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. Leo Liu

    What does this integral notation mean?

    I saw it somewhere but I did't know exactly what it meant. Could someone explain it to me like I am 5? Does it mean we integrate with respect to x n times? $$\int_{\mathbb{R}^n}f\, \mathrm{d}^n x$$
  2. M

    I Summation notation and general relativity derivatives

    Does $$\partial^\beta(g_{\alpha\beta}A_\mu A^\mu)$$ mean the same as $$\frac {\partial (g_{\alpha\beta}A_\mu A^\mu)}{\partial A^\beta} ?$$ If not could someone explain the differences?
  3. K

    B Power of ten and math power notation

    Dear PF Forum, I watched this video 10 ^ 10 ^ 10 ^ 5600 The narative says, It is 1 followed by 5600 zeros But that's not what I think, I think it is 1 followed by I don't know. What does this number means? Is it A: 10 ^ (10 ^ (10 ^ 56))) or B: ((10 ^ 10) ^ 10) ^ 56? It says that "As...
  4. C

    ##G## is Injective ##\iff ## ## f ## is onto ## Y ## (Lambda Notation)

    My attempt: ## ( \rightarrow ) ## Suppose G is injective. Let ## y \in Y ## be arbitrary, denote A = ## \{ y \} ## so that ## G(A) = G(\{ y \}) = f^{-1}[\{ y \}] = \{ x \in X | f(x) \in \{ y \} \} =\{ x \in X | f(x)= y \} ##. [ However, now I am stuck because I don't know if ## G(A)=...
  5. C

    Finding inverses of two functions in Lambda Notation

    I found the following functions ( In lambda notation ) to be injective, and now I am trying to find the inverse functions for them ( the inverse for the Image of ## f ## ) but I am stuck and I need help: 1. ## f = \lambda n \in \mathbb{N}. (-1)^n + n^2 ## 2. ## f = \lambda g \in \mathbb{R}...
  6. C

    I What does V^G mean in linear algebra?

    Hi. Newbee question. What does the notation V^G mean where V is a vector space and G is a group? I found it in: A linear algebraic group G is called linearly reductive if for every rational representation V and every v in V^G \ {0}, there exists a linear invariant function f in (V^*)^G such that...
  7. stevendaryl

    I Covariant derivative notation

    [Moderator's note: Thread spun off from previous thread due to topic change.] This thread brings a pet peeve I have with the notation for covariant derivatives. When people write ##\nabla_\mu V^\nu## what it looks like is the result of operating on the component ##V^\nu##. But the components...
  8. S

    A Index notation and partial derivative

    Hi all, I am having some problems expanding an equation with index notation. The equation is the following: $$\frac {\partial{u_i}} {dx_j}\frac {\partial{u_i}} {dx_j} $$ I considering if summation index is done over i=1,2,3 and then over j=1,2,3 or ifit does not apply. Any hint on this would...
  9. B

    B Traveling wave solution notation

    This is probably kind of dumb, but it's really bothering me for some reason. I originally saw traveling wave solutions to the wave equation as ##f(kx−\omega t)## for right traveling (as t gets bigger, x needs to be bigger to "match" it's previous value) and ##f(kx+\omega t)## for left-traveling...
  10. S

    Art Notation for drum parts when scores were hand written?

    In the days when scores were written by hand, how were parts for drums written? It's clear that ordinary notation is sufficient to indicate the duration of dumb beats - although writing each beat for a drum would be tedious. Was there some system of abbreviation? Did composers attempt to...
  11. P

    Can't understand ket notation for spin 1/2

    I can't why there are four elements in each ket instead of only two
  12. M

    Probability notation: question about joint and conditional probability

    Hi, Just a quick question about conditional and marginal probabilities notation. Question: What does ## p(a|b, c) ## mean? Does it mean: 1) The probability of A, given (B and C) - i.e. ## p[A | (B \cap C)] ## OR 2) The probability of (A given B) and C - i.e. ## p[(A | B) \cap C] ## I was...
  13. F

    Python Dot Notation: Access Functions, Classes, Objects & Variables

    Hello (again). I have become quite familiar with the dot notation in Python. The dot "operator", assuming operator is the right term, seem to have many uses. For example: 1) After an instance name, it can be used to access instance attributes and apply instance methods to the object/instance...
  14. S

    I Matrix Notation for potential in Schrodinger Equation

    I'm working on the time-dependent Schrodinger equation, and come across something I don't understand regarding notation, which is not specific to TDSE but the Schrodinger formalism in general. Let's say we have a non-trivial potential. There is a stage in the development of the TDSE where we...
  15. N

    Set Notation: A x B Product of Powers of Prime Factors

    I get 2^5 x 3^80 Am I correct?
  16. U

    MHB Precalculus: What is the value of this sigma notation?

    Hi, I'm currently a Grade 11 student and I need help for this question (Precalculus): If $\sum\limits_{i=1}^{50} f(i)=90$ and $\sum\limits_{i=30}^{50} g(i)=60$, what is the value of $\sum\limits_{i=1}^{50} (7 g(i)-f(i)+12)/(2)$? P.S. To those who could answer this, it would be a great help...
  17. R

    A Dirac Notation: Why is order reversed in ket expasion?

    Shankar Prin. of QM 2nd Ed (and others) introduce the inner product: <i|V> = vi ...(Shankar 1.3.4) They expand the ket |V> as: |V> = Σ vi|i> |V> = Σ |i><i|V> ...(Shankar 1.3.5) Why do they reverse the order of the component vi and the ket |i> when they...
  18. L

    A Understanding Tensor Notation: What is the Difference?

    I am struggling with tensor notation. For instance sometimes teacher uses \Lambda^{\nu}_{\hspace{0.2cm}\mu} and sometimes \Lambda^{\hspace{0.2cm}\nu}_{\mu}. Can you explain to me the difference? These spacings I can not understand. What is the difference between...
  19. chwala

    Solve for x in this index notation problem

    ok, by direct substitution i know that either ##x=2## or ##x=4## but i would like to prove this analytically, would it be correct saying, ##xln 2= 2ln x## ##xln_{2}2=2 ln_{2}x## ##x=2 ln_{2}x## ##\frac {1}{2}=\frac { ln_{2}x}{x}## ##ln_{2}x^{1/x}##=##\frac {1}{2}## →##2^{1/2}##=##x^{1/x}##...
  20. Frabjous

    Geometry Calculations with tensors in modern notation

    Is there a book that emphasizes performing calculations with tensors in modern notation?
  21. S

    B Question about Notation of Function

    In the notation of Function ---> f(x)=y Here f represents the function and x is the variable in the function. we read f(x) as "f of x"or "function of the variable x" what does "function of x " mean that we read ? in this notation what does round brackets ()...
  22. E

    B Can someone please explain Feynman's index notation?

    I found some parts of Vol II, Chapter 25 basically unreadable, because I can't figure out his notation. AFAICT he's using a (+,-,-,-) metric, but these equations don't really make any sense: The first one is fine, and so is the second so long as we switch out ##a_{\mu} b_{\mu}## for ##a_{\mu}...
  23. E

    B Notation for indexing a crystal direction

    Given a crystal basis ##\{\vec{a}, \vec{b}, \vec{c} \}##, the two lattice vectors ##\vec{r}_1 = u_1 \vec{a} + u_2 \vec{b} + u_3 \vec{c}## and ##\vec{r}_2 = 2u_1\vec{a} + 2u_2 \vec{b} + 2u_3 \vec{c}## both obviously point in the same direction whilst ##\vec{r}_2## is twice as long as...
  24. I

    Expectation Value Notation in Griffiths QM Textbook Third Edition

    In the 3rd edition of the Introduction to Quantum Mechanics textbook by Griffiths, he normally does the notation of the expectation value as <x> for example. But, in Chapter 3 when he derives the uncertainity principle, he keeps the operator notation in the expectation value. See the pasted...
  25. L

    MHB Summation and product notation rules

    As per the image, I am supposed to select all the valid statements. Apparently I'm only partially correct, and so I took another look at the statements. I believe the third statement is wrong, since c * (a_m*a_{m+1}*a_{m+2}*...*a_n) =/= (c*a_m)(c*a_{m+1})(c*a_{m+2})*...*(c*a_n) Thus there...
  26. nomadreid

    I Did von Neumann coin the eth or dyet for the inexact differential?

    Today the inexact differential is usually denoted with δ, but in a text by a Russian author I found a dyet (D-with stroke, crossed-D) instead: In response to my question to the author about this deviation from normal usage, he stated that this was a suggestion from von Neumann. (Which of course...
  27. V

    Understanding Subsitution Notation: Exploring (a,b)

    For the first one so far I have (3 · a + 5 · b)[a, b ≔ b, a] =⟨ Substitution ⟩ (3 · b + 5 · a) So far this is right, however I don't really know the difference between the others. For the second one I did (3 · a + 5 · b)[a ≔ b][b ≔ a] =⟨ Substitution ⟩ (3 · b + 5 · b) For this one I got it...
  28. H

    Proof of a dot product using sigma notation

    Mentor note: Moved from a technical section, so is missing the homework template. Hi, I'm always not sure how to prove something in math and I'm wondering if this is enough. ##\vec r \cdot (\vec u + \vec v) ## ##\vec u + \vec v = (u_1+v_1, u_2+v_2,u_3+v_3) = \vec s## ##\vec r \cdot (\vec u +...
  29. patric44

    Quantum Dirac notation based quantum books?

    hi i am recently following the nptel course in quantum mechanics (The Course ) and it seems like a really good course , but i can't find the book that it based on . my question is : had anyone saw that course before to suggest a QM book related to it ? - she began by an introduction to vector...
  30. entropy1

    I The significance of the Dirac notation

    If we have the wavefunction ##|ab \rangle##, what do the a and b stand for? In particular, do a and b signify an outcome of some pending or possible measurement, or do they signify some aspect of the wavefunction, and if so, which aspect?
  31. Anonymous1

    B Vector Notation: Italic Boldface Symbolization

    is it true that vectors are symbolised as an italic boldface 'a'
  32. K

    Does Summation Over n from -∞ to +∞ in Quantum Mechanics Equal Ψ(x)?

    I have a (trivial) question regarding summation notation in Quantum mechanics. Does ∑cnexp(iknx) = Ψ(x) imply that n ranges from -∞ to +∞ (i.e. all possible combinations of n)? i.e. n ∞ ∑exp(iknx) -∞ I believe it does to be consistent with the Fourier series in terms of complex exponentials...
  33. I

    Griffiths Problem 3.35. Harmonic Oscillator, Bra-ket notation

    Firstly, apologies for the latex as the preview option is not working for me. I will fix mistakes after posting. So for ##<x>## = (##\sqrt{\frac{\hbar}{2m\omega}}##) ##(< \alpha | a_{+} + a_{-}| \alpha >)## = (##\sqrt{\frac{\hbar}{2m\omega}}##) ##< a_{-} \alpha | \alpha> + <\alpha | a_{-}...
  34. anuttarasammyak

    B Question about notation in the Feynman Lectures on Physics III 3-1

    I have a question on formula (3.1) and (3.2) in Feynman Lectures on Physics III 3-1, available online, https://www.feynmanlectures.caltech.edu/III_03.html <x|s> here can be interpreted also as inner product of bra <x| and ket |s>, following usual Dirac notation ? For example, ##<r_1|r_2>## in...
  35. George Jones

    Symbol ##\supset## Meaning in Eqs. 3.1 & 3.2

    What does the symbol ##\supset## mean as used in equations (3.1) and (3.2) of https://arxiv.org/pdf/1701.07427.pdf
  36. John Greger

    A Understanding Killing Vector Equation Notation

    Hi all, The killing vector equation reads: ##\nabla_{(\mu K_{\nu})} = 0## What do the parenthesis mean explicitly? Moreover, I know that ##\nabla_\mu x^\nu = \partial_\mu x^\nu+ \Gamma_{\rho \mu}^\nu x^\rho## So if the parentheses mean symmetric the Killing equation will read...
  37. R

    MHB Problem using big O notation

    Functions defines on the plane $\mathbb{R}^2$ or open subsets , using $X=(x_1,x_2)\in\mathbb{R}^2$ asthe coordinates Find all $\alpha \in \mathbb{R}$ such that $(\ln x_1)(x_2^2+x_2)=O(||X||^{\alpha})$ as $||X||\to 0$. and $|X|| \to \infty$ (note that $x_1>0)$
  38. T

    Nolting Theoretical Physics 1, Jacobian Notation Question

    On Page 406 of Nolting Theoretical Physics 1 he has the following notation for the Jacobian determinant $$\frac{\partial( x_{1}, x_{2})}{\partial (y_{1}, y_{2})} = \begin{vmatrix} \left (\frac{\partial x_{1}}{\partial y_{1}} \right )_{y_{2}}& \left ( \frac{\partial x_{1}}{\partial y_{2}}...
  39. jedishrfu

    B Bartlett's Calculus Paper: Confusing Calculus Notation & Differentials

    Bartlett’s Calculus Paper Reviewed in Mathematics Magazine https://mindmatters.ai/2020/03/bartletts-calculus-paper-reviewed-in-mathematics-magazine/
  40. G

    I Confused by Notation? Perturbation Theory Explained

    Looking at. <psi|AB|theta>, under what conditions would this be equal to <psi|A|theta> * <psi|B|theta> I’m just getting into perturbation theory and am running into confusing notation. Thanks john
  41. Quark Effect

    B What is the significance of 'i' in quantum computation notation?

    Hi guys, I am currently having some difficulties with this quantum state. I don't entirely understand what that letter 'i' means, where it comes from and why it appears in brackets [1, i]. Shouldn't there be a '0' instead? I am an absolute beginner in quantum computation. I've been following a...
  42. L

    U-Substitution Notation as division

  43. berlinspeed

    I Notation inquiry - bar over basis set....

    What's the meaning of the "bar" on the basis set of W at bottom right corner?
  44. chriscarson

    Young's modulus question with answer notation issue

    Summary:: why this answer ? I have the result of a young s modulus that is 358280256.25 and the answer the teacher gave us is 3.58 x 10 to the power of 8 . why not 358.3 x 10 to the power of 6 ? how she s deciding how many steps goes back with the point , the answer of a sum before this...
  45. Z

    Writing a squared observable in Dirac notation

    Edited after post below: Hi, I need to show that the square of the expectation value of an observable takes a certain form in Dirac notation. I know in wave notation that the expectation value is a sandwich integral which looks like this: ##<A>=\int_{-\infty}^\infty \Psi^*(x) \hat A \Psi (x)...
  46. K

    I Relativistic Notation in Waves: Confusion Solved

    If we have a plane wave, usually in Relativity notation it is written as ##A^\alpha = a^\alpha \exp(i x_\alpha k^\alpha)##. (I know we need to take the real part in the end). In cartesian coordinates, and two dimensions say, that ##x_\alpha k^\alpha## would be ##x^\alpha k_\alpha = x k_x + y...
  47. Adesh

    Understanding the notation in Group Theory

    I was studying mathematical logic and came across this statement of group theory I'm having a hard time in understanding it. I have concluded that ##G## is any set but not an empty one, ##\circ## is a function having input as two variables (both variables are from set...
  48. Arman777

    Deriving an identity using Einstein's summation notation

    I have an identity $$\vec{\nabla} \times (\frac{\vec{m} \times \hat{r}}{r^2})$$ which should give us $$3(\vec{m} \cdot \hat{r}) \hat{r} - \vec{m}$$ But I have to derive it using the Einstein summation notation. How can I approach this problem to simplify things ? Should I do something like...
  49. K

    I Question regarding notation when omitting terms

    If we want to expand a function ##f(x)## up to first order around ##x = 0## say, we usually write ##f(x) = f(0) + (df/dx)|_0 x + \mathcal O(x^2)##. But what if I want to expand ##f(x)## in the whole series, and showing only the first order term in x? What notation do you use for that? (Aside...
  50. S

    I Is Joon-Hwi Kim's idea of graphical notation for vector calc any good?

    Here is his paper. I don't see what the big deal about it is. https://arxiv.org/pdf/1911.00892.pdf
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