In ordinary arithmetic, the resulting value will be from an infinite set of values but in case modular arithmetic, resulting value will be from a finite set of values.
e.g. in ordinary arithmetic, the sum of two integers, the result will be an integer in the range {..., -3, -2, -1, 0, 1, 2, 3, ...}
for modular arithmetic, the sum of two integers
like (a+b)mod n will be in the range {0, 1, 2, ... n-1}
Difference between modular and non-modular bricks
given any positive integer n and any integer a , if we divide a by n, we get an integer quotient q and an integer remainder r that obey the following relationship where [x] is the largest integer less than or equal to x
additional ports can be added in modular routers.
According to Wikipedia, Carl Friedrich Gauss invented it. Quote Wikipedia,"Modular arithmetic was introduced by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801."
Yes, because that is how remainder is defined. If the remainder was bigger, you would subtract one (or more) modular values until the remainder became smaller than the modulus.
On a basic level, the difference between mobile and modular homes is quality. Mobile homes have not been built since 1976 because of stricter standards enacted by the US Department of Housing and Development (HUD). Modular homes are movable, but like site-based homes, have strict codes and standards to meet before being made for sale to a prospective home owner.
It is impossible to make 23 from four 9's unless modular arithmetic is involved, in this case in mod 40, 57, 58, 59, 76, 697, 6538. I personally can't see any other way to obtain 23 other than modular arithmetic.
They are essentially equivelent in common usage, but technically, a pre-fab home has its components all built offsite and assembled at the building site while modular homes generally don't.
They are sets with a finite number of elements. For example the days of the week, or the 12 months of the year. Modular arithmetic is based on finite sets.
One is built inside a factory and moved to the location in typically two pieces, the other is made in "sections" and moved and built onsite.
Louise Hoy Chin has written: 'Distributive and modular laws in the arithmetic of relation algebras' -- subject(s): Abstract Algebra, Algebra, Abstract
Of or pertaining to mode, modulation, module, or modius; as, modular arrangement; modular accent; modular measure.