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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0
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0answers
28 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 \\ ...
15
votes
2answers
417 views

Looking for an approach to mathematical notation wherein the universe is divided into disjoint worlds.

Is there a rigorous approach to mathematical notation wherein the "universe" is divided into disjoint "worlds," and the meaning of notation is world-dependent? This would solve a few pesky problems. ...
1
vote
2answers
1k views

What does “versus” mean in the context of a graph?

Say you have a graph of say $y=mx+b$, with $x$ on the horizontal axis and $y$ on the vertical axis. You need to give the graph a title, would you say: This is a graph of "$y$ versus $x$?" or This ...
1
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0answers
10 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 ...
1
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1answer
24 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 ...
17
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6answers
7k views

Contradiction! Any Symbol for?

Perhaps, this question has been answered ago but I don't aware of its existing answer. Is there any international icon or symbol for showing Contradiction or reacing a contradiction in Mathematical ...
3
votes
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 ...
0
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1answer
23 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 $\kappa_A$, ...
0
votes
5answers
182 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 ...
0
votes
1answer
23 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 ...
0
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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 $f \in C^1$
3
votes
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 ...
1
vote
1answer
45 views

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

Is $(x^2+y^2+x)dx+xydy$ the same as ${dy\over dx}(x^2+y^2+x)+{dx\over dy}(xy)$? Is this just a different notation?
6
votes
2answers
82 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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2answers
49 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 ...
1
vote
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. ...
0
votes
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 ...
5
votes
1answer
125 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!
5
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2answers
84 views

Is there a symbol for ‘equal if defined’

Can anybody recommend a symbol for ‘equal if defined’ as an asymmetric concept? In contexts where one might write down notation for an undefined quantity (such as $1/x$ when $x$ might be $0$), ...
4
votes
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 ...
0
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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 ...
0
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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?
0
votes
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 ...
1
vote
1answer
64 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 ...
14
votes
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 ...
0
votes
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 ...
0
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0answers
43 views

Question about the classification theorem for finitely generated graded $F[t]$-modules

I am in the beginnings on learning persistence homology, and as a start I'm studying Gunnar Carlsson's survey "Topology and Data". Theorem 2.10 states the following: "Suppose $M_{\star}$ is a ...
1
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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 ...
1
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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 ...
0
votes
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 ...
1
vote
1answer
32 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 ...
1
vote
1answer
85 views

Tensor notation for 3-D matrix expression

I have the expression $y_i = \displaystyle\sum_j x_j \!\cdot\!a_{ij} \!\cdot\! \exp \Big(\sum_k b_{ijk} \!\cdot\! x_k \Big)$ which I want to shorten without introducing more notation than necessary. ...
0
votes
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. ...
4
votes
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 $A$"?
0
votes
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 ...
0
votes
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
votes
0answers
30 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 ...
2
votes
1answer
207 views

Notation for free graded resolutions of graded modules?

I am now reading a paper about Castelnuovo-Mumford regularity and in this paper, there is a notation as following: Let $S=k[x_1,...,x_{n}]$, by Hilbert's syzygy theorem, if $N$ is a graded module ...
0
votes
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
votes
3answers
666 views

Confusion regarding $\log(x)$ and $\ln(x)$

I was solving an integral and I encountered in some question $$\displaystyle \int_{2}^{4}\frac{1}{x} \, \mathrm dx$$ I know its integration is $\log(x)$. But my answer comes correct when I use ...
3
votes
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, ...
4
votes
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
votes
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."?
1
vote
1answer
31 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 ...
0
votes
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?
5
votes
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
votes
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 \\ ...
3
votes
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 ...
2
votes
2answers
47 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 ...