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Employment record book. An employment record book is an official personal document recording the employment status of its owner over time. Some European countries issue such documents, others did earlier. The first employment record books are said to have been issued in German Reich in 1892 in the mining industry. [1]
A minimal element of a subset of some preordered set is defined dually as an element of that is not greater than any other element in . The notions of maximal and minimal elements are weaker than those of greatest element and least element which are also known, respectively, as maximum and minimum. The maximum of a subset of a preordered set is ...
In mathematics, particularly in group theory, the Frattini subgroup of a group G is the intersection of all maximal subgroups of G. For the case that G has no maximal subgroups, for example the trivial group {e} or a Prüfer group, it is defined by . It is analogous to the Jacobson radical in the theory of rings, and intuitively can be thought ...
one of the longest increasing subsequences is. 0, 2, 6, 9, 11, 15. This subsequence has length six; the input sequence has no seven-member increasing subsequences. The longest increasing subsequence in this example is not the only solution: for instance, are other increasing subsequences of equal length in the same input sequence.
A maximal order for ω ( n) is ln n / ln ln n. [1] : 83. For the number of prime factors counted with multiplicity Ω ( n) we have a trivial lower bound 1 ≤ Ω ( n ), in which equality occurs when n is prime. A maximal order for Ω ( n) is ln n / ln 2 [1] : 83. It is conjectured that the Mertens function, or summatory function of the Möbius ...
The number 2,147,483,647 is the eighth Mersenne prime, equal to 2 31 − 1. It is one of only four known double Mersenne primes. [ 1 ] The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772. [ 2 ] Euler used trial division, improving on Pietro Cataldi 's method, so that ...
Maximal ideal: A proper ideal I is called a maximal ideal if there exists no other proper ideal J with I a proper subset of J. The factor ring of a maximal ideal is a simple ring in general and is a field for commutative rings. [12] Minimal ideal: A nonzero ideal is called minimal if it contains no other nonzero ideal.
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a ...