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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3
votes
2answers
201 views

Is $\infty$ enough or do I need to write $+\infty$

This is a question of notation. I have seen in many articles that people often denote $+\infty$ when talking about 'positive infinity' of the real numbers. Is that a convention, or it can be written ...
2
votes
4answers
2k views

Second order partial derivatives - notation

I have seen both of these used, and people around me seem to disagree, so which one is correct: (first derivative with respect to x, then y): (1) $$\frac{\partial }{\partial y}(\frac{\partial ...
1
vote
1answer
34 views

writing a formulation in a smaller form

Is it possible to write this in a smaller form: $(A \neq \emptyset) \vee (B \neq \emptyset)$ ? is it for example mathematically correct to write it as: $A \vee B \neq \emptyset$ ?
3
votes
2answers
144 views

What is the difference between these two derivative expressions?

is there a difference between $\frac{\partial^2 }{\partial x^2}$ and $(\frac{\partial }{\partial x})^{2}$? I have to tell if a differential equation is linear, and $(\frac{\partial }{\partial x})^{2}$ ...
0
votes
2answers
960 views

function, vertical line and two values (notation for evaluation at 1 point or 2 endpoints)

What does it mean when you have notation like this $$F\bigl(g(u)\bigr)\Bigr|_0^t,$$ where $F$ and $g$ are some general functions?
3
votes
2answers
782 views

What do curly brackets mean in this formula?

In this paper, in the Formula at the beginning of 2.2, we have $B=\{b_i(O_t)\}$ where $i=0,1$ - the number of probability formula $O_t$ - the state at moment $t$ $b_i(O_t)$ - two probabilities ...
3
votes
3answers
383 views

Notation pedantry (integration by substitution)?

In a summative assessment, I lost a mark due to this: $$f_X(x)=\frac{\lambda}{\sqrt{2\pi}}\int_{-\infty}^\infty y^2\exp\left\{-\left(\frac{1}{2}+\lambda x\right)y^2\right\} \; dy$$ Now let ...
1
vote
1answer
2k views

How should one interpret a double slash, //?

Example usage I've seen: $x^2 / (y // z)$ Context: I recently started learning some fundamental electrical engineering, where I saw I calculated the power doing $vs² / (r1 + ron + ron // ...
2
votes
2answers
82 views

How do I describe summations across sets of data?

Assume that there are several geographical regions and within each region there may be many buildings. Buildings may or may not be created and destroyed from time to time hence the requirement to ...
0
votes
1answer
225 views

What’s the significance of o(delta) notation

In my notes I have a definition for $o(\Delta)$ which states that if a function $f$ is $o(\Delta)$ then as $\Delta$ approaches zero, $f(\Delta)/\Delta = 0$. Then the notation gets used in equations ...
1
vote
1answer
241 views

What does $~ u(\cdot, t)$ mean when referring to a function?

I sometimes stumble over professors defining a function $u$ using regular (but quite sloppy) notation like $u(x,t) = A\sin(x)e^{-kt}$. Later in their notes, they state something like $u(\cdot, t)$ = ...
1
vote
1answer
763 views

Notation for an arbitrary set of N elements

Is there any notation for referring to a general set of $N$ elements? Currently I'm using $\{1, \dots, N\}$, but the fact that the set consists of natural numbers is irrelevant. I'd prefer to just ...
1
vote
3answers
332 views

Sum without an index

Is $\sum a$ a customary (standard) shorthand for $\sum_{i\in\operatorname{dom}a} a_i$, where $a$ is an indexed family of say integers?
0
votes
1answer
536 views

Represent loop nests as multiple summations?

This may be trivial but I would appreciate if someone could point me in the right direction here.. I am trying to express the number of instances in a loop nest in a general form. As a mathematical ...
2
votes
2answers
2k views

Convert for-loop into mathematical expression

I'm facing a simple problem actually: for (int i = 0; i < noutput_items; i++){ out[i] = in[i] * in[i]; } When I want to formalize this as a math ...
4
votes
0answers
280 views

Divisibility notation history

I'm writing a paper project for school about divisibility, so I'd like to include a bit of history about that subject. I'm mostly interested in notation of $|$ sign used in past, but everything else ...
3
votes
1answer
1k views

Limits notation

I'm wondering what is the difference in the use of $$\lim\limits_{x \downarrow a}$$ $$\lim\limits_{x \searrow a}$$ $$\lim\limits_{x \nearrow a}$$ $$\lim\limits_{x \uparrow a}$$ I see them ...
3
votes
1answer
230 views

Why does no one use the notation $f(x)^2$?

It seems to me that "$f(x)^2$" couldn't mean anything other than "$[f(x)]^2$", so there shouldn't be any ambiguity involved, but people always tend to put an extra pair of brackets around the "$f(x)$" ...
13
votes
1answer
15k views

What's the correct notation for log squared?

I ran across these two notations for the log function (squared), which one is more conventional. $\log^2(n)$ or $[\log(n)]^2$
1
vote
0answers
238 views

A contradiction in notation

How to deal with the following contradiction in notation? $\bigcup a$ may mean both: the union of a collection of sets $a$; $\bigcup_{i\in \operatorname{dom}a} a_i$ for an indexed family $a$ of ...
0
votes
1answer
116 views

notation for symmetry types

I am reading an article and in one of the sections the article mentions the symmetry group. The symmetry group of one of the objects the article talks about is the dihedral group of order 12, using ...
3
votes
1answer
134 views

What do mathematicians call the Two's Complement on 8-bits group?

It is isomorphic to $\mathbb{Z}_{2^8},$ only difference is the symbols usually identifying the elements of the set are from $\{-128, \ldots, 127 \}$ and not $\{0, \ldots, 256\}.$ What is an elegant ...
8
votes
4answers
23k views

What do Subscripted numbers in an equation mean?

$F_n= F_{n-1}+ F_{n - 2}$ I know that when a number is superscripted it means "to the power of", but what does the subscript mean?
3
votes
2answers
334 views

Notation for covariant derivative

I'm reading John M. Lee's book " Riemannian Manifolds". On page 57, the covariant derivative of $V$ along a curve $\gamma$ is defined, where $V$ is a vector field along $\gamma$. It is denoted by ...
1
vote
0answers
35 views

About order of an index

I have a simple question on precedence of operators, especially applying a function and an index. Can we write $q(F)_i$ (without an additional pair of parentheses) for $(q(F))_i$? Maybe, it would be ...
2
votes
2answers
240 views

Using nabla with partial derivatives and the Laplace operation $\partial_x^2+\partial_y^2+\partial_z^2$

Source of the problem p.812 here. Suppose $$\bar{F}(x,y,z)=(xy-z^2)\bar{i}+(xyz)\bar{j}+(x-y^2-z^2)\bar{k}.$$ I am concerned where I need to nabla an unit vector for example with $$\triangledown ...
1
vote
2answers
155 views

Notation for denoting one argument fixed and acting upon the other

Given a function $f_1:\mathbb R^n\mapsto \mathbb R$, and a fixed vector $v\in \mathbb R^n$ I construct another function $f_2:\mathbb R^n \times \mathbb R^n\mapsto \mathbb R$ such that ...
2
votes
3answers
452 views

Field of fractions of $R[X]$

Let $R$ be a domain and let $Q$ be its field of fractions. Show that the field of fractions of $R[X]$ is isomorphic to $Q(X)$. By the way, I don't know exactly what $Q(X)$ is. It means $Q[X]$? Or ...
0
votes
1answer
34 views

Notation of instantiating variables by their value in a constraint set

I have a constraint set $C = \{1 \leq x \leq i, j \leq y \leq j+2\}$, now I would like to get another constraint set $C'$ from $C$ to instantiate all $j$ by a value 5, so $C' = \{1 \leq x \leq ...
3
votes
2answers
1k views

$\{0,1\}^n$ and $[0,1]^n$ notations

Can someone please help me clarify the notations/definitions below: Does $\{0,1\}^n$ mean a $n$-length vector consisting of $0$s and/or $1$s? Does $[0,1]^n$ ($(0,1)^n$) mean a $n$-length vector ...
1
vote
1answer
79 views

Product of ordinals notation

How to denote product of ordinals: $\cdot$ or $\times$? I'm not sure which of these two multiplication symbols to use.
2
votes
3answers
244 views

How to formulate a theorem about bijections between several sets

I have several sets $A_i$ and bijections between them. (As stated in my theorem) no composition of these bijections produces a permutation of $A_i$ not equal to identity. So every bijection is ...
4
votes
3answers
283 views

Is it mathematically correct to write $a \mod n \equiv b$?

This is not a technical question, but a question on whether we can use a particular notation while doing modular arithmetic. We write $a \equiv b \mod n$, but is it right to write $a \mod n \equiv ...
6
votes
2answers
2k views

How do you pronounce (partial) derivatives?

I am not an English speaker that is why I asked this question. In addition, I think english.stackexchange.com is not the proper place to ask this because (I am so sorry) I don't think most of them ...
1
vote
1answer
162 views

Name of binary relation: if $(x, y)\in R$ then there is no $z$ such that $(y, z)\in R$

Is there a term for a binary relation $R\subset A^2$ on some set $A$ such that if $(x, y)\in R$ then there is no $z$ such that $(y, z)\in R$ ? Are there any examples of it? Are there any related ...
2
votes
1answer
712 views

Uparrow sign (convergence?)

Im not entirely sure what this definition means, whilst I'm reading up. Let $X_n \in$ some sigma algebra $\mathcal{F}$. $X_n \uparrow X = X_n \subseteq X_{n+1}, \forall n \in \mathbb{N}$ and $\cup ...
0
votes
1answer
434 views

Query about Cartesian vector notation.

I'm just starting to teach myself about covariant and contravariant vectors. With the little knowledge I've acquired so far I'm wondering if, for an ordinary Cartesian vector $\mathbf{V}$, it's OK to ...
1
vote
2answers
171 views

The names of two unfamiliar operations

I am currently researching a QR-based root finding algorithm encountered two operations that I don't understand. I'd love to look them up, but I can't find the names of these operations/notations. ...
10
votes
3answers
4k views

A digital notebook for Mathematics?

When I studied math 15 years ago, I was dreaming of having a math repository with tags to navigate between the different entries. I imagined it would come eventually to the market, and was hopefull ...
2
votes
2answers
203 views

What does $\sqrt[n]{z}$ mean, when $z$ is an arbitrary complex number?

What does $\sqrt[n]{z}$ mean, when $z$ is an arbitrary complex number? Is it a single complex number, or the set of $n$-th roots of $z$?
0
votes
1answer
1k views

Right and Left arrow notation in proof.

I'm studying vector spaces and I'm reading a proof where the authour uses the symbols $$(\Rightarrow)$$ and $$(\Leftarrow)$$ when proving a theorem. He doesn't use them in context, but rather ...
1
vote
1answer
225 views

What's are these index objects called? And $\mathrm{\LaTeX}$ \sum question

I want to refer to $$A_iB_jC_k$$ using $$\psi(ijk) = A_iB_jC_k$$ So that I can write out quite overwhelming-looking sums of ABC terms as sums of terms that look like 123, 231, 113, etc. If I am not ...
1
vote
1answer
507 views

Notation of partition

I look for an elegant way to notate a partition $\mathcal{Q}$ based on another partition $\mathcal{P}$. Two elements who are already in the same partition in $\mathcal{P}$ also belong to the same ...
1
vote
4answers
891 views

Coordinates notation in Spherical polar system

There is a number of conventions for specifying coordinates in Spherical polar coordinate system: ($r$, $θ$, $φ$), ($r$, $φ$, $θ$), ($\rho$, $\theta$, $\phi$) and even ($r$, $\psi$, $θ$). The article ...
0
votes
1answer
121 views

Are there names for the indices of the spherical harmonics?

I know that physicists call $\ell$ and $m$ the "azimuthal" and "magnetic" quantum numbers, respectively. But those sound very physics-y. (I am actually a physicist, but still.) Are there names for ...
2
votes
1answer
185 views

What do these notations actually mean?

I apologize if this question sounds weird, but I have come across this function (which I am trying to replicate using C# code), which has left me a bit confused. The way I am understanding, is that ...
1
vote
2answers
290 views

Particular Use of Big O Notation

I'm reading a theorem that states "...Then for each $j$ and $\epsilon>0$, there exists $n\leq 2^{O(j/\epsilon)}$..." What exactly is the big-oh notation saying in this case? I guess it must be ...
1
vote
1answer
507 views

Sequence Notation

I have come across the following in the book "Principles of Program Analysis" by Nielson, Nielson and Hankin to represent a sequence and I am unsure of what its constituent parts mean. Obviously ...
1
vote
2answers
678 views

What is the meaning of $\operatorname{ord}_{p}(n)$?

In number theory, where $p$ is a prime number and $n$ is an integer not equal to zero, what is the definition of the function $\operatorname{ord}_{p}(n)$ in the context of $p$-adic valuations?
0
votes
1answer
59 views

Representing relations among several long formulae

I have several long formulae, each formula occupies almost the whole width of the line: $$ 1 * 2 + 3 * 4 + 5 * 6 + ( 7 * 8 ) \tag{a}$$ $$= 1 * 2 + 3 * 4 + 5 * 6 + 7 * 8 ...