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In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set . There are several variants and generalizations of the lexicographical ordering.
Index k = 2, because 3 is placed at an index that satisfies condition of being the largest index that is still less than a[k + 1] which is 4. Index l = 3, because 4 is the only value in the sequence that is greater than 3 in order to satisfy the condition a[k] < a[l]. The values of a[2] and a[3] are swapped to form the new sequence [1, 2, 4, 3].
Subgroup. In group theory, a branch of mathematics, given a group G under a binary operation ∗, a subset H of G is called a subgroup of G if H also forms a group under the operation ∗. More precisely, H is a subgroup of G if the restriction of ∗ to H × H is a group operation on H.
Order of operations. In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression . These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and ...
In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way. The distinction between "canonical" and "normal ...
The order of flats is B♭, E♭, A♭, D♭, G♭, C♭, and F♭ (reverse order of sharps), which can be remembered using the phrase: Battle Ends And Down Goes Charles' Father; Blanket Exploded And Dad Got Cold Feet. Before Eating A Doughnut Get Coffee First. To remember the difference between the whole rest and the half rest:
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