Questions tagged [notation]
Question on the meaning, history, and usage of mathematical symbols and notation. Please remember to mention where (book, paper, webpage, etc.) you encountered any mathematical notation you are asking about.
11,670
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Operations on elements of 2 sets. Similar to nested forEach loops.
Does this make sense?
$$ \{ p \in P_n | \{g \in \Bbb G, q \in P_n: (q * g) \in P_n \}\}$$
Intention: all $p \in P_n$ that are products of $q \in P_n$ and $g \in \Bbb G$
If not what would be the right ...
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Formal definition of Real Numbers
I was recently getting started with mathematic formal notation by defining sets of numbers. In Wikipedia, there are some of them definited as:
$\mathbb{Z} = \{\ldots -3,-2,-1,0,1,2,3\ldots\}$
$\mathbb{...
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Showing a relation between two specific elements of two different sets, simultaneously as showing their set-membership
I found myself using the following notation, wondering if it was conventional or clear:
$$X \ni x = g \in G$$
Meaning that $x$, from the set $X$, is equal to $g$, from the set $G$. More generally, I'm ...
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What do $\frac{\partial}{\partial z}$, $\frac{\partial}{\partial x}$, $\frac{\partial}{\partial y}$ mean?
Maybe a dumb question but I'm relatively new to this topic so I'd still ask this:
I saw it here: https://en.wikipedia.org/wiki/Wirtinger_derivatives
In ordinary derivatives, I know $\frac{d}{dx}$ is ...
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Notation for an approximately defined interval
Is there a concise notation to express the following "inequality"?
$$a\lesssim x\lesssim b$$
For proper inequalities like $a< x\leq b$ we write $x\in(a, b]$, or sometimes also $x\in]a, b]$...
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Explanation of summation notation when inequality and equality are in the index
I recently came acrossed the following notation:
$\sum_{\substack{
j\leq j'=1}}^{2^i-1} a_{j,j'}$
Frankly, I don't know how to interpret the index portion correctly. Say that i=2 (as is the case I ...
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Notation for infinite-dimensional vector output of a function $f: X \rightarrow \mathbb{R}$ on an interval
I have a function $f: X \rightarrow \mathbb{R}$. I want to create a vector of the "outputs" of the function, in the following sense: if $X$ was discrete, e.g., $X = \{x_1, x_2, \dots, x_K\}$,...
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1
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Determinate $d^{k}f_{c}$ for function $f(x,y)$ with k and c given
In my Calculus 3 class I have been given following problem:
Determinate: $d^{k}f_{c}$ for function $f(x,y)$ where $c = (c1,c2)$ and $k = 2$.
My problem is that I have no clue what does $d^{k}f_{c}$ ...
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Parenthesis needed? in $(S\subset T)\vee(S=T)\iff S\subseteq T$ [closed]
In the statement
$$(S\subset T)\vee(S=T)\iff S\subseteq T$$
are the parenthesis
formally incorrect
correct but deemed best removed
correct and optional
correct and deemed required for readability
...
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How to express a sequence of matrix multiplications $\prod_{i=1}^{n}M_i$ but starting from $n$
Having square matrices $M_j\in\mathbb{R}^{m\times m}$, with $j\in\{1\,..\,n\}$, what notation should be used to express the following sequence of multiplications?:
\begin{align}
M_n\to M_{n-1}M_n\to ...
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1
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A question about the meaning of the notation $(\frac{\partial}{\partial \cosh r})^2 F(r,x).$ [closed]
I am studying a book and I found the expression
$$(\frac{\partial}{\partial \cosh r})^2 F(r,x).$$
Any help about the meaning of the notation that uses the author?
About the exponent, I am sure that he ...
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I canot find what does $\langle,\rangle$ mean in a cooperative game theory book
Does anyone know what here on the page 83 it holds that $ \langle x,y\rangle\geq \langle x,y'\rangle$ in taking the minimum ?
I.e. I cannot find the notation $\langle,\rangle$ in the book.
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Notation of math expressions
Let $h \in \mathcal{H}$ be a classifier from a hypothesis class $\mathcal{H}$ trained to infer $\mathcal{y}$ from $\mathcal{x}$, $\mathcal{h} : \mathcal{X} \rightarrow [0,1]^{|\mathcal{Y}|}$. We use $\...
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Shorthand set builder notation?
I was reading some papers and they had the following notation:
$$
\big\{k\big\}_{k=0}^n
$$
I assume this implies that
$$
\big\{k\big\}_{k=0}^n = \{k \in \mathbb{WHAT} : 0 \leq k \leq n\}
$$
What is $k$...
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For $f : \mathbb{R} \to \mathbb{R}$, what is $\sup\limits_{x \in A} f(x)$ if $A=\emptyset$? [duplicate]
Let $f : \mathbb{R} \to \mathbb{R}$ and $A$ be an empty set. What is $\sup\limits_{x \in A} f(x)$ equal to? I reckon it should just be undefined or is there an alternative convention?
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Matrix entry notation and plane coordinate notation
Let $A$ be an $m \times n$ matrix, and $a_{ij}$ a matrix entry.
Usually the index $i$ indicates the row and $j$ the column of the matrix.
So changing the index $i$ makes you move in the $vertical$ ...
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Notation: function returning the element of a partition containing $x$
Suppose $Y=\{y_1,\ldots,y_m\}$ partitions the set $X=\{x_1,\ldots,x_n\}$. I would like to define a function $y: X \to Y$ which returns $y \in Y$ if and only if $x \in y$. Is there a way to write this ...
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What is the difference between the principal square root of $x$ and $x^{1/2}$?
Today I learned that the square root symbol ($\sqrt{}$) represents only the "principal" square root of a number. What about exponents?—if I write $x^{1/2}$, would that encompass the negative ...
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Meaning of Big O notation with Index $[O_{\epsilon}(n^{\epsilon})]$
I found this notation in a book and can't figure what it means. I haven't found any other examples. This is $$O_{\epsilon}(n^{\epsilon})$$ One can see it in context at page $186$ of book. Anyone know ...
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Notation for probability density function in Bayesian context
The Bayes theorem is often quoted as,
$$P(\theta|X) = \frac{P(X|\theta)P(\theta)}{P(X)}.$$
In my use case, I'm dealing with Gaussian continuous variables. So, by $P(X|\theta)$ I'm referring to the sum ...
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2
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Understanding random variables as functions
First of all, I have read What is a function and I have understood it basically and it is clear to me that in order to caluclate statistics "things" have to be transformed or mapped to ...
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What is the notation of length of vector?
I am looking for a symbol to express the length of a vector or table,
For example we have a vector V, len(V)==5 ( for example).
How can I represent it by a symbol ?
- 103
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Confusing $\min$, $\max$ notations for $k$-Means
If I have a graph like the one below:
and I want to describe at what $k$ does the function stop decreasing the most, it would be $k=2$. But how would I put it notation-wise? Should I do this:$$\...
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Notation for smallest value greater than a number in a sorted set
In a finite set, is there a concept/notation for the smallest value larger than a particular element? For example, I have a sorted set as $ A = \{a_1, a_2, ..., a_k \} $ where $ a_2 > a_1, a_3 >...
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Notation: set X whose elements are smaller than each elements of set Y
Does there exist some notation to indicate that all elements of a set X are smaller than all elements of a set Y?
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Summation: Adding all scores with a min and max (score) of 10 and multiply by (amount of Issues) Y - Notation Formatting Advice
I am new this portal and haven't done any maths for a very long time.
For an academic project I am working on, I attempting to create a equation (not even sure that's the right language to use) where ...
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Could someone explain this notation and line inthe transcendence proof of $\pi$?
In the following linked proof for the transcendence of pi https://fermatslibrary.com/s/the-transcendence-of-pi, the author uses the notation $\theta_1(x)=(e^{\alpha_1}+1)(e^{\alpha_2}+1)(e^{\alpha_3}+...
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What does $d^n\textbf{x}$ mean in this context?
I found the following on Wikipedia.
Integration over more general domains is possible. The integral of a function $f$, with respect to volume, over an $n$-dimensional region $D$ of $\mathbb{R}^{n}$ ...
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Correct notation to illustrate the product of a weighted path
I am struggling to represent a situation using the correct mathematical notation. I have a graph that consists of a series of nodes (1-4) and edges which represent movement pathways between nodes. The ...
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why is the notation for sums and integrals so different?
An integral over some set $A$ is typically written
$$\int_A f(x) \,\mathrm{d}x$$
whereas a sum over a set $A$ is written
$$
\sum_{i\in A} f(i).
$$
To me, these "feel" different. Why not ...
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Notation for adding elements to ordered set
Say I have an ordered set $E_1 = (e_1, e_2, ..., e_j)$ composed of some elements. I'd like to add a few more elements $E_2 = (e_k, e_{k+1}, ..., e_\ell)$ to this ordered set so as to obtain set $E_3 = ...
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What do you call it when, in the limit, two functions are proportional by a factor of 1?
Two functions $f(x)$ and $g(x)$ have the property that $$\lim_{x\to\infty}\frac{f(x)}{g(x)}=1$$. What is this referred to as commonly?
All I know of is Big-$\Theta$ notation, which says $$f(x)\in\...
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Notation $(S,*)$ or $(\mathbb S,*)$ for semigroup leading to group $(\mathbb G,*)$
In a number-theoretic context, is it best to use the notation $(S,*)$ or $(\mathbb S,*)$ for a generic semigroup leading to group $(\mathbb G,*)$ by taking equivalence classes under an equivalence ...
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The set $X$ can be seen as index set?
Let $X$ be a set, and the power set of $X$ be $\mathcal P(X).$
For $\mathcal B \subset \color{red}{\mathcal P(X)},$
does
\begin{align}
&\quad \ \left\{ U\subset X \mid \exists \Lambda : \mathrm{...
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Abbreviating lots of consecutive indexed summations
I have lots of equations of the following form
$$\sum_{r_0}\sum_{r_1}\sum_{r_2}\cdots\sum_{r_N} x_{r_0} x_{r_1} x_{r_2}\cdots x_{r_N} $$
I can use the following notation for the product of $x$s
$$x_{...
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The Derivative Operator vs $f'(x)$
For the sake of example, suppose $f(x) = \sin(x) $.
Then,
$$f'(x) = \frac{d}{dx}[f(x)] $$
But
$$f'(0) = 1 \neq \frac{d}{dx}[f(0)] = 0. $$
Why is this the case? Usually, when you have two equivalent ...
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What is the best way to write a function having many arguments?
I'd like to ask you guys what is the best way to write a function having a sequence of arguments?
If a function has $x$ and $y$ as its arguments then we write,
$$
f\left(x,y\right)
$$
What if we have ...
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Notation of there exists
I have the following matrix, which represents a state of a state machine:
$$
\mathbf{F} = \begin{pmatrix}
f_\mathrm{1} & f_\mathrm{2} & f_\mathrm{3}
\end{pmatrix}
$$
I now want to show in my ...
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Meaning of this symbol: "inverted product"
I am reading algebraic geometry from notes of a senior and I am struck on this terminalogy.
Question: In the definition of Closed subvarities of $\mathbb{P}^n$, the author write $\mathbb{P}^n= \...
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How do I denote a set where the order is important?
I am trying to formulate a special kind of the VRP with a vertex set $N=\{1,...,n\}$, but in this problem there exist a duplicate vertex for each $i \in N$ lets call this set $\tilde{N}$.
I want to ...
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1
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22
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How to denote the limit of a function with a vector input?
Suppose that I have a function $y(v)$ such that $v \in \mathbb{R}$ and $\lim_{v \to 0} y(v) = \infty$.
How would I use the limit notation if $v$ is instead a vector $V = (v_1,v_2,..,v_N)$. That is, ...
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What is the $T$ parameter of a linear interpolation (lerp) function formally called?
What is the $T$ parameter of a linear interpolation (lerp) function formally called?
I only ever see it called $T$. I know it's a ratio or percentage, but does it have a formal name?
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Name and notation of the sum of cardinalities of finite sets
Given a finite set $S = \{s_1, s_2, ..., s_n\}$, where each $s_i$ is a finite set of $|s_i|$ elements, let
$$
N = \sum_{s \in S}{|s|}
$$
Is there a canonical name and notation for $N$?
On a ...
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Mathematical notation on a matrix
Matrix notation question (in reference to "simultaneous interconnection and damping assignment passivity based control"):
We select an $n\times n$ matrix called $F_d(x)$. Let $G(x) := F_d(x)+...
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Notation: What is $C(G)$?
$G$ is the order $55$ group described by $G=\langle x,y \mid x^{11}=y^5=1, yxy^{-1}=x^4\rangle$. I am tasked with showing $|G/C(G)|=5$, but I don't know what $C(G)$ is supposed to be. It can't be the ...
0
votes
2
answers
46
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Standard notation for algorithm (instead of function)?
I am writing a math paper and defining various algorithms.
A function takes at least one input, and (may) output a result. The notation is
$$
\begin{align}
f :& \mathbb{R} \to \mathbb{R}\\
&(x)...
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Is Euler's identity really that beautiful or is it notationally contrived to be beautiful?
When I first saw the identity $e^{i\pi} + 1 = 0$, I was awestruck at how $5$ fundamental mathematical constants could combine so elegantly, finding invariance in all their numerical chaos. It was one ...
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notation for replacing values in one matrix with another with condition
I have two matrices of equal size. $'A'$ is a binary image, and '$B$' has values ranging between $0$ and $1$.
What's the correct notation which would demonstrate that foreground elements of A (equal ...
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1
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Is this expression correct ? $\sum x_i \xrightarrow{\Delta x_i\ \sim \ \ 0^+} \int x\ dx$
I like math and I always add some mathematical notations, and formulas to my profile picture, which might help the people who are in my contacts to know more about maths.
Today I created the following ...
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0
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Integrating w.r.t. to $\mathrm d\mu(x)$ vs $\mu(\mathrm dx)$
When integrating a function $f$ with respect to a measure $\mu$, I often see two different notations
$$ \int_A f(x) \mathrm d\mu(x) $$
and
$$ \int_A f(x) \mu(\mathrm dx) $$
How are these two different?...
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