Modulus of a number

Asked Aug 01 '23 at 07:22

Active Aug 01 '23 at 07:22

Viewed 46 times

Is the modulus of a number n just n mod n

In school I was taught the modulus is the absolute value of a number, when we take the mod of a negative number, the remainder is always positive, even if the number itself is negative, so for example

-5 mod 2 = 1

So is the definition of the modulus of a number |a| just a mod a? Or is it just a coincidence the modulus and modulo are so closely in name, and the modulus is defined as something else?

asked Aug 01 '23 at 07:22

Dan Lupu

3

Check this: What is the difference between Modulus, Absolute value and Modulo? – Martin R Aug 01 '23 at 07:25
@MartinR Oh okay, so they have no relation just happened to be named similarly, thank you! – Dan Lupu Aug 01 '23 at 07:43
$n$ mod $n$ is always $0$ – Peter Aug 01 '23 at 08:05
The remainder is not unique , it is only unique modulo $n$ , so we can add or subtract $n$ as often as we want to get another equivalent remainder. Therefore , we can always achieve that the remainder is positive. If the remainder is $0$ , we could as well chose $n$. Usually , we choose the number in the range $[0,n-1]$ (so not necessarily a positive remainder) or the smallest absolute value (that is we subtract $n$ if the result is larger than n/2). – Peter Aug 01 '23 at 08:07

Modulus of a number

0 Answers0