In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value So the point of modular arithmetic is to do our normal arithmetic operations wrap around after reaching a certain value.
Arithmetic could roughly be described as working with the numbers we know within a particular system of numbers, and is often related in some way to working with things called integers (whole numbers) and fractions.
The reason that equivalence class arithmetic proves smoother is that congruence mod m is not only an equivalence relation but is, additionally, an arithmetic congruence relation, i.e. it respects the arithmetic operations. This implies that all of the integer arithmetic laws (ring structure) are preserved in modular arithmetic.
I am studying an undergraduate book of mathematical logic. After proving the two Gödel's theorems of incompleteness of formal theories, it asserts that some proofs of arithmetic's consistency exis...
What is the general formula for a sequence that is neither arithmetic nor geometric? [duplicate] Ask Question Asked 6 years, 5 months ago Modified 6 years, 5 months ago
Bill Gosper has invented an algorithm for performing analytic addition, subtraction, multiplication, and division using continued fractions. It requires keeping track of eight integers which are conceptually arranged at the polyhedron vertices of a cube. Although this algorithm has not appeared in print, similar algorithms have been constructed by Vuillemin (1987) and Liardet and Stambul (1998 ...
Recently I had this doubt about the order of precedence of mathematical operations multiplication and division. Given that we have a simple question like this 80 / 10 * 5 without parenthesis, what
I'm trying to mentally summarize the names of the operands for basic operations. I've got this so far: Addition: Augend + Addend = Sum. Subtraction: Minuend - Subtrahend = Difference. Multiplicati...
