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Can you please tell me how much is (-2) % 5?
According to my Python interpreter is 3, but do you have a wise explanation for this?
I've read that in some languages the result can be machine-dependent, but I'm not sure though.
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The modulus of a negative number is found by ignoring the minus sign. The modulus of a number is denoted by writing vertical lines around the number. Note also that the modulus of a negative number can be found by multiplying it by −1 since, for example, −(−8) = 8.
These functions give the same values for positive arguments, but the modulus always returns positive results for negative input, whereas the remainder may give negative results.
Therefore, the modulus of a number is always positive.
By the way: most programming languages would disagree with Python and give the result -2. Depending on the interpretation of modulus this is correct. However, the most agreed-upon mathematical definition states that the modulus of a and b is the (strictly positive) rest r of the division of a / b. More precisely, 0 <= r < b by definition.
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