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Hi! Can anyone explain to me what this sign means. [itex]\equiv[/itex]

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Hi! Can anyone explain to me what this sign means. [itex]\equiv[/itex]

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shmoe

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arildno

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If, for example, you want to introduce a new notation for something, many prefer to do it with this sign.

For example, a standard notation for the "normal derivative" of a function f is often introduced as follows:

[tex]\frac{\partial{f}}{\partial{n}}\equiv\vec{n}\cdot\nabla{f}[/tex]

where the symbols on the right-hand side are assumed known.

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Okej. Great!!

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arildno

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I was unaware of the formal use of this sign in modular arithmetic.

Without having seen your example, I suspect it means "equal, by definition" there..

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Galileo

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In physics, it's often used for defining new things (notations, substitutions and such).

[itex]k \equiv \frac{\sqrt{2mE}}{\hbar}[/itex].

In mathematics, they use " := "for such definitions.

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shmoe

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I'm thinking of using it in place of the usual equality sign "=", not as a definition here. This notation is more commonplace in introductory texts in my experience. I think it's to draw attention to the fact that it's a congruence and not a usual integer equality, in case the student misses the flashing "mod d" that follows. It's tough to get the neon lights around that part in a text!arildno said:Without having seen your example, I suspect it means "equal, by definition" there..

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arildno

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(He'd encountered it when reading of the Uncertainty Principle)

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Yes it was in it's meaning as defination i encounter it.

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jcsd

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For example in x^2 - x - 2 = 0, the equals sign means 'equal for some x', but in x(x + 5) [itex]\equiv[/itex] x^2 + 5x the equivalent sign means 'equal for all x'.

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tokiga svenskar

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cepheid

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[tex] K \equiv \frac{1}{2} mv^2 [/tex]

[tex] \vec{a} \equiv \frac{d\vec{v}}{dt} [/tex]

[tex] S \equiv \int_{t_1}^{t_2}{L(Q, \dot{Q}, t) dt} [/tex]

etc...

nobody ever does that. Is there an error in my reasoning? Because the symbol's use is so haphazard that it might crop up once or twice in a document in random places, leaving me wondering why the author chose those two instances to use it, and why he/she bothered using it at all.

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jcsd

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http://scienceworld.wolfram.com/physics/Acceleration.html

http://scienceworld.wolfram.com/physics/KineticEnergy.html

The author will generally use the symbol to emphaize that it is a definition or that the relationship holds without exception.

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James R

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[tex]\vec{a} \equiv \frac{d\vec{v}}{dt}[/tex]

defines the symbol [itex]\vec{a}[/itex]. Whereas, a statement like

[tex]K=\frac{1}{2} mv^2[/tex]

is not a definition, since it is derived from more fundamental principles.

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Generically it means,

However, whenever things are equivalent by definition we can always use the regular equals sign to equate them as well because it's certainly also true. So author's usually only use the special "defined as" symbol to stress a definition. Many of them don't bother with this special symbol and simply use the regular equals symbol while just mentioning somewhere in the text that the equivalency is a definition.

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The "[itex]\equiv [/itex]" should put in 2 places only:NeutronStar said:

"is formally defined as"- to express a formal definition.

"let this symbol or expression be defined as"- to create an informal definition within the context of a discussion.

"this expression is, by definitions, equivalent to"- showing that two expressions are equivalent by previous or formal definitions.

Generically it means,"equivalent by definition".

However, whenever things are equivalent by definition we can always use the regular equals sign to equate them as well because it's certainly also true. So author's usually only use the special "defined as" symbol to stress a definition. Many of them don't bother with this special symbol and simply use the regular equals symbol while just mentioning somewhere in the text that the equivalency is a definition.

1.A definiton.E.g.[itex] \vec{v}\equiv\frac{d\vec{r}}{dt} [/itex].

2.An identity. E.g.[itex] (a+b)^{2}\equiv a^{2}+b^{2}+ab+ba [/itex]

The rest is just interpretation.Erroneous,sometimes.

Daniel.

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