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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Conventional notation for congruence to multiple numbers

Is there a more concise notation for the following sentence? "Thus $ f(n) \equiv 0 \pmod{12} $ for all $ n \equiv x \pmod{12} $ where $ x \in \{ 0, 1, 3, 6, 7, 11\} $." Is this an acceptable ...
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As $a \in\left\{ 1,2,3 \right\}~~$ is held, can I write $f(a=1)=k~~$ rather than $\text{As}~a=1, f(a)=f(1)=k~~$?

$$ x \in\left\{1,2,3\right\} $$ $$ f(x):=\text{function which returns certain value depending on argument }x $$ Assume the below statements . $$ \text{As }x=1 ~,~ $$ $$ f(x)=f(1)=k $$ Can I write ...
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What is the notation $u \xleftarrow{\text{R}} \mathbb{Z}_n^{\ast}$ mean?

I am reading a cryptography paper titled "Dealing Cards in Poker Games" by P. Golle. In the section titled "key generation", the author says "choose $u \xleftarrow{\text{R}} \...
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Are notations intened to look nice? [closed]

I was just wondering: when mathematicians come up with new concepts that requieres new notations, do they only look at how practical it is, or does asthetic also play a role? For example, I have seen ...
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Notation for set containing combinations of sets given by multinomial coefficient number of options.

Assume there are sets $A_1,A_2,\dots,A_n$. Let $m\leq n$ and now partition $\{1,\dots,n\}$ into $m$ subsets $N_1,\dots,N_m$. So, there are basically $$\sum_{l_1+\dots+l_m = n} {{n}\choose{l_1,\dots,...
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Does the notation “$a,b\neq 0$” mean that $a$ and $b$ must both be non-zero?

Consider the statement: $$a^2+b^2+2ab=0, \text{where}\; a,b\neq 0$$ What does "$a,b\neq0$" mean? Is it necessary that both $a\neq 0$ and $b\neq0$ simultaneously? Can one of them be $0$ and ...
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29 views

Notation for multiplying each element of n-tuple with scalar

I've got an n-tuple $T$ of the following form: $T \subseteq \mathbb{R}_{++}^n$. I'd like to multiply each element of this tuple with a constant $k=5$ (or any other real number). Is there a neat (short)...
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1answer
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Question about notation for defining homotopies

I'm looking at this part of a statement regarding homotopic paths: Given homotopies $$h: f \simeq f' : X \rightarrow Y, k: g \simeq g' : Y \rightarrow Z$$ Now here I'm a bit confused of whether $h$ ...
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Help understanding notation in matrix transformation

In my notes it's written that, for two basis $B={e_i}$ and $B'=e'_i$, the transformation rule is: $e'_j = c^i{}_j e_i$ This I can understand, every vector of the $B'$ basis is a linear combination of ...
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When to suppress parameter in function notation

For example, a differential equation of the form $$\frac{dy}{dx}+P(x)y=f(x),$$ has the general solution $$y=\mu^{-1}\int\mu f(x)\,dx +C\mu^{-1},$$ where $\mu$ is the integrating factor $\mu(x)=\exp{(\...
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When was the first recorded use of subscript in mathematics to represent index? [migrated]

(Disclaimer: apologies for any incorrect usage of mathematical terminology throughout this question.) In modern mathematical notation, a variable with a subscript can represent a couple of different ...
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Some help understanding probability notation

Can someone write the below expression out to me in plain English? I don't have a stats background and so am not sure how to interpret the notation. Any links to this notation would also be welcome, ...
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Preferred Way to Write Domain

Suppose a complex function is defined everywhere on the complex plane except for at 0 and the negative integers. Is this the preferred way to write the domain? $$\mathbb{C}\setminus\mathbb{Z}_{\le0}$$ ...
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1answer
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The meaning of arrow in an optimization problem

I would like to know the interpretation of the following notations in the context of an optimisation problem. I want to minimize $f_0(\vec{x})$, where the vector $\vec{x}=(x_1,x_2,\cdots,x_n)$ is the ...
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Integer (Euclidean) Division Notation in maths

I'm looking for a formal "operational" expression / definition in maths for the division between integers (https://en.wikipedia.org/wiki/Euclidean_division) but I cannot find it. Is this ...
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Confused with infinity notation in limits

I'm taking a course on real analysis and I wondered if $\lim_{x \to \infty} f(x)$ is the same as $\lim_{x \to +\infty} f(x)$ but why would one use +∞ notation then.. or does $\lim_{x \to \infty} f(...
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How to read variables having superscript? Also how to read those with both super- and subscript?

To read $x_i$, we say "$x$ sub $i$". How do we read $x^i$ where $i$ is not a exponent number and is just a superscript for the variable $x$? How do we read a variable when having both super- ...
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How is “X with tilde on top” pronounced when spoken?

How is $\tilde{X}$ pronounced when a paper is being read out loud? Sorry if this is a duplicate but couldn't figure out how to search for it. TIA
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1answer
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Multiset/Set/List initiation and use in pseudocode

I'm writing a paper and I've come across interesting problem. In my algorithm, I create a list of 0's (example [0,0,0,0]), where the number of 0's is given by parameter "x". Later I want to ...
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How to write out the mathematical expression for maximizing a set of function outputs

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and let $a, b \in \mathbb{R}$. If one is interested in finding the larger of $f(a)$ and $f(b)$, one could write $$max \{f(a), f(b)\}$$ Now suppose $g: \...
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What does $\bigoplus$ mean when applied to two sets? [closed]

What does $\bigoplus$ mean when applied to two sets? For example if $A=\{a,b,c\}$ and $B=\{1,2,3\}$, then what is $A\bigoplus B$?
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Set notations? set B has all elements of set A except element j

How can I write the following sentence in proper mathematical notation? I have 2 sets: $A$ and $B$, and I want to say that $B$ has all elements of $A$ except for one or more specific elements. $B$ is ...
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How does the variable placement in $\sum$ work? [closed]

I was doing some Brainly and decided to go for a Math question for solving a standard derivation of a set of numbers and I encountered the symbol $\sum$, thanks to this equation: $$\sigma = \sqrt{\...
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1answer
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Hungerford Page 153 Corollary 5.6

I don't understand what this theorem is saying: $\textbf{Corollary 5.6}$ If $\phi:R\to S$ is a homomorphism of commutative rings and $s_1,...,s_n\in S$, then the map $R[x_1,...,x_n]\to S$ given by $f\...
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1answer
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Notation for pdf of normal distribution [closed]

Suppose I want to notate "the density of normal probability distribution with mean $\mu$ and standard deviation $\sigma$ computed for value $x$", is there a commonly accepted way to notate ...
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1answer
88 views

What is this stylish R-like symbol?

What is that stylish R-like symbol at the end of the statement? I combed the lists of linear algebra symbols from almost every source online. Some guesses were Row space (which might make sense, just ...
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1answer
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What is meant by binding strength of binary operators?

Dr Frederic P. Scheuller writes at 33:55 of this video the decreasing order of binding strength in the sequence: $$\neg, \wedge , \lor , \implies, \iff$$ But what does it mean for binary operators to ...
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Can ℜ be used instead of ℝ to represent a real coordinate space? If not, what alternatives are commonly used?

When going through logistic regression I was writing some documentation using classic troff and eqn UNIX tools. In logistic ...
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Question about notations

I am confused. Please, could you help me with this notation $$\exists x_{\delta, \varepsilon}$$ And if possible with some example.
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Making a sequence non-recursive

I have a sequence that produces outputs: 1, 4, 13, 40, 121... I know that for the nth term, the output would be $3^0 + 3^1 + \ldots + 3^n$ But I don't know how to write this without it being recursive....
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Correct notation for the CDF of a uniform distribution

I have a random variable, $x$, distributed uniformly on $[0,\frac{4}{3}]$. The probability that $x$ is greater than some $a\in \mathbb{R}$ is, of course, given by $(1-0.75(a))$. I want the value of ...
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Notation to distinguish “indifference” and “drawn from”

I am writing a paper in which I need to denote indifference (with respect to some preference ordering) as well as sampling from a distribution. Unfortunately, both are typically represented using the $...
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Notating infinite sums with different increments

I have a function that when I plug it into wolframalpha, gives me an answer. When I try to make it only the even numbers, however, it doesn't read the equation. $$\sum_{n=6}^\infty \frac{(3^{n-5}+3^{...
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2answers
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Prime Notation in Transpositions

My textbook has the following problem: Consider the group $S_n.$ Prove that if $\sigma$ and $\tau$ are any pair of distinct transpositions such that $\tau(1)\neq1$ then there exists $\sigma'$,$\tau'$ ...
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Is $2^{o(k)} = 2^{o(3k)}$?

I am having a little trouble understanding little-o notation when it appears in the exponent. I understand the $2^{3k} \notin 2^{o(k)}$ since $2^{o(k)}$ is not an upper bound for $2^{3k}$. But how can ...
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What is the correct notation to find the logarithm of the market capitalization? [closed]

Good morning everybody. I would like to write on Word the perfect mathematical notation to find the logarithm of the market capitalization. |Photo of the notation I made|. I don't know what to write ...
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Is there a symbol for 'that satisfies'? eg, $\{s\mid s\in\mathbb{N} \;\text{'that satisfies'}\; P_k\}$

Is there a symbol for 'that satisfies'? For instance, a symbol to use in the following line: Since $k=\min\{s\mid s\in\mathbb{N}\;\text{'that satisfies'}\;P_k\}$ Thank you!
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1answer
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Using existential statements in informal mathematical reasoning

In symbolic logic, existence statements are normally written as $\exists x P$ where $P$ is some smaller statement. The $x$ is bound by the existential quantifier and the scope of $x$ is $P$. When ...
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1answer
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Difference of kernels, (basis of a Jordan Block )

Basis of a Jordan block Reference Given an endomorphism $f$, the basis of a Jordan block of order $n$ has the form $$B=\{v_1,(f-\lambda Id)(v_1),\ldots,(f-λId)^{n-1}(v_1)\}$$ Where $v_1$ belongs to $(...
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Strange functional notation in a paper: $y_h(A^2(x_1,x_2,x_3,x_4))$

I am reading a paper on using surrogate models to approximate multi-fidelity simulation optimisation problems and I can't quite understand what is meant by this notation they are using to construct ...
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1answer
63 views

Comparing approaches to managing free and bound variables.

Corrections: I originally said $\varphi(x, w_1 \cdots w_n, a)$ was a closed well-formed formula. It is not. I meant to say that within $\varphi$ the only free variables come from $x, w_1 \cdots w_n, a$...
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Is $\mathbb{R}^1$ really the same as $\mathbb{R}$?

We write $\mathbb{R}^n$ to be the set $\{(x_1,\dots,x_n): x_i \in \mathbb{R} \mbox{ for } i=1,\dots,n\}$, so $\mathbb{R}^n$ is the set of $n$-tuples of real numbers. Is then $\mathbb{R}^1$ a set of 1-...
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Is $G=\langle r, f\,:\, r^3=e , f^3=e, fr=r^2f\rangle$ well known?

In trying to construct a non-commutative group with exactly $1$ nilpotent of degree $2$, I ended up constructing one with the following presentation: $$G=\langle r, f\,:\, r^3=e , f^3=e, fr=r^2f\...
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What does it mean (given that $M$ is an R-module), that $M=0$? That it is a module generated by the zero of ring $R$?

I've seen this kind of notation in the context of Nakayama's Lemma, but I don't get it if this means that M is a module generated by R's zero, or if this means that M is simply the empty set?
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1answer
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Confusion regarding notation in Alfsen's proof of Haar's existence theorem.

I am working through Alfen's proof that there exists a unique Haar measure on any locally compact group. There are a few propositions which have an unexplained notation which I am not familiar with - ...
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1answer
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Arrow down notation with sets

I am reading Probability for Statistics and Machine Learning. I have trouble understanding the arrow notation (similar to Knuth's arrow notation) in the following definition: Theorem 1.1. Let $A_1 \...
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What is $(\cal I,I$ $X)$?

I read Algebras, Rings and Modules by Hazewinkel and I don't understand what is $(\cal I,I$$X)$. Could you please tell me the meaning of this denotation?
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1answer
28 views

How can I represent simple percentage calculation in mathematical notation?

I want to show my calculation/logic using mathematical notation but have no experience of this other than seeing them in research papers I have read. In my example I have three values 90, 11, 57 and I ...
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Show that $\int _0^x\left[\int _0^tf\left(u\right)du\:\right]dt\:=\:\int _0^x\:\:f\left(u\right)\left(x-u\right)du$ Notation confusion [duplicate]

Show that $\int _0^x\left[\int _0^tf\left(u\right)du\:\right]dt\:=\:\int _0^x\:\:f\left(u\right)\left(x-u\right)du$ EDIT: (USING integration by parts) Okay I think I have few ideas how to do this. I ...
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1answer
33 views

Set notation for conditional probabilities

Consider this definition for the probability that a given document $d$ contains a term $t$ as the relative document frequency: $$P(t|D)={\frac {|\{d\in D:t\in d\}|}{N}}$$ What does $:$ mean in the ...

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