflects the dominant position within the World Council of Churches when he says, `` We must claim absoluteness and finality for Christ and His finished work, but that very claim forbids us to claim absoluteness and finality for our understanding of it ''.
* " We therefore find that Professor Behe ’ s claim for irreducible complexity has been refuted in peer-reviewed research papers and has been rejected by the scientific community at large.
In response to the claim in Whewell's treatise that " We may thus, with the greatest propriety, deny to the mechanical philosophers and mathematicians of recent times any authority with regard to their views of the administration of the universe ", Charles Babbage published what he called The Ninth Bridgewater Treatise, A Fragment.
The Court responded, " We reject this claim because neither the Supreme Court, nor this circuit, has ever held that evolutionism or Secular Humanism are ' religions ' for Establishment Clause purposes.
We claim the rational, eschew the irrational ,( contrary to reason ) and question the non-rational ( that which is neither provable nor disprovable by reason alone, i. e. life after death ).
We can also, rationally accept a claim on the basis of another persons testimony unless at least one of the following is found to be true: 1. the claim is implausible ; 2.
A famous claim of the self-evidence of a moral truth is in the United States Declaration of Independence, which states, " We hold these Truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.
We recognize that Jesus is telling a story to illustrate a moral point, and that such stories often don't claim to correspond to actual events.
We must, however, handle these with some caution, since some of the poems ( Idylls ) commonly attributed to him have little claim to authenticity.
We note again that no claim is made that the activity is not sufficiently connected to the State to justify a tax, or that the tax is not fairly related to benefits provided the taxpayer, or that the tax discriminates against interstate commerce, or that the tax is not fairly apportioned.
The 25th anniversary issue of Biblical Archeological Review ( March / April 2001 edition ), editor Hershel Shanks quoted several biblical scholars who insisted that minimalism was dying, although leading minimalists deny this and a claim has been made " We are all minimalists now ".
They claim that they are entitled to compensation for Pepsi's use of the song " Why Can ’ t We Be Friends?
" She argues that Dissenters deserve the same rights as any other men: " We claim it as men, we claim it as citizens, we claim it as good subjects.
Announcing the death of Life, Maxwell declared: “ We cannot claim, like Mr. Gene Tunney, that we resigned our championship undefeated in our prime.
We claim that c < sub > i </ sub > ≥ i-2 for each i with 2 ≤ i ≤ d: Just before y < sub > i </ sub > was made a child of x, y < sub > 1 </ sub >,..., y < sub > i − 1 </ sub > were already children of x, and so x had degree at least i − 1 at that time.
At the Eleventh Annual Assembly in 1915, the General Overseer stated in his annual address, " We do not claim to have reached perfection ; we are only searching for it.
We and field
We do not favor one field over another: we think that all inquiry, all scholarly and artistic creation, is good -- provided only that it contributes to a sense and understanding of the true ends of life, as all first-rate scholarship and artistic creation does.
We can do this through the characteristic values and vectors of T in certain special cases, i.e., when the minimal polynomial for T factors over the scalar field F into a product of distinct monic polynomials of degree 1.
We might not see any rotation initially, but if we closely look at the right, we see a larger field at, say, x = 4 than at x = 3.
We have evidence that Jupiter has a magnetic field and that birds are oviparous, but as of yet, we do not seem to have found evidence of moral properties, such as " goodness ".
We have previously mentioned that there can be more than one way of indexing the degrees of freedom in a quantum field.
) We can construct field operators by applying the Fourier transform to the creation and annihilation operators for these states.
We take the velocity field associated with this current as the velocity field whose integral curves yield the motion of the particle.
We conclude that, in the field of public education, the doctrine of " separate but equal " has no place.
We provide a sketch of a proof for the case where the underlying field of scalars is the complex numbers.
We have, therefore, directed the Irish Army authorities to have field hospitals established in County Donegal adjacent to Derry and at other points along the Border where they may be necessary.
( We developed ) a theory to explain how solar protons can diffuse inward and gain energy in the Earth's magnetic field.
We now recognise this as part of the ideal class group: in fact Kummer had isolated the p-torsion in that group for the field of p-roots of unity, for any prime number p, as the reason for the failure of the standard method of attack on the Fermat problem ( see regular prime ).
We can assume that A contains ¬ φ, the field axioms, and, for some k, the first k sentences of the form 1 + 1 +...+ 1 ≠ 0 ( because adding more sentences doesn't change unsatisfiability ).
We can construct a classical continuous random field that has the same probability density as the quantum vacuum state, so that the principal difference from quantum field theory is the measurement theory ( measurement in quantum theory is different from measurement for a classical continuous random field, in that classical measurements are always mutually compatible — in quantum mechanical terms they always commute ).
We assume that the underlying field is not of characteristic 2: that is, that where 1 denotes the multiplicative identity and 0 the additive identity of the given field.
We and quotient
We can expect the coarse quotient to be a smooth manifold if for example the stabilizer groups are trivial ( as in the example of the Čech groupoid ).
( 1 ) We could just stop there and say that the dividend divided by the divisor is the quotient written at the top with the remainder written at the bottom ; equivalently we could write the answer as the quotient followed by a fraction that is the remainder divided by the dividend.
the quotient ring of the polynomial ring K by the principal ideal generated by P, is a field extension of K. We have
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