Existence
Existence can be seen by an explicit construction of . We will use the notation to denote the multiplicative inverse of, it is defined exactly when and are coprime; the following construction explains why the coprimality condition is needed.
Read more about this topic: Chinese Remainder Theorem
Famous quotes containing the word existence:
“There surely is a being who presides over the universe; and who, with infinite wisdom and power, has reduced the jarring elements into just order and proportion. Let speculative reasoners dispute, how far this beneficent being extends his care, and whether he prolongs our existence beyond the grave, in order to bestow on virtue its just reward, and render it fully triumphant.”
—David Hume (1711–1776)
“The duty of the State toward the citizen is the duty of the servant to its master.... One of the duties of the State is that of caring for those of its citizens who find themselves the victims of such adverse circumstances as makes them unable to obtain even the necessities for mere existence without the aid of others.... To these unfortunate citizens aid must be extended by government—not as a matter of charity but as a matter of social duty.”
—Franklin D. Roosevelt (1882–1945)
“In a sense the world dies every time a writer dies, because, if he is any good, he has been a wet nurse to humanity during his entire existence and has held earth close around him, like the little obstetrical toad that goes about with a cluster of eggs attached to his legs.”
—E.B. (Elwyn Brooks)