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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1answer
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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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7 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 ...
3
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0answers
47 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
17 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
42 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
42 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? [on hold]

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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22 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
43 views

Is there no (basic) math webfont? [on hold]

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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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
61 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
30 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 ...
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0answers
31 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. ...
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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
118 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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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 $z$?
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27 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 ...
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4answers
98 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 $A$"?
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3answers
42 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) ...
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2answers
57 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 ...
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47 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."?
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1answer
16 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
27 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 ...
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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 ...
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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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0answers
25 views

Trying to print a document with mathematical notation [closed]

I tried to print a document which includes mathematical notation and some of it is rendered fine but much of it is replaced by a box and I'm not entirely sure why. I thought perhaps it may be an ...
4
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2answers
78 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
84 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 $L_i = \underset{u}{\mathbf{E}} \, [u \in At^m ...
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2answers
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Mathematical usage of “$\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 ...
4
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1answer
41 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 ...
1
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1answer
23 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.
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2answers
28 views

What does this matrix operation mean in MATLAB: X\y [closed]

I'm reading somebody's code and I'm trying to figure out what this line means X\y where X is a 100x2 matrix and y is a 100x1 vector
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1answer
30 views

Is $(x^2+y^2+x)dx+xydy$ is the same as ${dy\over dx}(x^2+y^2+x)+{dx\over dy}(xy)$ ? Is this just a different notation?

Hello :) Its my first post :O Thnk you for the help :) !!! Is $(x^2+y^2+x)dx+xydy$ is the same as ${dy\over dx}(x^2+y^2+x)+{dx\over dy}(xy)$ ? Is this just a different notation? Thnx :)
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2answers
33 views

Is there a difference between modulo groups with and without asterisks ($\mathbb{Z}_{38}$ vs $\mathbb{Z}_{38}^*$)?

I know modulo group $\mathbb{Z}_{38}$ but I saw it with a star in some question: $\mathbb{Z}_{38}^*$. Is it is the same as $\mathbb{Z}_{38}$ or a different group? If it refers to the same group does ...
1
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1answer
20 views

4th order mixed leibniz derivative

How exactly is the order of mixed partials read in Leibniz notation? In Lagrange notation, we just read from left to right. $$f_{xyzz} = (\frac {\partial} {\partial z}(\frac {\partial} {\partial ...
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1answer
41 views

higher order partial derivative notation (Leibniz)

Which one of the following two are correct? $$ f_{xy} = \frac {\partial} {\partial y} (\frac {\partial f} {\partial x}) = \frac {\partial ^2 f} {\partial xy}$$ or $$ f_{xy} = \frac {\partial} ...
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0answers
18 views

How to assign variables to points on the cartesian plane?

Suppose I want to name the point $(3,4)$ a name say A. Can I just say $A=(3,4)$?
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1answer
30 views

How to neatly summarize indexes of a matrix where there are a lot of i's x j's [closed]

As you can see from the subject line, I can't even think of the word of what I need to do. I am trying to write in text that I multiplied columns of a matrix (n columns, i = 1:n). There are many ...
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0answers
24 views

Set, n-Tuple, Vector and Matrix — links and differences

I know this question has been asked like 1000 times, however all supplied answers were not really satisfying to me. My question concerns the similarities and differences between these mathematical ...
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0answers
19 views

Examples of sans serif Greek used in published mathematics

Unicode contains several thousand mathematical symbols, including individual code points for different maths alphabets. For example, U+1D434 is "mathematical italic capital A" (𝐴), U+1D63C is "math ...
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1answer
30 views

What is the difference between disjoint union and union?

If $S = A \cup B$, then $S$ is the collection of all points in $A$ and $B$ What about $S = A \sqcup B$?, I think disjoint union is the same as union, only $A, B$ are disjoint. So the notation is a ...
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2answers
19 views

What do we call the set of elements fixed by an involution of the second kind?

If $A$ is an algebra over a field $F$, and $\sigma:A\rightarrow A$ is an involution of the second kind, then it seems natural to talk about the set $S=\{a\in A\mid\sigma(a)=a\}$. I am not finding any ...
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1answer
55 views

Never seen this notation before: $\int (y-f(x))^2 Pr(dx,dy) $

I have never seen an integral like this: $$\int (y-f(x))^2 Pr(dx,dy) $$ What is that? More precisely what is $Pr(dx,dy)$? And how is that integral defined? I found it in Elements of Statistical ...
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18 views

Notation for Line Segment vs. Directed Line Segment

This may be nit-picky, but I noticed inconsistencies in a high school math text I was reading, and I'm curious what the world thinks. For the most part throughout this textbook, notation is used as ...
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20 views

What is the standard notation for the Banach space of functions that vanish at infinity?

Given a topological space $X$ and a real (or complex) valued function $f$ on $X$, we say that $f$ vanishes at infinity if for any $\varepsilon>0$ there is a compact $K \subseteq X$ such that ...