What is Notation: Definition and 1000 Discussions

In linguistics and semiotics, a notation is a system of graphics or symbols, characters and abbreviated expressions, used (for example) in artistic and scientific disciplines to represent technical facts and quantities by convention. Therefore, a notation is a collection of related symbols that are each given an arbitrary meaning, created to facilitate structured communication within a domain knowledge or field of study.
Standard notations refer to general agreements in the way things are written or denoted. The term is generally used in technical and scientific areas of study like mathematics, physics, chemistry and biology, but can also be seen in areas like business, economics and music.

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  1. sams

    I A question about writing the notation of the nabla operator

    I have a simple question about the notation of the nabla operator in Vector Analysis. The nabla operator is a vector differential operator and it is written as: $$\nabla = \hat{x} \frac {∂} {∂x} + \hat{y} \frac {∂} {∂y} + \hat{z} \frac {∂} {∂z}$$ Is it okay if we accented nabla by a right...
  2. S

    I Ambiguities of the "...." notation

    A popular response to a novice asking whether .999... = 1 is for an expert to demand that novice define what the notation ".999..." means. I think this is the best response. However, I note that many experts tend to accept the "..." notation in other contexts without demanding an explanation...
  3. R

    Can I Use Vector Notation for Graph Translations?

    Homework Statement Hi. Its not really a problem but just a general question. When doing graph translations, such as move the parabola x units right or y units up etc, Is it okay to use vector format. So instead of saying move this equation 4 units left, could you write it like this -> <-4,0>...
  4. C

    MHB Math induction with sigma notation

    Prove by math induction that n sigma 3i + 1 = n/2 (3n + 5) i = n
  5. P

    I Index notation for inverse Lorentz transform

    Hi all, just had a question about tensor/matrix notation with the inverse Lorentz transform. The topic was covered well here, but I’m still having trouble relating this with an equation in Schutz Intro to GR... So I can use the following to get an equation for the inverse...
  6. Martin T

    I About Arnold's ODE Book Notation

    In Arnold's book, ordinary differential equations 3rd. WHY Arnold say Tg:M→M instead of Tg:G→S(M) for transformations Tfg=Tf Tg, Tg^-1=(Tg)^-1. Let M be a group and M a set. We say that an action of the group G on the set M is defined if to each element g of G there corresponds a...
  7. sams

    Representing Vectors in Newton's Notation: How to Use Overdot and Arrow Symbols?

    A very simple question. How do we represent a vector with Newton's notation (writing the arrow symbol with the overdot notation)? Can we write them both above each other. First, the overdot notation and then the arrow symbol? Thank you a lot for your help...
  8. Theta_84

    Can Einstein Index Notation Help Me Solve Equations in Continuum Mechanics?

    Hello I am doing some exercises in continuum mechanics and it is a little bit confusing. I am given the following equations ## A_{ij}= \delta_{ij} +au_{i}v_{j} ## and ## (A_{ij})^{-1} = \delta_{ij} - \frac{au_{i}v_{j}}{1-au_{k}v_{k}}##. If I want to take the product to verify that they give...
  9. S

    B Conjugation , involving operators in Dirac Notation.

    In a PDF i was looking through i came about a question for the operator P = |a><b| find Px(adjoint) the adjoint was defined as <v|Px|u> = (<u|P|v>)* where u and v can be any bra and ket now for the question: (<u|a><b|v>)* = <v|Px|u> this is the confusing step , i thought conjugated simply...
  10. S

    B Ambiguity w/ Newton's dot notation + vector-magnitudes

    Stumbled on a potential pitfall that can arise if you combine Newton's overdot notation (for time-derivatives) with boldface/non-boldface notation for vectors/vector-magnitudes. Say you have ##\textbf{v}## for velocity and ##\dot{\textbf{v}}## for acceleration. Speed is then ##v## (magnitude of...
  11. S

    I Dirac Notation: Bra & Ket Conjugation Rules

    hey guys just a quick question , within the Dirac notation I we have bras and kets.Is it allowable to simply hermitianly conjugate everything , e.g: <w|c> = <b|c> - <d|c> Can we then: <c|w> = <c|b> -<c|d> Or is there some subtly hidden rule.
  12. V

    I What does this notation mean? ex: 1s:A, 1s:E

    From this paper, on page 2: https://arxiv.org/pdf/1606.03488.pdf. I know the spectroscopic notation part, but what is the meaning of the symbol after the colon?
  13. bornofflame

    [LinAlg] Describe Ker(T) using set notation for T:P^1 -> R

    Homework Statement 2. Let ##T: \mathbb{P}^1 \rightarrow \mathbb{R} \text{ be given by } T(p(x)) = \int_0^1 p(x)~dx## Describe ##Ker(T)## using set notation. Homework Equations ##p(x) \in \mathbb{P}^1~|~ p(x) = a_0 + a_1x## The Attempt at a Solution ##T: \mathbb{P}^1 \rightarrow \mathbb{R}##...
  14. E

    I Understanding the Semicolon Usage in Meijer's G-Function Notation

    Hello, What are the semicolons in the this Meijer's G Function (picture is attached)? The notation I saw in different books and in the Internet doesn't include semicolons. Do they signify something that is not in the other notations? Thanks
  15. DuckAmuck

    I Is Braket Notation Causing Confusion in Quantum Mechanics?

    Is |x+y> = |x> + |y> ? Thank you.
  16. shintashi

    B When do we use which notation for Delta and Differentiation?

    I was taking notes recently for delta y/ delta x and noticed there's more than one way to skin a cat... or is there? I saw the leibniz dy/dx, the triangle of change i was taught to use for "difference" Δy/Δx, and the mirror six ∂f/∂x which is some sort of partial differential or something...
  17. J

    Conversion of Piezoelectric coefficients

    Hello everyone, I am interested on simulating the converse Piezoelectric effect of materials and I have given the mechanical (Youngs modulus and Poissoin's ratio) and electric material properties (Electric Permittivity, Piezoelectric coupling matrix etc). However from the literature I got...
  18. bornofflame

    [LinAlg] Set Notation, Subspaces, Bases, Ranges, & Kernels

    Homework Statement I don't want to clog up the forums with a few "small" problems so I am lumping them together here. 2. Let ##T:P^1 → R \text { be given by } T(p(x)) = \int^b_a p(x)dx##. Describe Ker(T) using set notation. 3. Let ##H = \left\{f ∈ C[a, b] | f'(x) ≥ 0 ~\text for...
  19. M

    How to Write the Inverse of a Matrix Using Einstein Summation Notation?

    Homework Statement I am unsure as to how to write the dot product in terms of the summation notation? May you please explain? Homework EquationsThe Attempt at a Solution
  20. E

    Finding the net gravitational force with Vector Notation

    Information Given: In the figure, a square of edge length 17.0 cm is formed by four spheres of masses m1 = 4.70 g, m2 = 2.90 g, m3 = 0.800 g, and m4 = 4.70 g. Question: In unit-vector notation, what is the net gravitational force from them on a central sphere with mass m5 = 2.90 g? Attempted...
  21. W

    Superposition of Plane EM Waves Using Complex Notation

    Homework Statement I have a simple problem relating to the superposition of plane EM waves that I'd to try out using complex notation. Could anyone run through the work to see if my understanding is right? Many thanks in advance! The incident E bit of the wave is $$\vec{E}_I = E_0 \sin(ky -...
  22. Z

    Is the Notation Implied for a Singleton Set or Can It Have Multiple Elements?

    Homework Statement For the following notation, D \subseteq \{ z | \exists x,y \in S (z = x - y ) \} I'm wondering if S can only have one element, or does the notation imply that | S | > 1 Homework EquationsThe Attempt at a Solution For example, if I have S = \{ 3 \} is z = 3 - 3? Or...
  23. N

    Mathematical Induction with Sigma notation

    Prove by mathematical induction that n sigma r^3 = n^2(n+1)^2/4 r = 1 so far I have 1 sigma r^3 = 1^2(1+1)^2/2 r=1 1 = 1(4)/2 1 = 4/2 1 = 2 I'm not sure what to do after this for the k+1 case.
  24. binbagsss

    I Delta Notation in GR: Replacing vs Raising/Lowering

    Hi So we write ##g_{ab}g^{ac}=\delta^{(4)c}_b ##, but this simply means to replace ##b## with ##c## or vice versa, so, why don't we write ##\delta_{bc}##? Thanks i.e. the affect is not to replace and raise/lower, it is simply to replace, so I'm a bit confused by the notation...
  25. chwala

    Atomic symbol notation question

    considering the symbol of an element, under the cambridge curriculum , is the nucleon number written on top or at the bottom on the left side of the element?
  26. T

    Vector Notation in Nolting Theoretical Physics 1

    On pg. 60 of Nolting Theoretical Physics 1 for the definition of a vector multiplied by a scalar the book shows two little up arrows if the scalar is greater than zero and an little up arrow and then a little down arrow if the scalar is less than zero. Then again on pg. 61 for definition 1.139...
  27. R

    Set Notation Question: Converting to Set Builder Notation | Homework Help

    Homework Statement So I have the set {...(1/8),(1/4),(1/2),(1),(2),(4),(8)...} I am suppose to put it in set builder notation.. Homework EquationsThe Attempt at a Solution my answer was { x = {\frac {1}{2^n} : n \in ℤ } } but my books was { x = {{2^n} : n \in ℤ } } I understand both...
  28. A

    I What does the vertical line in this equation mean?

    Hey, What does the vertical line with the "I_b" on the bottom right mean? Link here: https://imgur.com/a/nII9g Thanks, -Yael
  29. Math Amateur

    I Directional Derivatives .... Notation .... D&K ....

    I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with an aspect of D&K's notation for directional derivatives ... ... D&K's definition of directional and partial...
  30. M

    Understanding Big-O Notation: Exploring Growth Rates and Upper-Bound Orders

    I am learning about Big-O notation, and am kind of confused. So, Big-O notation is the upper-bound order that measures the amount of required resources as n approaches a sufficient size. It essentially measures the scalability of an algorithm. My question, however, is with the notation.If an...
  31. H

    I Correct notation for some functional expressions

    Having some trouble determining the most mathematically correct way to express something I understand only numerically and physically. Basically I am modeling radiation within a volume. 1. For each point dV within a volume V there is a scalar value e(dV), which is an amount of radiation emitted...
  32. E

    I Derivation notation with capital D?

    Hi, I came across a derivation notation I didn't recognize: Let ##s## be some four-vector and ##\tau## the proper time. What is the significance of $$\frac{Ds}{\mathrm{d}\tau}?$$ I know ##Ds## can be used to mean the Jacobian, but I've never come across the notation above. Does someone...
  33. Dethrone

    MHB Layout Notation for matrix calculus

    Hi, I guess this could be a rather silly question, but I got a bit confused about the "numerator layout notation" and "denominator layout notation" when working with matrix differentiation...
  34. RoboNerd

    I Question about simplifying Sigma notation

    Hello everyone! I have this expression which I have to simplify: ∑i=1log(n) 1(log(n) - i) And my book apparently simplifies it to being log(n). I am struggling to figure out why this is the case. Could anyone help? Thanks!
  35. D

    I Understanding the Induction Axiom: Notation & Equivalence

    So , what I was wondering about was a slight difference in notation, for which I am not certain if correct (mine, in particular.). The induction axiom says: If M is a subset of ℕ, and if holds that: a)1∈M b)(∨n∈ℕ)(n∈M→s(n)∈M) then M=ℕ. Now my question is: why do we write (∨n∈ℕ)(n∈M→s(n)∈M)...
  36. J

    Clock Notation of Star-Delta 3-phase transformer

    Homework Statement Homework Equations Dot is A2. A1-A2 of star is in phase with A1-A2 of delta The Attempt at a Solution I'm getting answer as Y-Delta - 1. Assuming Y is HV. How is C right answer?
  37. J

    I How Does Dirac Notation Simplify Quantum Mechanics for Harmonic Oscillators?

    I am completely baffled by bit of notation in Quantum Mechanics Concepts and Applications by Zitteli. He is trying to get the differential equation for the ground state of a harmonic oscillator using the algebraic method as opposed to Schrodinger's equation. I suspect he is compressing a lot of...
  38. J

    A Simmons notation for transfinite ordinals

    Harold Simmons defined a simple but powerful notation for transfinite ordinals described in several articles available at http://www.cs.man.ac.uk/~hsimmons/ORDINAL-NOTATIONS/ordinal-notations.html . In summary : - It uses lambda calculus formalism - Fix f \zeta = f^\omega (\zeta+1) = limit...
  39. J

    Clock face notation of a Transformer's "Vector Group"

    Hi, I'm studying transformer and am a bit confused. Say for vector group: Dy11, I guess it's the line voltage of LV leads the Line voltage of HV by 30 degrees. Book says phase angle. The phase angle is line voltage right, since the phase voltage of HV and LV will always be in phase with each...
  40. MichPod

    School math notation - x for multiplication or a variable?

    I got my education out of the American continent, yet currently I live in Canada and my son goes to school here (5th grade + some additional math training) What puzzles me is that currently he may write things like $$5\times-1$$ meaning ##5\cdot(-1)##, which I can only read as ##5x-1## (i.e...
  41. N

    Spectroscopic Notation Problem

    Question (a) Write down the quantum numbers for the states described in spectroscopic notation as 2S3/2, 3D2 and 5P3. (b) Determine if any of these states are impossible, and if so, explain why. (Please note that these could describe states with more than one electron.) My Attempt A) I came...
  42. Y

    I What does this vector notation mean?

    Hello, I'm currently doing vectors in class, but I don't know what these parts mean. Especially φ(a,b). I understand cos(φ), but I don't understand cos(φ(a,b)). φ is the angle between two vectors a and b, but what does the (a,b) part add? I tried to google, but I couldn't really find...
  43. B

    I Notation for systems of simultaneous equations

    What notation would I need to use in order to write a mathematical statement to define a System S of simultaneous equations - let's say ax+by=c and ex+fy=g.
  44. TAKEDA Hiroki

    I Double sided arrow notation in Dirac Field Lagrangian

    In a thesis, I found double sided arrow notation in the lagrangian of a Dirac field (lepton, quark etc) as follows. \begin{equation} L=\frac{1}{2}i\overline{\psi}\gamma^{\mu}\overset{\leftrightarrow}{D_{\mu}}\psi \end{equation} In the thesis, Double sided arrow is defined as follows...
  45. V

    Could someone please tell me what this notation means?

    Homework Statement Erica goes swimming three out of the seven days of the week. How many possibilities are there for her swim schedule if she goes swimming on Monday or Tuesday or both? (Define M to be the set of schedules in which Erica goes swimming on Monday. Let T be the set of schedules in...
  46. whitsona

    B Teacher needs help: Bra–ket notation for parabolas?

    I am about to do a unit on the wonders of vector decomposition for year 2 in a 3 years science curriculum where the kids follow along with the historical developments of science. It's the science class I wish I'd had before becoming an engineer at MIT. In year 3, we are with Einstein and...
  47. E

    I Confusion about Dirac Notation (interferometer)

    Hello everybody, Dirac notation uses "bras"( <a| ) and "kets"( |b> ), which are row vectors and column vectors respectively, but what would something like |a, b> mean? It makes no notational sense to me Context: A couple of photons going through beam splitters in an interferometer. One is...
  48. sams

    I What does the j means in this notation?

    This section of Introduction to Electrodynamics by Griffiths, section 8.2.2 (page 363), is talking about the Maxwell's Stress Tensor. I do not quite understand what the j means on the left = sign (for either of the two representations) in the attached figure highlighted in yellow color. I have...
  49. Moayd Shagaf

    I Difference Between d3x and triple Integral

    So My Question Is Simple, But It confuse me too much! What Is Difference between the notation ∫d3x and ∫∫∫dxdydz ?
  50. R

    Very quick question on notation, M vs. M/L

    From this paper... http://pubs.acs.org/doi/pdf/10.1021/jp020363g there is a graph... Which I've been told the M means moles per litre. I now have another graph from this paper... http://pubs.acs.org/doi/abs/10.1021/jp9937407 ... Which has mM, so is this mM/L or just milli moles? Sorry for...
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