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:
“Opinions are to the vast apparatus of social existence what oil is to machines: one does not go up to a turbine and pour machine oil over it; one applies a little to hidden spindles and joints that one has to know.”
—Walter Benjamin (1892–1940)
“We are compelled by the theory of God’s already achieved perfection to make Him a devil as well as a god, because of the existence of evil. The god of love, if omnipotent and omniscient, must be the god of cancer and epilepsy as well.... Whoever admits that anything living is evil must either believe that God is malignantly capable of creating evil, or else believe that God has made many mistakes in His attempts to make a perfect being.”
—George Bernard Shaw (1856–1950)
“This perceiving, active being is what I call mind, spirit, soul, or myself. By which words I do not denote any one of my ideas, but a thing entirely distinct from them, wherein they exist, or, which is the same thing, whereby they are perceived; for the existence of an idea consists in being perceived.”
—George Berkeley (1685–1753)