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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35 views

Notation in sums

What do those sum notations exactly mean? Are my interpretations correct? (Do they need more context to make sense?) $$\sum_{\left<i,j\right>}^{i=3} ij \stackrel?= 1\cdot 2 + 2 \cdot 3 + 3 ...
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1answer
25 views

What is the terminology for assigning $K_{m_i}$ (complete graph) to the $i$ th vertex, 'joining' if the corresponding vertices are adjacent?

Given a connected graph $G$ with $n$ vertices and given set of $\{m_1,m_2,...,m_n\}$ $n$ integers, we form a new graph $G^$ by considering the complete graph $K_{m_i}$ for each vertex i and 'join' ...
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2answers
23 views

Sequence of points that is dense in a compact set.

I am reading a proof of Tietze extension theorem from a book Deimling - Nonlinear functional analysis, page 6. What is the plain meaning of following sentence: "Since $A \subset \mathbb{R}^n$ is ...
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1answer
26 views

Predicates about functions in 1st order logic

Given the usual definition of function as a subset of $ D \times C $. What is the correct way to write "All functions $ f $ from $ D $ to $ C $ have property $P(f)$". This is both a question about ...
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0answers
23 views

What do graph formulas within curly parentheses mean?

What do functions enlisted within curly brackets mean and how can I combine them and put them in a calculator and graph it? Thanks
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2answers
29 views

What is the correct notation for every nth term in a sequence?

How do I denote every nth term in a sequence? For example, if sequence $C$ contains: $C = \{ 2, 5, 3, 6, 4, 5, ...\}$ And sequence $Q$ contains every 4th term in C: $Q = \{C_{4}, C_{8}, ...
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0answers
35 views

Standard name or notation for the “even part” of an integer?

\begin{align} 0 & \mapsto 0 \\ 1 & \mapsto 0 \\[6pt] 2 & \mapsto 2 \\ 3 & \mapsto 2 \\[6pt] 4 & \mapsto 4 \\ 5 & \mapsto 4 \\[6pt] 6 & \mapsto 6 \\ 7 & \mapsto 6 \\ ...
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1answer
14 views

Is it possible to write the Hadamard product of two matrices in tensor notation?

Say I have two $4 \times 4$ matrices $(A^{\alpha \beta})$ and $(B^{\mu\nu})$ and want to compute the Hadamard (entry-wise) product. Is there an elegant way of writing this down in the common ...
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1answer
26 views

Einstein's summation convention and double indices

So I'm actually rather familiar with Einstein' summation notation and I understand objects like $a^{\mu \nu} a_{\mu \nu}$ just fine. But now I'm suddenly wondering why I've never come across objects ...
0
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0answers
48 views

Is there no difference in symbols between the floor and the ceiling of x?

Source: Discrete Mathematics with Applications, Susanna S. Epp The symbol of floor of x is [x] and so is the symbol [x] of ceiling of x. Is it correct that there's no difference in symbols between ...
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1answer
36 views

Completing the square (and variants thereof)

When dealing with quadratics, completing the square is ubiquitous, and I can summarise my interpretation of it as the formula: $$x^2-2ax=(x-a)^2-a^2$$ Likewise, when working with circles (and, more ...
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1answer
25 views

What is the best notation for this problem?

Assume you have defined variables $A$, $B$ and $C$ in the text. There is also a defined function $f$ that applies on those variables. In addition you may have some variables such as $\kappa_A$, ...
3
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2answers
30 views

What is the meaning of the notation [A|B] in Linear Algebra.

I am going through Linear Algebra right now, we are using the book Elementary Linear Algebra by Andrilli. In one of the theorems he uses this notation without really introducing it. Here is the ...
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1answer
18 views

Standard notation for class of lipschitz continuous functions?

What is the widely used notation to denote the class of Lipschitz continuous functions? i.e. suppose $f$ is continuously differentiable, then $f \in C^1$
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5answers
191 views

Why are the symbols of operations written on the left or right of the objects to which they apply? [on hold]

I was wondering why operations, actions and other stuff in mathematics are always defined "on the right" or "on the left". Is that a reflex of our (western) way of writing? For example, japanese is ...
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1answer
33 views

Meaning of $\partial f /\partial x$

I have an exercise in complex analysis that begins, If $U\subset \mathbb C$ is an open set and $f:U\to \mathbb C$ is real differentiable.... Later on, it allows me to assume $f$ is holomorphic. ...
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1answer
24 views

Convert hexadecimal to binary scientific notation using IEEE 754 single-precision floating point

I am trying to convert these numbers to binary scientific notation, but I cannot figure out the process. Could someone please the process of going about solving this? For IEEE 754 single precision ...
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0answers
69 views

Einstein notation

I'm confused about a specific issue that I have with the Einstein notation (for tensor fields on manifolds). I want to write the following thing: Let $X$ be a smooth manifold. Choosing local ...
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2answers
20 views

A little question about notation: set operators or logic operators

The question arise from the definition of conditional probability, that is defined as $$\Pr[A\cap B]=\Pr[A|B]\cdot\Pr[B]$$ Alternatively, in the context of cummulative joint probability ...
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2answers
53 views

mathematical symbol for a new member replacing a member in a set

Assume $b$ is going to replace member $a$ in set $S$. That is, the set S is initially like this $S=\{a\}$, but now the new member $b$ is going to replace $b$ to have $S=\{b\}$ at the end. How do you ...
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1answer
48 views

Are there any proposals for special parentheses for function arguments?

A few times, I wanted to highlight that a variable in the right-hand side of an equation depended on other variable. I can't recall a good example right now, but consider this one: $\tau = F ...
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1answer
43 views

What does $x_{1:n}$ notation mean? [closed]

Notation in my book, Introduction to Probability and Mathematical Statistics by Bain and Engelhardt, is $x_{1:n}$. Can anybody tell me what this denotes?
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0answers
24 views

When do we write a superscript before a smbol?

In what contexts is it conventional to write $ ^a B$, and in those contexts what does it mean? I remembering seeing this but I can't remember where. I believe we would expect $a$ to be a function ...
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0answers
46 views

Is there no (basic) math webfont? [closed]

This is a typographical question that is too esoteric from the viewpoint of graphicdesign.stackexchange --- but a rather natural occurrence for daily users of math, so I think this is the place to put ...
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0answers
27 views

Integral in vector form

I have two vectors $x_{1}$ and $x_{2}$ and some function $f(x, k)$. So for example function $f$ can be evaluated at some point say $f(x_{1}, 10)$. Then I have an integral written ...
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1answer
65 views

Does every diagonal intersection contain $0$?

This might even be a notational nuisance, but here it goes. Let $\kappa$ be a cardinal, $X_\alpha\subseteq\kappa$ for all $\alpha<\kappa$. As you know, the diagonal intersection of ...
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3answers
2k views

What do $\{ceps_q\}_{q=0}^Q$ and $\{a_q\}_{q=1}^p$ mean?

As a programmer who hasn't had any higher mathematical training, I sometimes find mathematical equations described in books or online that I'd like to implement in my programs, but they have symbols ...
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0answers
25 views

What is a mathematical symbol for the angle of two sub-spaces?

Assume you have two subspaces $\mathcal{A}$ and $\mathcal{B}$. In general, these are matrices that the span of the columns makes the subspace. Now: What is the best symbol for denoting the angle of ...
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1answer
33 views

How to denote raising $x^1$ to a power in differential geometry

I'm working from a text in which the coordinates of a point in $\mathbb R^n$ are denoted $(x^1,\dots,x^n)$. I'm wondering if there is a standard way to denote the sum of the squares of these ...
0
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0answers
33 views

What does the capital $E$ notation followed by curly bracket mean?

While reading through a statistics book earlier today I came across a notation I'm unfamiliar with and can't find a way to search for it. It is not expected value $E[\,]$, but instead the following. ...
0
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1answer
28 views

Question on statement of Cauchy-Schwarz inequality: $\vert\langle x,y \rangle \vert \leq \Vert x \Vert \cdot \Vert y \Vert$

Denoting the Cauchy-Schwarz inequality as Wikipedia does, $$\vert\langle x,y \rangle \vert \leq \Vert x \Vert \cdot \Vert y \Vert$$ and noting that $$\vert\langle x,y \rangle \vert = \Vert x\cdot y ...
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1answer
126 views

Why is $s$ used for arc length?

Why is $s$ used for arc length? I looked around online, but I can't find a definite answer. Thank you!
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0answers
17 views

If $b \in (-\infty, \infty)$ in $z=a+bi$, then how to mark the range of $z$?

Let $a$ be fixed. If $b \in (-\infty, \infty)$ in $z=a+bi$, then how to mark the range of $z$?
0
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0answers
33 views

What does $D(f(\textbf{x}))$ mean

If we have a nonlinear dynamical system with $$\dot{x_1}=a-x_1-\frac{4x_1x_2}{1+x_1^2}$$ $$\dot{x_2}=bx_1 \bigg( 1- \frac{x_2}{1+x_1^2} \bigg)$$ what do we need to do to find $D(f(\textbf{x}))$? Is it ...
4
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4answers
105 views

What does $f|_A$ mean?

If $f$ a is a function and $A$ is a set, what could the notation $$f|_A$$ mean? Is it perhaps "restricted to set $A$"?
3
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3answers
43 views

What's the point of the fancy notation for surface integrals and line integrals?

Most of the times you see line integrals of a vector field written as this $$ \int_C\mathbf{F\cdot ds} $$ And surface integrals like $$\iint_\Sigma \mathbf{F\cdot n}\,\mathrm dS$$ My question is, ...
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1answer
28 views

Which definition of convergence of subsequence is correct

Suppose that $(x_n)$ is a convergent sequence on a metric space $(M,d)$ with limit $x \in (M,d)$ Let $(x_{n_k})$ be the sub-sequence of the sequence $(x_n)$ Then is it more appropriate to write 1) ...
4
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2answers
58 views

Is there a difference between $f(x,y)$ $f(x;y)$ and $f(x\mid y)$?

While reading I have come across all three of these notations seemingly at random, and as far as I can tell they are all positional arguments to a function, but I can't tell if they mean different ...
0
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0answers
48 views

Is there any difference between “for any” and “for all”?

When we prove something, we use mathematical symbol ∀ to stand for "for all." Does it make any difference if we use same symbol for "for any."?
0
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1answer
17 views

What does $u_0(x)$ represent?

I am looking at the heat equation and in my notes it says the initial temperature distribution $u(0,x)=u_0(x)$. what does this mean? What does $u_0(x)$ represent?
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1answer
28 views

Set Notation: How to denote ALL points in some space satisfying a condition?

I am integrating a function over the multidimensional domain $\Omega$, which is a subset of a larger domain $X$. Omega is defined by ALL points $x \in X$ that satisfy some condition, the details of ...
5
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2answers
69 views

Notation: $\mathbb{Z}[\sqrt{-5}]$

Show that the elements 2,3, and $1 \pm \sqrt{-5}$ are irreducible elements of $\mathbb{Z}[\sqrt{-5}]$. I have never seen this notation before. From another post I am interpreting this to mean the ...
0
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0answers
11 views

Matrix notation: How would you apply a function to every column/row of a matrix?

Let's consider a real matrix A = \begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ ...
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2answers
83 views

Why was $\aleph$ (aleph) chosen for infinities?

Why did Cantor choose a letter from the Hebrew alphabet to represent infinities, rather than using some Greek letter?
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1answer
85 views

Uppercase E notation for sets?

In Jónsson and Tarski's (1951) paper Boolean Algebras with Operators, Part I from the American Journal of Mathematics, they write formulae such as $L_i = \underset{u}{\mathbf{E}} \, [u \in At^m ...
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2answers
48 views

Mathematical usage of “$\dots$” during enumeration, is it ok to be imprecise?

I am guilty of writing things like the following in proofs: so by lemma 1.2 we have that for $k<n$ all of the integers $k,k+1,k+2,k+3,\dots ,n$ are pompous. I really like how this looks, the ...
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1answer
42 views

$\frac {\partial}{\partial t}T$ vs $\frac d{dt} T$.

Suppose we have a function $T_1=F(x,y,t)$. Now suppose that $x=g(t),y=h(t)$, so we have a new $T_2=F(x(t),y(t),t)$, so then we have that $\frac \partial{\partial t} T_2=F_t$ and $\frac d{dt}T_2=F_x ...
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1answer
24 views

Notation conversion help with respect to combinatorical proof

First off, I wouldn't bring this to SO, but my teacher refuses to teach me notation. Anyhow... I'm doing a proof. The proof says: "Show that $8^n - 3^n$ is a multiple of 5 for all ...
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2answers
22 views

Notation question. How to write the set of all polynomials (over $ \mathbb{R}$) of degree at most $p$.

The question is pretty much in the title. I have been using $\mathrm{poly}_p$ but I don't like it.
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3answers
55 views

What is this set $\mathbb{R}$ mod $2\pi$

What does it mean for S = $\mathbb{R}$ mod $2\pi$? Can someone please explain as this notation is new to me.