The method of successive approximations is often applied to proving existence of solutions to various classes of functional equations; moreover, the proof of convergence of these approximations leans on the fact that the equation under study may be majorised by another equation of a simple kind. Similar proofs may be encountered in the theory of infinitely many simultaneous linear equations and in the theory of integral and differential equations. Consideration of semiordered spaces and operations between them enables us to easily develop a complete theory of such functional equations in abstract form.
Leonid KantorovichRelated topics
abstract convergence differential equation form functional integral kind linear proof proving simple study under operationsRelated quotes
In my study of the Ayodhya controversy, I noticed that the frequent attempts to conceal or deny inconvenient evidence were an integral part of a larger effort to rewrite India's history and to whitewash Islam. It struck me that this effort to deny the unpleasant facts of Islam's destructive role in Indian history is similar to the attempts by some European writers to deny the Nazi holocaust. Its goal and methods are similar, even though its social position is very different: in Europe, Holocaust negationists are a fringe group shunned by respectable people, but in India, jihad negationists are in control of the academic establishment and of the press.
Koenraad Elst
While we could study any of the world's dictators to see how they gained control over their people, Hitler is probably the best known and most well documented example. I believe his persecution of the Jews was Satan's trial run for the end time events coming upon us soon including the 3½ years of "great tribulation” (4D). Hitler's method of getting Germans to hate and then kill the Jews should be studied carefully. I am convinced similar methods will be used to bring persecution against any who will not go along with Satan's plans for his New World Order, especially Christians and anyone else who won't take the mark (Revelation 13-14).
Kent Hovind
The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation to establish the science of Logic and construct its method; to make that method itself the basis of a general method for the application of the mathematical doctrine of Probabilities; and, finally, to collect from the various elements of truth brought to view in the course of these inquiries some probable intimations concerning the nature and constitution of the human mind.
George Boole
In relativity, movement is continuous, causally determinate and well defined, while in quantum mechanics it is discontinuous, not causally determinate and not well defined. Each theory is committed to its own notions of essentially static and fragmentary modes of existence (relativity to that of separate events, connectable by signals, and quantum mechanics to a well-defined quantum state). One thus sees that a new kind of theory is needed which drops these basic commitments and at most recovers some essential features of the older theories as abstract forms derived from a deeper reality in which what prevails in unbroken wholeness.
David Bohm
Markets are institutions that exist to facilitate exchange, that is, they exist in order to reduce the cost of carrying out exchange transactions. In an economic theory which assumes that transaction costs are nonexistent. markets have no function to perform, and it seems perfectly reasonable to develop the theory of exchange by an elaborate analysis of individuals exchanging nuts for apples on the edge of the forest or some similar fanciful example. This analysis certainly shows why there is a gain from trade, but it fails to deal with the factors which determine how much trade there is or what goods are traded.
Ronald Coase