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Given an integer a and a non-zero integer d, it can be shown that there exist unique integers q and r, such that a = qd + r and 0 ≤ r < | d |. The number q is called the quotient, while r is called the remainder. (For a proof of this result, see Euclidean division. For algorithms describing how to calculate the remainder, see division algorithm.)
The role of 0 as additive identity generalizes beyond elementary algebra. In abstract algebra, 0 is commonly used to denote a zero element, which is the identity element for addition (if defined on the structure under consideration) and an absorbing element for multiplication (if defined).
Upside-down marks, simple in the era of hand typesetting, were originally recommended by the Real Academia Española (Royal Spanish Academy), in the second edition of the Ortografía de la lengua castellana (Orthography of the Castilian language) in 1754 [3] recommending it as the symbol indicating the beginning of a question in written Spanish—e.g. "¿Cuántos años tienes?"
A car attack at a Christmas market in Magdeburg, Germany, kills five people and injures more than two hundred others.; In France, Dominique Pelicot and 49 other men are convicted of the serial rape of his then-wife Gisèle Pelicot (portrait shown).
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
Cryptic crosswords often use abbreviations to clue individual letters or short fragments of the overall solution. These include: Any conventional abbreviations found in a standard dictionary, such as:
In older texts one occasionally finds (−) n, which means the same. When the standard presumption that the plus-or-minus signs all take on the same value of +1 or all −1 is not true, then the line of text that immediately follows the equation must contain a brief description of the actual connection, if any, most often of the form "where the ...
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.