1.
Exclamation mark
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The exclamation mark or exclamation point is a punctuation mark usually used after an interjection or exclamation to indicate strong feelings or high volume, and often marks the end of a sentence. Similarly, an exclamation mark is often used in warning signs. Other uses include, In mathematics it denotes the factorial operation, at the beginning of an expression to denote logical negation, e. g. A means the logical negation of A, also called not A. Graphically the exclamation mark is represented as a stop point with a vertical line above. One theory of its origin is that it is derived from a Latin exclamation of joy, the modern graphical representation is believed to have been born in the Middle Ages. Medieval copyists wrote the Latin word io at the end of a sentence to indicate joy, over time, the i moved above the o, and the o became smaller, becoming a point. The exclamation mark did not have its own dedicated key on standard manual typewriters before the 1970s, instead, one typed a period, backspaced, and typed an apostrophe. In the 1950s, secretarial dictation and typesetting manuals in America referred to the mark as bang, appeared in dialogue balloons to represent a gun being fired, although the nickname probably emerged from letterpress printing. This bang usage is behind the names of the interrobang, an unconventional character, and a shebang line. In the printing world, the mark can be called a screamer, a gasper. In hacker culture, the mark is called bang, shriek, or, in the British slang known as Commonwealth Hackish. For example, the password communicated in the spoken phrase Your password is em-nought-pee-aitch-pling-en-three is m0ph. n3, the exclamation mark is common to languages using the Latin alphabet, although usage varies slightly between languages. The exclamation mark was adopted in languages written in other scripts, such as Greek, Russian, Arabic, Hebrew, Chinese, Korean, Japanese and Devanagari. A sentence ending in an exclamation mark may be an exclamation, or an imperative, or may indicate astonishment or surprise, They were the footprints of a gigantic hound. Exclamation marks are occasionally placed mid-sentence with a similar to a comma, for dramatic effect, although this usage is obsolescent, On the walk. Informally, exclamation marks may be repeated for emphasis. The exclamation mark is used in conjunction with the question mark. This can be in protest or astonishment, a few writers replace this with a single, nonstandard punctuation mark, the interrobang, which is the combination of a question mark and an exclamation mark

2.
ASCII
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ASCII, abbreviated from American Standard Code for Information Interchange, is a character encoding standard. ASCII codes represent text in computers, telecommunications equipment, and other devices, most modern character-encoding schemes are based on ASCII, although they support many additional characters. ASCII was developed from telegraph code and its first commercial use was as a seven-bit teleprinter code promoted by Bell data services. Work on the ASCII standard began on October 6,1960, the first edition of the standard was published in 1963, underwent a major revision during 1967, and experienced its most recent update during 1986. Compared to earlier telegraph codes, the proposed Bell code and ASCII were both ordered for more convenient sorting of lists, and added features for other than teleprinters. Originally based on the English alphabet, ASCII encodes 128 specified characters into seven-bit integers as shown by the ASCII chart above. The characters encoded are numbers 0 to 9, lowercase letters a to z, uppercase letters A to Z, basic punctuation symbols, control codes that originated with Teletype machines, for example, lowercase j would become binary 1101010 and decimal 106. ASCII includes definitions for 128 characters,33 are non-printing control characters that affect how text and space are processed and 95 printable characters, of these, the IANA encourages use of the name US-ASCII for Internet uses of ASCII. The ASA became the United States of America Standards Institute and ultimately the American National Standards Institute, there was some debate at the time whether there should be more control characters rather than the lowercase alphabet. The X3.2.4 task group voted its approval for the change to ASCII at its May 1963 meeting, the X3 committee made other changes, including other new characters, renaming some control characters and moving or removing others. ASCII was subsequently updated as USAS X3. 4-1967, then USAS X3. 4-1968, ANSI X3. 4-1977 and they proposed a 9-track standard for magnetic tape, and attempted to deal with some punched card formats. The X3.2 subcommittee designed ASCII based on the earlier teleprinter encoding systems, like other character encodings, ASCII specifies a correspondence between digital bit patterns and character symbols. This allows digital devices to communicate each other and to process, store. Before ASCII was developed, the encodings in use included 26 alphabetic characters,10 numerical digits, ITA2 were in turn based on the 5-bit telegraph code Émile Baudot invented in 1870 and patented in 1874. The committee debated the possibility of a function, which would allow more than 64 codes to be represented by a six-bit code. In a shifted code, some character codes determine choices between options for the character codes. It allows compact encoding, but is reliable for data transmission. The standards committee decided against shifting, and so ASCII required at least a seven-bit code, the committee considered an eight-bit code, since eight bits would allow two four-bit patterns to efficiently encode two digits with binary-coded decimal

3.
Factorial
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In mathematics, the factorial of a non-negative integer n, denoted by n. is the product of all positive integers less than or equal to n. =5 ×4 ×3 ×2 ×1 =120, the value of 0. is 1, according to the convention for an empty product. The factorial operation is encountered in areas of mathematics, notably in combinatorics, algebra. Its most basic occurrence is the fact there are n. ways to arrange n distinct objects into a sequence. This fact was known at least as early as the 12th century, fabian Stedman, in 1677, described factorials as applied to change ringing. After describing a recursive approach, Stedman gives a statement of a factorial, Now the nature of these methods is such, the factorial function is formally defined by the product n. = ∏ k =1 n k, or by the relation n. = {1 if n =0. The factorial function can also be defined by using the rule as n. All of the above definitions incorporate the instance 0, =1, in the first case by the convention that the product of no numbers at all is 1. This is convenient because, There is exactly one permutation of zero objects, = n. ×, valid for n >0, extends to n =0. It allows for the expression of many formulae, such as the function, as a power series. It makes many identities in combinatorics valid for all applicable sizes, the number of ways to choose 0 elements from the empty set is =0. More generally, the number of ways to choose n elements among a set of n is = n. n, the factorial function can also be defined for non-integer values using more advanced mathematics, detailed in the section below. This more generalized definition is used by advanced calculators and mathematical software such as Maple or Mathematica, although the factorial function has its roots in combinatorics, formulas involving factorials occur in many areas of mathematics. There are n. different ways of arranging n distinct objects into a sequence, often factorials appear in the denominator of a formula to account for the fact that ordering is to be ignored. A classical example is counting k-combinations from a set with n elements, one can obtain such a combination by choosing a k-permutation, successively selecting and removing an element of the set, k times, for a total of n k _ = n ⋯ possibilities. This however produces the k-combinations in an order that one wishes to ignore, since each k-combination is obtained in k. different ways. This number is known as the coefficient, because it is also the coefficient of Xk in n

4.
Derangement
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In combinatorial mathematics, a derangement is a permutation of the elements of a set, such that no element appears in its original position. In other words, derangement is a permutation that has no fixed points, the number of derangements of a set of size n, usually written Dn, dn, or. n, is called the derangement number or de Montmort number. The subfactorial function maps n to. n, no standard notation for subfactorials is agreed upon, n¡ is sometimes used instead of. n. The problem of counting derangements was first considered by Pierre Raymond de Montmort in 1708, he solved it in 1713, as did Nicholas Bernoulli at about the same time. Suppose that a professor has had 4 of his students – A, B, C, of course, no student should grade his or her own test. How many ways could the hand the tests back to the students for grading. Out of 24 possible permutations for handing back the tests, there are only 9 derangements, in every other permutation of this 4-member set, at least one student gets his or her own test back. Suppose that there are n people who are numbered 1,2, let there be n hats also numbered 1,2. We have to find the number of ways in which no one gets the hat having same number as their number, let us assume that the first person takes hat i. There are n −1 ways for the first person to such a choice. There are now two possibilities, depending on whether or not person i takes hat 1 in return, Person i does not take the hat 1. This case is equivalent to solving the problem with n −1 persons and n −1 hats, Person i takes the hat 1. Now the problem reduces to n −2 persons and n −2 hats, from this, the following relation is derived. Where. n, known as the subfactorial, represents the number of derangements, notice that this same recurrence formula also works for factorials with different starting values. =1 and n. = which is helpful in proving the relationship with e below. Also, the formulae are known. E +12 ⌋, n ≥1 where is the nearest integer function, the following recurrence relationship also holds. N = n + n Starting with n =0, the numbers of derangements of n are,1,0,1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841,2290792932

5.
Negation
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Negation is thus a unary logical connective. It may be applied as an operation on propositions, truth values, in classical logic, negation is normally identified with the truth function that takes truth to falsity and vice versa. In intuitionistic logic, according to the Brouwer–Heyting–Kolmogorov interpretation, the negation of a proposition p is the proposition whose proofs are the refutations of p. Classical negation is an operation on one logical value, typically the value of a proposition, that produces a value of true when its operand is false and a value of false when its operand is true. So, if statement A is true, then ¬A would therefore be false, the truth table of ¬p is as follows, Classical negation can be defined in terms of other logical operations. For example, ¬p can be defined as p → F, conversely, one can define F as p & ¬p for any proposition p, where & is logical conjunction. The idea here is that any contradiction is false, while these ideas work in both classical and intuitionistic logic, they do not work in paraconsistent logic, where contradictions are not necessarily false. But in classical logic, we get an identity, p → q can be defined as ¬p ∨ q. Algebraically, classical negation corresponds to complementation in a Boolean algebra and these algebras provide a semantics for classical and intuitionistic logic respectively. The negation of a proposition p is notated in different ways in various contexts of discussion and fields of application. Among these variants are the following, In set theory \ is also used to indicate not member of, U \ A is the set of all members of U that are not members of A. No matter how it is notated or symbolized, the negation ¬p / −p can be read as it is not the case p, not that p. Within a system of logic, double negation, that is. In intuitionistic logic, a proposition implies its double negation but not conversely and this marks one important difference between classical and intuitionistic negation. Algebraically, classical negation is called an involution of period two and this result is known as Glivenkos theorem. De Morgans laws provide a way of distributing negation over disjunction and conjunction, ¬ ≡, in Boolean algebra, a linear function is one such that, If there exists a0, a1. An ∈ such that f = a0 ⊕ ⊕, another way to express this is that each variable always makes a difference in the truth-value of the operation or it never makes a difference. Negation is a logical operator

6.
!!!
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. is a dance-punk band that formed in Sacramento, California, in 1996 by lead singer Nic Offer. Came from other bands such as The Yah Mos, Black Liquorice. They are currently based in New York City, Sacramento, and Portland, the bands sixth full-length album, As If, was released in October 2015. is an American band formed in the summer of 1995 by the merger of part of the group Black Liquorice and Popesmashers. After a successful joint tour, the two decided to mix the disco-funk with more aggressive sounds and integrate the hardcore singer Nic Offer from the Yah Mos. The bands name was inspired by the subtitles of the movie The Gods Must Be Crazy, however, as the bandmembers themselves say. Is pronounced by repeating thrice any monosyllabic sound, Chk Chk Chk is the most common pronunciation, and the URL of their official website and the title of their Myspace page suggest it is the preferred pronunciation. The bands full-length debut record out in 2000 as a self-titled album on the label Gold Standard Laboratories. A second full-length, Louden Up Now, was released on Touch and Go in America, released a new EP covering Take Ecstasy with Me by The Magnetic Fields, and Get Up by Nate Dogg. The following December, the drummer for the band, Mikel Gius, was struck. They released their album, Myth Takes in 2007. is composed of Mario Andreoni, Dan Gorman, Nic Offer, Tyler Pope. Touring members include Shannon Funchess and Paul Quattrone, the band also shared membership with the similar, defunct group Out Hud. Vocalist and drummer John Pugh officially left the band in July 2007 to concentrate on his new band Free Blood, Shannon Funchess stood in for Pugh during much of their 2007 tour. GSL26/LAB SERIES VOL.2 Live Live Live Take Ecstasy with Me/Get Up Yadnus Jamie, stereolad, a Stereolab cover band side project, containing the members of