true quotient

[shahar]

In C language Help Window you see:
When op1 and op2 are integers and the quotient is not an integer:
1. If op1 and op2 have the same sign, op1 / op2 is the largest integer less than the true quotient, and op1 % op2 has the sign of op1.
2. If op1 and op2 have opposite signs, op1 / op2 is the smallest integer greater than the true quotient, and op1 % op2 has the sign of op1.

The sign % is getting the remainder from number.
For example, 2%1 say how many times 2 is in the smallest multiple of 1, and the answer is zero. So, the remainder of 2 by 1 is 0.
1. What the difference between remainder to modulus?
2. What is true quotient?
3. Is there exist the expression false quotient?
4. Is there are more words or expressions that means quotient? true quotient?

Thanks to who is help.

 

[Dr.Peterson]

1. Remainder and "modulus" are different with regard to signs. See Wikipedia. (Footnote 7 refers to something I wrote about this that is not currently available.) Ultimately, though, such definitions are language-dependent. (Actually, the word "modulus" is often misused, particularly in programming, and really means the divisor, not the remainder.)

2. The true quotient refers to the actual result of a division. The true quotient of 5/2 is 2.5; the integer (truncated) quotient is 2.

3. Anything other than the true quotient would be false, I suppose; but that is not the distinction they are making. The distinction is between true quotient and integer quotient (the result of the computer operation).

4. A quotient is a quotient. On the other hand, there are different contexts in which the word means different things. Consider this, where what is called the quotient is not the "true quotient": https://en.wikipedia.org/wiki/Euclidean_division#Division_theorem . This is, in fact, what "quotient" means when students first learn about division (the result being a quotient and a remainder).