Chinese Remainder Theorem - Existence

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:

    And from a cliff top is proclaimed
    The gathering of the souls for birth,
    The trial by existence named,
    The obscuration upon earth.
    Robert Frost (1874–1963)

    If the heart beguiles itself in its choice [of a wife], and imagination will give excellencies which are not the portion of flesh and blood:Mwhen the dream is over, and we awake in the morning, it matters little whether ‘tis Rachael or Leah,—be the object what it will, as it must be on the earthly side ... of perfection,—it will fall short of the work of fancy, whose existence is in the clouds.
    Laurence Sterne (1713–1768)

    Generality is, indeed, an indispensable ingredient of reality; for mere individual existence or actuality without any regularity whatever is a nullity. Chaos is pure nothing.
    Charles Sanders Peirce (1839–1914)