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Moving past the intuition for how division and remainders work for real numbers, there are other ways to look at "obvious" answers that suggests -7/2=4. Consid

Moving past the intuition for how division and remainders work for real numbers, there are other ways to look at "obvious" answers that suggests -7/2=4. Consider x/3=y. For real numbers, it's trivial to manipulate this equation into (x-3)/3=y-1. However, this only works when integer division rounds down. 5/3 = 1 rem 2 or 1 rem 2 4/3 = 1 rem 1 or 1 rem 1 3/3 = 1 rem 0 or 1 rem 0 2/3 = 0 rem 2 or 0 rem 2 1/3 = 0 rem 1 or 0 rem 1 0/3 = 0 rem 0 or 0 rem 0 -1/3 = -1 rem 2 or 0 rem -1 -2/3 = -1 rem 1 or 0 rem -2 -3/3 = -1 rem 0 or -1 rem 0 One of these has a consistent pattern, the other doesn't. All of this is a fairly moot point: The answer is it should do what the algorithm using it needs it to do.

superjan 5y ago
It is not so much my intuition but the intuition of the language designers. I would prefer euclidian division personally.
strenholme 5y ago
True, but both Python’s “int()” operation and the C99 and C11 standard for division operators truncate towards 0. [1] [1] e.g. http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf PDF page 94/physical page 82
- housecarpenter 5y ago
  Python's int() truncates towards 0, but (at least in Python 3, I don't know if it was always the same in older versions) its division operator always floors, so -7 // 2 gives -4 even though int(-3.5) is 3. (The int() function is best thought of as just "make this float into an integer, I don't really care how"; if you want to be more specific, you have math.floor(), math.ceil() and math.trunc(), and you also have round(), which rounds towards the closest integer; if the float is evenly between the two integers, it goes towards 0 when the integer part is even and away from 0 when the integer part is odd.)

superjan 5y ago

It is not so much my intuition but the intuition of the language designers. I would prefer euclidian division personally.

strenholme 5y ago

True, but both Python’s “int()” operation and the C99 and C11 standard for division operators truncate towards 0. [1] [1] e.g. http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf PDF page 94/physical page 82

housecarpenter 5y ago
Python's int() truncates towards 0, but (at least in Python 3, I don't know if it was always the same in older versions) its division operator always floors, so -7 // 2 gives -4 even though int(-3.5) is 3. (The int() function is best thought of as just "make this float into an integer, I don't really care how"; if you want to be more specific, you have math.floor(), math.ceil() and math.trunc(), and you also have round(), which rounds towards the closest integer; if the float is evenly between the two integers, it goes towards 0 when the integer part is even and away from 0 when the integer part is odd.)