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.

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Ravi Vakil's notation $\operatorname{Proj}_A S$

I saw the notation $\operatorname{Proj}_A S$ for a ring $A$ and a graded $\mathbb{Z}^{\geq 0}$-graded ring $S$ being used in Ravi Vakil's notes on Algebraic Geometry. I first came across the notation ...
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Understanding the notation $\pi(y) \text{d}y = \int \dots$

In Understanding the Metropolis-Hastings Algorithm (Chib and Greenberg, 1995), the authors write the following (their eq. $1$): The invariant distribution satisfies $$ \pi^{*}(\text{d}y) = \int_{\...
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Notation: $\mathbb{P}(N(t) = n)$ unconditional on $t$

This is a question about notation. I find good notation always helps with thinking clearly. Consider a Poisson process with rate $\lambda$, and let $N(t)$ be the number of occurrences at time $t \geq ...
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How do you explicitly state domain and range subject to relational constraints?

I'm aware of interval notation and longer-hand set-builder notation, but I'm wondering how to use the latter fully to explicitly state e.g. a domain of a function per the constraints of interest, ...
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Doubt about index notations

I think the question can be written in a concise way: Why do Rotation are represented using two upper/lower index ($R_{ij}$), while, for example, Lorentz Transformation involve index up and index down ...
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28 views

Notation for the product of corresponding elements of two matrices

I'm not sure how to describe the multiplication of off-diagonal elements of a (co)variance matrix (covariances) with corresponding elements of it's correlation matrix, in a succinct way. In full, I ...
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Skew-Symmetric cross product notations

I am working on a function to find the rotation matrix to transform one vector to another, and the Wikipedia article has a notation that differs from a StackOverflow post that has come up in my search....
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Mathematical notation for Cartesian Product with conditions

I know this should be pretty easy, but I'm trying to add conditions to a cartesian product. If we have the sets L and S, where $$L = L_1, L_2 .... L_n$$ and $$S = S_1, S_2 .... S_m$$ with each element ...
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Name of a vector of 1s?

Let's consider an N dimensional vector where each coordinate takes the value 1. For example, for $N=5$ we have: $(1,1,1,1,1)$. Does this type of vector have a name (unary?). Are there any conventions ...
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How to precisely convey (in math sentences) one or more symmetries (wrt polar axis, θ=π, orand the pole)? Be there way conclusively to determine non?

The online math textbook accompanying the Precalculus course I'm taking provides methods in the form of basic substitution tests to guarantee whether each symmetry necessarily holds and posits that if ...
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Notation: What does $\mathop{Pr}_{x \sim y}[A]$ mean?

In the equation $$\epsilon_{t} = \mathop{Pr}_{x_{i} \sim P_{t}}[h_{t}(x_{i}) \neq y_{i}]$$ What does the tilde mean? I know from this answer what it means when you're doing expectation, but I'm not ...
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What does this notation mean: $\|\cdot \|_F$

For context, this paper defines the following equation as the accuracy metric for their function: $$ Acc(\hat{Y}) = 1-\frac{\|Y-\hat{Y}\|_F}{\|Y\|_F} $$ I assume it's probably just a weird notation ...
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Is it correct to say that an integer is congruent with a p-adic number $\text{mod }p^k$?

Is there a standard way to describe a class of $p$-adic numbers that share the same final digits? E.g., if $x$ is a $p$-adic number and the last four digits of its $p$-adic representation are $\ldots ...
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Best notation for partial derivatives

I know this one is a soft question so I will tag it as such, but I'm aware of the following ways in which derivatives are represented: lets say we have a function: $$f=f(x,y)$$ then the derivative wrt ...
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Are there rules for omitted bracket use?

In older work I often came across a somewhat inconsistent use of brackets. Specifically, I am readings the following paper: Self-inductance of air-core circular coils with rectangular cross section (...
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Notation for “S partitions into S1, S2”

Is there an established notation for "$S = S_1 \cup S_2 \cup \ldots$; where $S_i$ are pairwise disjoint"? In other words, $S$ partitions into the subsets $S_i$. I have seen a shorthand for &...
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Notation complete polynomial of order two

I don't know what notation to use for a complete second order polynomial in two variables. Let's say I use the monomial basis functions: $$ f(x)=a_1 + a_2 x_1 + a_3 x_2 + a_4 x_1^2 + a_5x_1x_2 + ...
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How is $A_3^3$ evaluated?

I stumbled upon the expression below, but I don't know how it is evaluated. Any help will be appreciated. $A_3^3 = 6$ Edited 1: It is a random expression that happen to be on a clock face which I hope ...
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Notation to represent constants as variables and solve for them in a function

I have a classic probability density function in the literature of the form $$ f(x) = \frac{4x}{\left(a^2b^2\right)} \Sigma(x, a, b) $$ where $\Sigma(x, a, b)$ is a complicated function full of ...
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What does $\sum_i\sum_j$ mean? eg, $\sum_i\sum_j\frac{\rho_1^i}{i!}\frac{\rho_2^j}{j!}$

I have a basic question, and I haven't found a confirmation if this is correct: If we have the notation $\sum_n n$, means the same as $\sum_{i=1}^{n} i$ so $i$ runs from its minimum value until its ...
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Is it proper integral notation to use “x=” in the bounds of a definite integral?

So, several years ago I skimmed through a calculus textbook and some of it stuck, some of it didn't. Now several years later I'm finishing up my second Calculus class at university, and I'm a little ...
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Big-Omega, how do I prove or contradict?

How do I prove or contradict the following: $$\alpha\cdot n^k-b\cdot n^{k-1}=\Omega(n^k)$$ where $a,b>0$ and $k\ge1$
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What is notation “$1_{\text{something}}$”? eg, $E(1_{\{X\leq t\leq X+Y\}}) $

In this mathStackExchange here, use notation $E(1_{\{X\leq t\leq X+Y\}}) $. What is this notation?
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Best notation for $\mathbb{Z}_m^n$ [closed]

This is an easy question. Which notation do you think is better for the set: $A:=\left\{x=[x_1,\dots,x_n]: x_i\in \mathbb{Z}_m\right\}$, where $\mathbb{Z}_m=\left\{i:0\leq i < m \right\}$. I've ...
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Distance Formula in Regression Context / Support Vector Machines

I am studying data science via "introduction to statistical learning in R". In chapter 9, we are learning about support vector machines and the maximal margin classifier. I generally ...
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How do I prove that $f(n)=o(g(n))$ if and only if $g(n)=\omega(f(n))$

I don't know how can I prove this: prove that $f(n)=o(g(n))$ if and only if $g(n)=\omega(f(n))$
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Double bars around poset?

Given a poset X that is contractible, I have a document that says: "If $H : \|X\| \times I \rightarrow \|X\|$ is a homotopy to the constant map" What does the $\|-\|$ signify? I have no idea ...
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Different vector notations

I've encountered at least the following vector notations: $ \overline{a}, \ \underline{a}, \ \vec{a},  $ and a. Are they alternative notations for the same thing, or is $\vec{a}$ only for physical ...
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Integral with set in the differential

I encountered several integrals by now that integrate over a "set of differentials" or is with respect to a set respectively, like the (physicist) partition function of a polymer with ...
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32 views

Summation with index $1\leq i<j\leq n$

What does the following index notation mean? $$ \sum_{1\leq i<j\leq n}\frac{1}{a_i+a_j} \tag 1 $$ Is it a short for: $$ \sum_{i=1}^j \Bigg ( \sum_{j=1}^n \frac{1}{a_i+a_j} \Bigg ) \qquad ? \tag 2 $...
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Generalized way to find mathematical symbols?

I have this problem frequently in math. Someone will decide to use some new symbol and you want to add it to your notes but without the name this has proven difficult. In my case, I'm currently ...
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2answers
43 views

What is the correct order of operations for expression $\sin\frac{\pi}{2} n$

What is the correct order of operations for $\sin\frac{\pi}{2} n$? Two options that come to mind are $\sin(\frac{\pi}{2} n)$ and $\sin(\frac{\pi}{2}) \cdot n$. Are there any rules for this and what ...
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$\displaystyle\lim_{x\to a} f(x)=\displaystyle\lim_{h\to 0}f(a+h)$ versus $\displaystyle\lim_{x\to a} f(x)=\displaystyle\lim_{x\to 0}f(a+x)$

Just had a quick question about the variable naming observed in the following statement: $\displaystyle\lim_{x\to a} f(x)=\displaystyle\lim_{h\to 0}f(a+h)$ Is the above statement equivalent to: $\...
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29 views

What does $\sum_{i/k_i = k}$ mean in the equation below?

I was reading chapter 5 of Dynamical Processes on Complex Networks, which discusses the Ising model, where I encountered the following equation for the average magnetization of the class of nodes with ...
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My professor used an arrow going to into an angle bracket to represent infinity in interval notation, and I've never seen it before, and got confused [closed]

the problem had a map on the interval [0,→〉and he described it meaning infinity, but I've never seen the notation before, and I was having trouble looking it up. any explanation of the notation would ...
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57 views

Why are the symbols $\cdot$ and $+$ used for the operations of Boolean algebra?

The symbols $\cdot$ and $+$ are often used to denote Boolean product and sum, but they make some of the system's properties, like distributivity over $\cdot$, counter-intuitive: $$a+(b\cdot{c})=(a+b)\...
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Typesetting a covector

I understand the notation of upper and lower indices for components of vectors and covectors, but when I write a vector not in component form I use an over-arrow notation e.g. $\vec r$. Is there a ...
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1answer
46 views

Is the $=$ in the preorder $\geq$ identity or equivalence in the preorder?

Question Is the $=$ in the preorder $\geq$ identity or equivalence in the preorder? Background By way of example, let $\geq$ be the preorder on the cyclic set $\Bbb Z/3\Bbb Z$ having the chain $0,1,2,...
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Proof of Big O of a Function [closed]

I am currently studying for my final data structures and algorithms exam. I encountered a big $\mathcal O$ notation question while solving a past exam and I realized I didn't remember anything about ...
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How to use maths symbols here [closed]

I still can't ask important questions that have been bugging me for a while since I can't write the integral sign or summation and the rest, how do you guys do it?
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How to notate the following three-dimensional matrix multiplication correctly?

I need to (multiply the first IxJxK(1) by 0.3) + multiply the second IxJxK(2) by 0.59 + multiply the third IxJxK(3) by 0.11. How can I notate this correctly?
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What do the different integral symbols mean, and how do they effect the calculation? [duplicate]

I see a lot of variations on the integral symbol, but I haven't quite grasped their effects on the computation of integrals. I'm sure there are many more variations, but these are a few of the symbols ...
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32 views

Is there a native notation for base 60/sexagesimal numbers?

I have been reading about the Babylonian-derived sexagesimal or base-60 number system. Is there a standard notation for base-60 numbers that is analogous to that used by binary (0-1), octal (0-7) and ...
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What is the difference between $\longmapsto$ and $\mapsto$? (I am aware of \to and $\mapsto$, but $\longmapsto$ is new to me)

Is $\longmapsto$ just another notation for $\to$ ? (I am aware of $\to$ and $\mapsto$, but $\longmapsto$ is new to me)
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When should the first letter of an abbreviated function be capitalised?

Many functions in mathematics are denoted using abbreviated names. However, the capitalisation of these function names seems to be inconsistent to me: functions like $\sin$, $\cos$ and $\exp$ are all ...
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How to formulate a complex process as a function for optimization

I originally posted just the notation question without context, because the background is extensive and I didn't know if it was suitable for this forum. I am now adding the context, as requested. I ...
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2answers
36 views

Mathematical notation of a cell based product between a vector and a matrix

What is the mathematical notation of an operation that multiplies a vector, $v$, with a matrix, $X$, as in the following example: $$ v = \begin{bmatrix} v_{1} \\ v_{2} \\ v_{3} \\ v_{4} \\ v_{5} \...
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How to define data within a 1D matrix as categorical [migrated]

Is there any way to clearly delineate that the data contained within a matrix is categorical to the reader? Ie: is there a symbol that I can use to mark the data as qualitative and not quantitative.
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Notation $\sum_{k \neq k'}$: is the order important?

I am reading The Elements of Statistical Learning. At pag. 309 the Gini index is defined as: $$ \text{Gini} = \sum_{k \neq k'} \hat{p}_{mk} \hat{p}_{mk'} $$ where the index $k = {1,2,\dots,K}$. In ...
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Are there any standards we can use to communicate math, e.g. ISO standards, does Category Theory aim eventually to be something like this?

I'm finding it difficult to read and express ideas in a standard way, I'm working in Computer Science and there are so many different math languages ways of communicating ideas. Is there a standard ...

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