Concepts inThe Euclidean definition of the functions div and mod

Modulo operation

In computing, the modulo operation finds the remainder of division of one number by another. Given two positive numbers, a and n, a modulo n (abbreviated as a mod n) can be thought of as the remainder, on division of a by n. For instance, the expression "5 mod 4" would evaluate to 1 because 5 divided by 4 leaves a remainder of 1, while "9 mod 3" would evaluate to 0 because the division of 9 by 3 leaves a remainder of 0; there is nothing to subtract from 9 after multiplying 3 times 3.  more from Wikipedia

Division (mathematics)

In mathematics, especially in elementary arithmetic, division (÷) is an arithmetic operation. Specifically, if b times c equals a, written: where b is not zero, then a divided by b equals c, written: a ÷ b = c For instance, 6 ÷ 3 = 2 since 6 = 3 * 2 In the expression a ÷ b = c, a is called the dividend, b the divisor and c the quotient. Conceptually, division describes two distinct but related settings. Partitioning involves taking a set of size a and forming b groups that are equal in size.  more from Wikipedia

Definition

A definition (¿) is a passage that explains the meaning of a term, or a type of thing. The term to be defined is the definiendum. A term may have many different senses or meanings. For each such specific sense, a definiens is a cluster of words that defines that term. A chief difficulty in managing definition is the need to use other terms that are already understood or whose definitions are easily obtainable. The use of the term in a simple example may suffice.  more from Wikipedia

Euclidean geometry

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system.  more from Wikipedia

Function (mathematics)

In mathematics, a function is a relation between a set of inputs and a set of potential outputs with the property that each input is related to exactly one output. An example of such a relation is defined by the rule f(x) = x, which relates an input x to its square, which are both real numbers. The output of the function f corresponding to an input x is denoted by f(x) (read "f of x"). If the input is ¿3, then the output is 9, and we may write f(¿3) = 9.  more from Wikipedia

Donald Knuth

Donald Ervin Knuth is a computer scientist and Professor Emeritus at Stanford University. He is the author of the seminal multi-volume work The Art of Computer Programming. Knuth has been called the "father" of the analysis of algorithms. He contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process he also popularized the asymptotic notation.  more from Wikipedia

Pascal (programming language)

Pascal is an influential imperative and procedural programming language, designed in 1968¿ and published in 1970 by Niklaus Wirth as a small and efficient language intended to encourage good programming practices using structured programming and data structuring. A derivative known as Object Pascal designed for object-oriented programming was developed in 1985.  more from Wikipedia

Modular arithmetic

In mathematics, modular arithmetic (sometimes called clock arithmetic) is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value¿the modulus. The Swiss mathematician Leonhard Euler pioneered the modern approach to congruence in about 1750, when he explicitly introduced the idea of congruence modulo a number N. Modular arithmetic was further advanced by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.  more from Wikipedia