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:
“Then I had only prisoners’ thoughts. I awaited the daily walk which I took in the yard, or my lawyer’s visit. I managed the remainder of my time very well. I have often thought that if I was made to live in a dry tree trunk, without any other occupation but to watch the flower of the sky above my head, I would have gradually gotten used to it.”
—Albert Camus (1913–1960)
“The dramatic art would appear to be rather a feminine art; it contains in itself all the artifices which belong to the province of woman: the desire to please, facility to express emotions and hide defects, and the faculty of assimilation which is the real essence of woman.”
—Sarah Bernhardt (1845–1923)
“Individually, museums are fine institutions, dedicated to the high values of preservation, education and truth; collectively, their growth in numbers points to the imaginative death of this country.”
—Robert Hewison (b. 1943)