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:
“To call a posit a posit is not to patronize it. A posit can be unavoidable except at the cost of other no less artificial expedients. Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built.”
—Willard Van Orman Quine (b. 1908)
“It would strike me as ridiculous to want to doubt the existence of Napoleon; but if someone doubted the existence of the earth 150 years ago, perhaps I should be more willing to listen, for now he is doubting our whole system of evidence.”
—Ludwig Wittgenstein (1889–1951)
“Some say existence like a Pirouot
And Pirouette, forever in one place,
Stands still and dances, but it runs away;
It seriously, sadly, runs away
To fill the abyss’s void with emptiness.”
—Robert Frost (1874–1963)