The Remainder For Real Numbers
When a and d are real numbers, with d non-zero, a can be divided by d without remainder, with the quotient being another real number. If the quotient is constrained to being an integer however, the concept of remainder is still necessary. It can be proved that there exists a unique integer quotient q and a unique real remainder r such that a=qd+r with 0≤r < |d|. As in the case of division of integers, the remainder could be required to be negative, that is, -|d| < r ≤ 0.
Extending the definition of remainder for real numbers as described above is not of theoretical importance in mathematics; however, many programming languages implement this definition—see modulo operation.
Read more about this topic: Remainder
Famous quotes containing the words remainder, real and/or numbers:
“The route through childhood is shaped by many forces, and it differs for each of us. Our biological inheritance, the temperament with which we are born, the care we receive, our family relationships, the place where we grow up, the schools we attend, the culture in which we participate, and the historical period in which we live—all these affect the paths we take through childhood and condition the remainder of our lives.”
—Robert H. Wozniak (20th century)
“Colloquial poetry is to the real art as the barber’s wax dummy is to sculpture.”
—Ezra Pound (1885–1972)
“Publishers are notoriously slothful about numbers, unless they’re attached to dollar signs—unlike journalists, quarterbacks, and felony criminal defendents who tend to be keenly aware of numbers at all times.”
—Hunter S. Thompson (b. 1939)