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:
““What have I gained?”
“Experience,” said Holmes, laughing. “Indirectly it may be of value, you know; you have only to put it into words to gain the reputation of being excellent company for the remainder of your existence.””
—Sir Arthur Conan Doyle (1859–1930)
““As for your world of art and your world of reality,” she replied, “you have to separate the two, because you can’t bear to know what you are.... The world of art is only the truth about the real world.””
—D.H. (David Herbert)
“I had a feeling that out there, there were very poor people who didn’t have enough to eat. But they wore wonderfully colored rags and did musical numbers up and down the streets together.”
—Jill Robinson (b. 1936)