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Questions tagged [notation]

Questions 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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5 votes
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How do I distinguish between "e" the natural log base and a variable conventionally referred to as "e"?

How does one distinguish between the natural base, usually indicated with "e" and a coefficient that, due to historical reasons, is referred to as "e" (such as in Weibull functions ...
Bryan's user avatar
  • 151
0 votes
0 answers
41 views

Writing/Typing Math in 2024 [closed]

When I was in math grad school three decades ago, everyone took notes, solved problems, and did research with pen and paper. For publication, 99% of work was prepared in LaTeX. (I'm more than a little ...
Elliotte Rusty Harold's user avatar
-1 votes
1 answer
53 views

Notation for double integral w.r.t. same variable [closed]

When taking the double integral of a function in terms of the same variable $x$, should I write $\int\int y~\text d^2x$ or $\int\int y~\text dx^2$, and why?
GPWR's user avatar
  • 212
2 votes
1 answer
36 views

Definition of mixture of two distributions

What is the formal definition of a mixture of distributions? Usually one says that we flip a coin, and then choose a distribution out of the two to follow. Is it formally correct, then, to say that a ...
xyz's user avatar
  • 1,022
0 votes
0 answers
14 views

Is there a name for non sparse linear operators which are products of convolution-like all-but-oneunities?

Is there a name for non sparse linear operators which are products of convolution-like all-but-one unities? I suppose I will have to apologize for the cryptic question phrasing, but I really could not ...
mathreadler's user avatar
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0 votes
1 answer
41 views

Differences in meaning for notations $\alpha_i$ versus $\alpha(i)$ and meaning of $\beta(ij)$ for denoting axioms in monomials

The following are partly taken from Malik and Sen's Fundamentals of Abstract Algebra Background First we note that we can reconstruct the monomial $x^\alpha=x_1^{\alpha_1}\cdots x_n^{\alpha_n}$ from $...
Seth's user avatar
  • 3,683
-2 votes
0 answers
21 views

How to read symbol and understand equivalent measure for a measurable space [closed]

referenceI am reading book on Stochastic Calculus by Gregory F Lawler and struggling with symbols. What does symbol mean and how to read ...
Ussu20's user avatar
  • 1
0 votes
0 answers
72 views

Notation for the set $\{[x, \infty) : x \in \mathbb{R}\}$?

Is there a special notation for the set $\{[x, \infty) : x \in \mathbb{R}\}$? This is, the set of all connected subsets of $\mathbb{R}$ that have a minimum element and no supremum. (Incidentally, this ...
lafinur's user avatar
  • 3,468
0 votes
0 answers
76 views

What symbol should I use for non linear proportional to?

Until now, if I had a function $f$ and a monotonic transformation of it $g$, I would write $f \propto g$, however, a colleague of mine pointed out that it's usually considered "proportional to&...
Alberto Sinigaglia's user avatar
0 votes
0 answers
46 views

Trouble understanding the proof of the theorem: If $f\in \mathfrak{a}$, then $m_i\in \mathfrak{a}$ for each $i$,

The following are from Froberg's Introduction to Grobner bases, Malik anad Sen's Fundamentals of Abstract Algebra Background Lemma: Let $I$ be a momomial ideal and $f\in K[x_1,\ldots,x_{n-1},x_n]$. ...
Seth's user avatar
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1 vote
1 answer
64 views

Tensor Notation with Basis in Differential Geometry

Let's say we have two smooth riemannian manifolds $\mathfrak{B}$ and $\mathfrak{S}$ and with coordinates $X^A$ on $\mathfrak{B}$ and $x^a$ on $\mathfrak{S}$, with $A,a \in \{1,2,3\}$ Let's now assume ...
Noiv's user avatar
  • 51
-4 votes
0 answers
195 views

∅ or Φ as the empty set? [closed]

I was just getting into set theory along with my friends and we noticed this confusion with notation of the empty set. Seeing that it is pronounced as "phi" we assumed to use the greek ...
Pranjal Kumar's user avatar
-6 votes
1 answer
97 views

Symbol for "sometimes equal to" [closed]

I am doing homework which could be reviewed by a mathematician. When evaluating the integrating factor for a differential equation, here is what I wrote: $$ I(x) = e^{\int\tan xdx} = e^{-\ln\lvert\cos ...
GPWR's user avatar
  • 212
1 vote
2 answers
129 views

What is the definition of a differential equation's general solution?

I'm not an English speaker. Sorry for my bad English. What is the definition of a differential equation's general solution? Definitions I've heard are "a solution containing arbitrary ...
hsk's user avatar
  • 13
-3 votes
2 answers
119 views

Is There a Notation for "Out of" That Does Not Connotate a Fraction? [closed]

This comes up in grading ... Is there a way to notate that someone got a fractional credit on each part, but that the "fractions" can't be operated on as fractions? I am looking for ...
BooBounder's user avatar
1 vote
0 answers
138 views

What is the difference between the notations $\beth_{\beth_{\beth_\ddots}}$ and $\beth_{\omega_{\omega_\ddots}}$ for the first beth fixed point?

Reading some papers on set theory I have found these two different notations used for the first beth fixed point. $\beth_{\beth_{\beth_\ddots}}$ $\beth_{\omega_{\omega_\ddots}}$ I don't think the ...
Hegel Gehel's user avatar
1 vote
1 answer
59 views

Notation for work integrals in non-stationary force fields

I'm writing about work integrals and would usually use an expression like the following: $$W = \int_C \vec{F} \cdot d\vec{s} = \int_0^T \vec{F}(p(t)) \cdot \vec{v}(t) dt$$ where $W$ is work, $\vec{F}$ ...
Count Dirac-ula's user avatar
1 vote
1 answer
41 views

Denote k-multi-subset

For a given set $A$, I would like to denote the set of k-multi-subsets, i.e., $B=[b_1, \ldots, b_n]$ satisfying $b_i\in A$ for all $i\in \{1,\ldots, n\}$, allowing $b_i=b_j$ for any $i,j\in \{1, \...
Robert O'Shea's user avatar
6 votes
3 answers
307 views

usage of Leibniz notation for things like $\frac{d^2y}{dt^2}$ and $\frac{dy'}{dy}$

I've read the other posts on this site about whether you can treat $\frac{dy}{dt}$ as a fraction. There are a lot of conflicting opinions, but many seem to be saying that treating it as a fraction ...
Ishaan Jain's user avatar
0 votes
0 answers
39 views

Question about notation in graph-theoretic context

the following is the first page of Chapter 6 in the book Probabilistic Combinatorics by Thomas Rothvoss. Can someone please help me understand what $n$ means when they say that $G$ and $H$ differ in $\...
Saksham Sethi's user avatar
1 vote
1 answer
39 views

What mathematical terminology and equations are used for variant assertions of finite sets?

Below there is a set of variants (or enumerations) of multiple finite sets with a different number of items in each set. I don't want to use the word combinations because I believe those are of the ...
JustBeingHelpful's user avatar
-5 votes
1 answer
101 views

Greek letter "Kappa" use in Set Theory

I have been given a definition that the Greek letter "K" is used when a cardinal and ordinal number of a set are the same. As I have NO knowledge of Set Theory, can someone explain this? I ...
John Bond's user avatar
2 votes
2 answers
73 views

Notation Dilemma in Formulas

Considering: 1. $$ w^{(k+1)} = w^{(k)} - \eta g_{w^{(k)}}$$ Given this, do I need to define $g_{w^{(k)}}$ with the index?: 2. $$ g_{w^{(k)}} = \frac{1}{m} \sum_{i=1}^m \nabla_{w^{(k)}} L(h(x_i, w^{(k)}...
slaky's user avatar
  • 21
0 votes
1 answer
90 views

Does there exist a widely-used operator $\boxdot$ such that $(\theta \boxdot \phi)(x) := \theta(x) \circ \phi(x)$?

Let $\forall X,Y : L(X,Y)$ symbolize the set of all linear operators from $X \rightarrow Y$. Let us have operator-valued functions $\theta : I \rightarrow L(Y,Z)$ and $\phi : I \rightarrow L(X,Y)$. It ...
Timothy Leong's user avatar
1 vote
3 answers
215 views

Can we *really* do algebraic operations involving roots on C?

With BSc in Maths and loads of grey hair, something has been on my mind for decades, and I couldn't quite enunciate it. Let me try. Root is inherently "multi-valued" operation. So $$ \sqrt{4}...
avloss's user avatar
  • 119
1 vote
1 answer
57 views

Short notation for $(u_1u_2\cdots u_n)' =u_1'u_2\cdots u_n + u_1u_2'\cdots u_n+\cdots+u_1u_2\cdots u_n'$

Looking for a Short hand notation for $(u_1u_2\cdots u_n)' =u_1'u_2\cdots u_n + u_1u_2'\cdots u_n+\cdots+u_1u_2\cdots u_n'$ Or some type of a rolling signifier notation that might already exists in ...
jimjim's user avatar
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9 votes
4 answers
907 views

Can the differential be unitless while the variable have an unit in integration?

Apologies for terminology inconsistencies, as I'm reading a Chinese statistics and probabilities textbook while looking up intrinsics on an English encyclopedia. This arose when I was reading the ...
DannyNiu's user avatar
  • 211
0 votes
1 answer
91 views

Must both conditions of operator "OR ($\vee$)" be defined in mathematics? [closed]

I am in the process of writing an article and to explain my question, am providing to you a smaller instance of my wondering so that you can understand it, suppose that $A=\{0,1\}$ and that I define ...
JKHA's user avatar
  • 131
1 vote
0 answers
48 views

Is there a rule for using parentheses or brackets after the summation symbol to indicate what is included in the sum? [duplicate]

Using parentheses or brackets removes ambiguity but is it necessary?
Alex's user avatar
  • 19
1 vote
2 answers
73 views

Exponentiation of a linear operator

I am trying to go through "Introduction to Functional Analysis" from MITOCW (MATH 18.102) by myself and I am confused by a question in the second problem set. Let $B$ be a Banach space. Let $...
Treely's user avatar
  • 13
1 vote
3 answers
201 views

Summation of arithmetic series [closed]

How to represent a sum of $n$ items of an arithmetic series with the use of the sigma notation? For the sum of the 10 first items, is the below one correct? $$ \color{gray}{ \sum_{\{{x_i: x_{i-1}+k \}}...
Damian Czapiewski's user avatar
1 vote
1 answer
94 views

Are there terminologies for "one-to-one" but not "onto" functions, and "onto" but not "one-to-one" functions?

One-to-one (injective) functions are not necessarily not onto (not surjective). Similarly, onto functions are not necessarily not one-to-one. So, a function can be one-to-one and onto (bijective). $f(...
Hussain-Alqatari's user avatar
0 votes
1 answer
27 views

meaning of $IBr(X | Q)$

In the paper 1, there is a notation used without specifying the meaning. It is $IBr(X | Q)$ in Definition $4.1$. What it means? Irreducible Brauer characters of the group X from a block with defect ...
scsnm's user avatar
  • 1,303
2 votes
1 answer
59 views

Question about notation in Durrett's book

I have been studying Markov Chains through Rick Durrett's book, more precisely I was focusing on the Markov Property (Theorem 5.2.3 on page 276 of the book available at: https://services.math.duke.edu/...
Monteiro_C's user avatar
2 votes
2 answers
91 views

If I have a sequence $a_0, a_1, a_2, \cdots$ , then is expressing the limit of this sequence as $a_\omega$ sensible?

If I have a sequence created by some rule which comes to a limit , then I can express it as $a_0, a_1,a_2,\cdots$. If I said $\lim_{n \to \infty} a_n = a_{\omega} $ , is that a sensible thing to do ? ...
Q the Platypus's user avatar
1 vote
0 answers
35 views

Further questions about correspondence theorem for rings and quotient ring isomorphism.

Background This is a continuation of a post about correspondence theorem for rings, I will repost what I have written here from the Background section of that post here for ease of reference: The ...
Seth's user avatar
  • 3,683
1 vote
1 answer
50 views

Notation question related to an exercise from Dummit & Foote in polynomial rings section

Background Exercise: Let $F[x,y_1,y_2,\ldots]$ be the polynomial ring in the infinite set of variables $x,y_1,y_2,\ldots$ over the field $F$, and let $I$ be the ideal $(x-{y_1}^2, y_1-{y_2}^2,\ldots,...
Seth's user avatar
  • 3,683
0 votes
0 answers
40 views

Notation of Expected value, when game with loss function and strategy as variable.

I have the case where I need to write the expected value of a score $\mathbb{E}[S]$ in a game where we can use different strategies $\sigma$ and also the loss function $f$ may change, which I write ...
Ziur Olpa's user avatar
  • 101
1 vote
0 answers
67 views

What's the equivalent to $\in$ notation for proper classes?

If I want to write that $n$ is a natural number, I'd write $n\in\mathbb{N}$. Likewise, if I want to state that something applies to all natural numbers or to at least one, I'd write the equation as $\...
SarcasticSully's user avatar
0 votes
0 answers
62 views

Question about notation: arg z

I am reading the "Handbook of Continued Fractions for Special Functions", and it has an odd notation that is not clearly explained. It will have, for example, a series expression with ...
Michael Lee Finney's user avatar
-1 votes
2 answers
185 views

What does "the set of all $x$'s" mean?

In the context of set theory, I see on websites that set builder notation like $$\{x \mid P(x)\}$$ is read in natural language as "the set of all $x$'s that satisfy the predicate $P(x)$". ...
John greg's user avatar
2 votes
1 answer
51 views

How to define a set without using itself in its definition?

I am trying to construct a set using set builder notation but I am not succeeding. Let $X$ and $Y$ be arbitrary finite sets, and let $Z\subsetneq Y$ be non-empty. Then, let $F=Y^X$ be the set of all ...
EoDmnFOr3q's user avatar
  • 1,226
2 votes
1 answer
68 views

How to write an inequality? [duplicate]

I have a very simple doubt regarding the writing of inequalities. Consider any arbitrary finite set $X$ and three functions $f,g,h:X\to\mathbb{R}$. Fix any element $x\in X$ and suppose the following ...
EoDmnFOr3q's user avatar
  • 1,226
2 votes
1 answer
151 views

Why don't we write complex numbers as $a i^{b}$?

Given that $a i^b$ = $ae^{\frac{\pi}{2}bi}$, why do we not prefer to write complex numbers in the form $a i^{b}$ instead of the usual polar form? Intuitively, fractional powers are a much simpler ...
jamie's user avatar
  • 31
0 votes
0 answers
10 views

Notation for empirical measure (Dirac measure)

I am writing a paper in an area that I am relatively unfamiliar with, and I am after suggestions concerning notation. Here the notion of empirical measure is introduced in the paper In the notation, ...
Daniele Avitabile's user avatar
0 votes
1 answer
43 views

How to state that a function has a certain trend in a limit

Assuming we have a function $f(r)$ that has the following limit $$ \lim_{r\to0} f(r) = \frac{5}{3 r^2} \,.$$ What is the correct symbol to express that the denominator goes like $r^2$? Is the ...
Aleph12345's user avatar
2 votes
1 answer
101 views

e{ } and e( ) Notation

I was reading An Introduction to the Theory of Numbers by Hardy and Wright, and on pages 66 and 67, I encountered the notation, as following What does the $e( )$ and $e\{\}$ notation mean? Any help ...
BakedPotato66's user avatar
2 votes
0 answers
25 views

What is the simplest symbolic expression for "for some choice of disjoint pairings of $i$, $j$, $k$, $n$, each variable equals its partner"?

I'm not sure if this is appropriate here since the question is about aesthetics and efficiency more than it's about mathematics, but here it is anyway. It's been surprisingly hard to find a short, ...
bjshnog's user avatar
  • 378
0 votes
1 answer
57 views

notation for double limits

I need to consider a double infinite limit for a function $f(v,w)$ where both $v, w$ go to infinity. Is the correct notation? The main point I want to emphasize is that there is no ordering, e.g. I ...
mathflow's user avatar
  • 175
1 vote
0 answers
27 views

Conventional notation for gcd and principal ideal in the context of Bezout domain [duplicate]

Background Definition 1: Let $R$ be a commutative ring with identity, $c\in R$ and let $I$ be the set of all multiples of $c$ in $R$, that is, $I=\{rc\mid r\in R\}$. Set $I$ is an ideal and is ...
Seth's user avatar
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