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...
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.
Here, an example is given that the arithmetic mean (s) of 2, 4, 6, 8, 10 are 4, 6, and 8 (which should be 6). Our material also mentions about inserting arithmetic means between two numbers like "Insert 4 arithmetic means between 7 and 47," wherein the answer would be 15, 23, 31, and 39 because it will form an arithmetic sequence.
The arithmetic mean is a number that when multiplied by the number of elements, gives you the sum of all the elements. Because of this fact, it can't be more than the maximum nor less than the minimum, and it should be located somewhat around the center. But I was wondering if there are other intuitions out there? Why does this formula work?
Modular arithmetic utilizes this "wrapping around" idea, after you reached the greatest element comes the smallest. So modular arithmetic is a sort of a mindset. A binary operation is an operation which combines two elements, for example addition is a binary operation since it combines two elements.
Modular arithmetic (clock arithmetic) is a system of integer arithmetic based on the congruence relation $a \equiv b \pmod {n}$ which means that $n$ divides $a-b$.
