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notation and was
The notation was introduced by Karl Weierstrass in 1841.
The system was revolutionary by including a zero and positional notation.
The decimal point notation was introduced by Sind ibn Ali, he also wrote the earliest treatise on Arabic numerals.
The notation was introduced in 1939 by Paul Dirac and is also known as Dirac notation, though the notation has precursors in Grassmann's use of the notation for his inner products nearly 100 years previously.
Bra-ket notation was designed to facilitate the formal manipulation of linear-algebraic expressions.
The notation was introduced by Andreas von Ettingshausen in 1826, although the numbers were already known centuries before that ( see Pascal's triangle ).
Here, the idea was to map mathematical notation to a natural number ( using a Gödel numbering ).
The current system of chemical notation was invented by Berzelius.
because it does not explicitly make use of religious titles for Jesus, such as " Christ " and Domin-(" Lord "), which are used in the BC / AD notation, nor does it give implicit expression to the Christian creed that Jesus was the Christ.
In some communist states during the Cold War period, usage of non-religious notation was mandated.
Although Xenakis could well have composed this music by hand, the intensity of the calculations needed to transform probabilistic mathematics into musical notation was best left to the number-crunching power of the computer.
While his system was less " scientific " than that of J. P. Lesley, it's other key features – notation, specificity, and versatility – make it deserving of the praise it has received.
There was a notation in use like ' tenth-metre ', meaning the tenth decimal of the metre, currently an Angstrom.
The example above shows a notation named " type-image-svg " that references the standard public FPI and the system identifier ( the standard URI ) of an SVG 1. 1 document, instead of specifying just a system identifier as in the first example ( which was a relative URI interpreted locally as a MIME type ).
Other notational traditions do exist ; Italian solo music is typically written at the sounding pitch, and the " old " German method sounded an octave below where notation except in the treble clef, where the music was written at pitch.
He was the first person to use algebraic notation and symbolism.
Some of the limitations of Diophantus ' notation are that he only had notation for one unknown and, when problems involved more than a single unknown, Diophantus was reduced to expressing " first unknown ", " second unknown ", etc.
Western musical notation was originally created to preserve the lines of Gregorian chant, which before its invention was taught as an oral tradition in monastic communities.
The only element lacking for the creation of these fields was an efficient algebraic notation in which to express his concepts.
His notation for the cardinal numbers was the Hebrew letter ( aleph ) with a natural number subscript ; for the ordinals he employed the Greek letter ω ( omega ).

notation and introduced
The language and notation introduced are standard throughout the chapter.
He introduced the Lewis notation or electron dot notation or Lewis dot structure in which valence electrons ( those in the outer shell ) are represented as dots around the atomic symbols.
In 1973, Texas Instruments ( TI ) introduced the SR-10, ( SR signifying slide rule ) an algebraic entry pocket calculator using scientific notation for $ 150.
In this system, the number ten may be written as " A ", " T " or " X ", and the number eleven as " B " or " E " ( another common notation, introduced by Sir Isaac Pitman, is to use a rotated " 2 " for ten and a reversed " 3 " for eleven ).
Diophantus introduced an algebraic symbolism that used an abridged notation for frequently occurring operations, and an abbreviation for the unknown and for the powers of the unknown.
It had an all-transistor design, 13-digit capacity on a CRT, and introduced Reverse Polish notation ( RPN ) to the calculator market at a price of $ 2200.
He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.
He also introduced the modern notation for the trigonometric functions, the letter for the base of the natural logarithm ( now also known as Euler's number ), the Greek letter Σ for summations and the letter to denote the imaginary unit.
As is the case with Reverse Polish notation, although R1C1-style formulas are more efficient than A1-style formulae ( for instance, relative and absolute references can be mixed in the same expression, as " R1C " to mean " row 1, this column "), most spreadsheet users prefer the A1 addressing style introduced by VisiCalc.
In his above-mentioned account, he introduced the bra-ket notation, together with an abstract formulation in terms of the Hilbert space used in functional analysis ; he showed that Schrödinger's and Heisenberg's approaches were two different representations of the same theory, and found a third, most general one, which represented the dynamics of the system.
Aryabhata of Kusumapura developed the place-value notation in the 5th century and a century later Brahmagupta introduced the symbol for zero.
Between 1880 and 1887, Heaviside developed the operational calculus ( involving the D notation for the differential operator, which he is credited with creating ), a method of solving differential equations by transforming them into ordinary algebraic equations which caused a great deal of controversy when first introduced, owing to the lack of rigour in his derivation of it.
When Hewlett-Packard introduced a later business calculator, the HP-19B, without RPN, feedback from financiers and others used to the 12C compelled them to release the HP-19BII, which gave users the option of using algebraic notation or RPN.
The language, including the control structures and the expression grammar, was modeled on C. The C shell also introduced a large number of features for interactive work, including the history and editing mechanisms, aliases, directory stacks, tilde notation, cdpath, job control and path hashing.
The Dirac delta function as such was introduced as a " convenient notation " by Paul Dirac in his influential 1930 book Principles of Quantum Mechanics.
Diagram showing the magnitude and direction of the cross product of two vectors, in the notation introduced by Gibbs
Gibbs introduced the now common notation for the dot product and the cross product of two vectors, and he was largely responsible for the development of the vector calculus techniques still used today in electrodynamics and fluid mechanics.

notation and by
No human being can write fast enough, or long enough, or small enough † ( †" smaller and smaller without limit ... you'd be trying to write on molecules, on atoms, on electrons ") to list all members of an enumerably infinite set by writing out their names, one after another, in some notation.
Algorithms can be expressed in many kinds of notation, including natural languages, pseudocode, flowcharts, programming languages or control tables ( processed by interpreters ).
signal " from the notation made by a volunteer on the project.
( b ) illustrates the same process using spectroscopic notation,. The Auger effect () is a physical phenomenon in which the filling of an inner-shell vacancy of an atom is accompanied by the emission of an electron from the same atom.
The first programmable computer built by Konrad Zuse used binary notation for numbers.
Binary operations are often written using infix notation such as a * b, a + b, a · b or ( by juxtaposition with no symbol ) ab rather than by functional notation of the form f ( a, b ).
* Given any combination of complex numbers, bras, kets, inner products, outer products, and / or linear operators, written in bra-ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.
The notation aspect of the Booch method has now been superseded by the Unified Modeling Language ( UML ), which features graphical elements from the Booch method along with elements from the object-modeling technique ( OMT ) and object-oriented software engineering ( OOSE ).
Primary sources include more than three hundred choreographies in Beauchamp-Feuillet notation, as well as manuals by Raoul Auger Feuillet and Pierre Rameau in France, Kellom Tomlinson and John Weaver in England, and Gottfried Taubert in Germany.
Since the elements can be uniquely sequenced by atomic number, conventionally from lowest to highest ( as in a periodic table ), sets of elements are sometimes specified by such notation as " through ", " beyond ", or " from ... through ", as in " through iron ", " beyond uranium ", or " from lanthanum through lutetium ".
The CE / BCE notation has been adopted by numerous authors and publishers wishing to be
Among the reasons given by those who oppose the use of Common Era notation is that it is selective as other aspects of the Western calendar have origins in various belief systems ( e. g., January is named for Janus ), Style guides for academic texts on religion generally prefer BCE / CE to BC / AD.

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