The downside of setting up identities was that someone would learn more detail about us than we'd previously released.
Betsy suggested we each assign our new identities without telling each other except our spouses.
"False identities aren't easy to get," I said, remembering Daniel Brennan obtaining ours.
Jude Bryce was the pedophile who claimed Howie wrongfully accused him, until we proved he had switched identities with his brother; his brother Owen!
He probably thought we'd have talked her out of leaving, or at least into leaving their new identities with us.
Similarly, by putting one or more of the deleted rows or columns equal to rows or columns which are not deleted, we obtain, with Laplace, a number of identities between products of determinants of complementary orders.
Function of separations of (li'12 2 13 3 ...) of specification (si 1 s 22 s 33) Suppose the separations of (11 1 13 2 1 3 3 ...) to involve k different specifications and form the k identities ï¿½1s ï¿½ s Al A 2 A3 ..
And we may suppose such identities between the symbols that on the whole only two, three, or more of the sets of umbrae are not equivalent; we will then obtain invariants of two, three, or more sets of binary forms. The symbolic expression of a covariant is equally simple, because we see at once that since AE, B, Ce,...
Symbolic Identities.- For the purpose of manipulating symbolic expressions it is necessary to be in possession of certain simple identities which connect certain symbolic products.
The identities are, in particular, of service in reducing symbolic products to standard forms. A symbolical expression may be always so transformed that the power of any determinant factor (ab) is even.
The number of different symbols a, b, c,...denotes the the covariants are homogeneous, but not in general isobaric functions, of the coefficients of the original form or forms. Of the above general form of covariant there are important transformations due to the symbolic identities: - (ï¿½b) 2 2)2 = a b - a b; (xï¿½ = as a consequence any even power of a determinant factor may be expressed in terms of the other symbolic factors, and any uneven power may be expressed as the product of its first power and a function of the other symbolic factors.
The verbal identities can only be explained in one of the following ways.
Henderson prefers the hypothesis that Lennox had lost Crawford's notes; and that the identities are explained by the "remarkably good memories of Crawford and Mary, or by the more likely supposition that Crawford, before preparing his declaration for the conference" (at Westminster, December 1568) "refreshed his memory by the letter."
Gregory's series and the identities 7 r /4 =5 tan1 + + 2 tan-',A (Euler, 1779), 7r/4 = tani ++2 tan-' s (Hutton, 1776), neither of which was nearly so advantageous as several found by Charles Hutton, calculated 7r correct to 136 places."
He agrees with Hegel that there are two fundamental identities, the identity of all reason, and the identity of all reason and all being.
If we were to say that on his view the essential step must be the establishment of identities or equivalences, we should probably be doing justice to his doctrine of numerical reasoning, but should have some difficulty in showing the application of the method to geometrical reasoning.
Leibnitz's treatment of the primary principles among truths of reason as identities, and his examples drawn inter alia from the " first principles " of mathematics, influenced Kant by antagonism.
Identities some of them manifestly were not.
All propositions not concerned with the existence of individual facts ultimately analyse out into identities - obviously lend themselves to the design of this algebra of thought, though the mathematician in Leibnitz should have been aware that a significant equation is never an identity.
The clue to the discovery of transcendental conditions Kant finds in the existence of judgments, most manifest in mathematics and in the pure science of nature, which are certain, yet not trifling, necessary and yet not reducible to identities, synthetic therefore and a priori, and so accounted for neither by Locke nor by Leibnitz.