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AMS-LaTeX is a collection of LaTeX document classes and packages developed for the American Mathematical Society (AMS). Its additions to LaTeX include the typesetting of multi-line and other mathematical statements, document classes, and fonts containing numerous mathematical symbols. [1] It has largely superseded the plain TeX macro package ...
2. Denotes the additive inverse and is read as minus, the negative of, or the opposite of; for example, –2. 3. Also used in place of \ for denoting the set-theoretic complement; see \ in § Set theory. × (multiplication sign) 1. In elementary arithmetic, denotes multiplication, and is read as times; for example, 3 × 2. 2.
The following symbols are reserved characters that either have a special meaning under LaTeX or are unavailable in all the fonts. ... _ 1 ^ 2 \!\Omega _ 3 ^ 4 ...
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
The summation of an explicit sequence is denoted as a succession of additions. For example, summation of [1, 2, 4, 2] is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need for parentheses, and the result is the same irrespective of the order of the summands ...
The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.
In the case of our word, 11 such patterns can be matched, namely 1 c 4 l 4, 1 cy, 1 d 4 i 3 a, 4 edi, e 3 dia, 2 i 1 a, ope 5 d, 2 p 2 ed, 3 pedi, pedia 4, y 1 c. For each position in the word, TeX will calculate the maximum value obtained among all matching patterns, yielding en 1 cy 1 c 4 l 4 o 3 p 4 e 5 d 4 i 3 a 4.
The values of a[2] and a[3] are swapped to form the new sequence [1, 2, 4, 3]. The sequence after k-index a[2] to the final element is reversed. Because only one value lies after this index (the 3), the sequence remains unchanged in this instance. Thus the lexicographic successor of the initial state is permuted: [1, 2, 4, 3].