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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0answers
7 views

Rearding notation of (Relatively)Projective/ (Relatively)Injective in Group cohomology

I am reading Group cohomology from Serre's Local Fields. I got confused with the notation he used... We know that : $A$ is Projective module if $Hom_R(A, \_)$ is exact $A$ is Injective module if ...
9
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4answers
344 views

Notation problem in integration: write $dx$ or ${\mathrm{d}}x$?

I have a question. When I write the integral of a generic function $f(x)$, do I have to write $$\int f(x) \color{red}dx$$ or $$\int f(x) \color{red}{\mathrm{d}}x \quad ?$$ Why? Thank you!
1
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2answers
33 views

Index notation for inverse matrices

I have a question: There is an standard way to write the inverse of a matrix in index notation?. The reason is that I don't want to write $(A^{-1})_{ij}$ or $(A^{-1})_i^j$ or $(A^{-1})^{ij}$ using ...
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1answer
26 views

Asymptotics of logarithm: $\frac{1}{n}\ln(a+o(1)) = \frac{1}{n}\ln(a)+o(\frac{1}{n})$

I am having problems with the use of the little oh notation my professor is adopting in the solutions to some exercises. As an example I do not understand why $$ \frac{1}{n}\ln(a+o(1)) = ...
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1answer
2k views

Boolean algebra operation precedence?

In my discrete mathematics class we wrote down the truth table for some Boolean functions and in that table they go in the following order: ¬, ∧, ∨, →, ~, ⊕, |, ↓ So, I assumed that this is the ...
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4answers
36 views

Notation for two-vertex graph with m edges

Is there standard notation for the graph on two vertices with $m$ edges between them?
2
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0answers
32 views

Specifying types of variables in pure mathematics and applied mathematics

In pure mathematics, we can write such as "an integer $a$ ..." to specify that $a$ is a given integer or $a$ runs through the ring of integers. But in contexts where mathematics is applied ...
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3answers
701 views

History of notation: “!”

Does anyone know where the factorial "!" symbol came from? I can't decide if it is my favorite or least favorite notation in mathematics...
3
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1answer
46 views

Formally correct way to define asymptotic notations

I found an algorithm book which tries to define asymptotic notations as sets and then used notations like $n=O(n^2)$. Is there a mathematically correct way to define asymptotic notations like $O(n), ...
0
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1answer
23 views

Explanation of notation $f(t)\in L_{\infty}$ in a control theory textbook

In a control theory textbook I saw the following notation : $$f(t)\in L_{\infty}$$ Since I am not familiar with this kind of notation could someone explain What does it mean?
2
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1answer
34 views

Two integers with the same prime factors notation

Let $m,n\in \mathbb{Z}$, what is the notation usually used to say that $m,n$ have the same prime factors, i.e. $m=p_1^{m_1}p_2^{m_2}\cdots p_2^{m_r}$, $n=p_1^{n_1}p_2^{n_2}\cdots p_r^{n_r}$ for some ...
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1answer
67 views
+50

Notation for the set of all arguments corresponding to local minima.

The notation $$\mathop{\mathrm{arg\, min}}_{x \in X} f(x)$$ is sometimes used for the set of all $x \in X$ corresponding to global minima of the function $x \in X \mapsto f(x).$ Is there notation for ...
0
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1answer
236 views

A question regarding case notation

Consider the parameter $P$ and a property $S$ associated with this parameter represented as $P_S$. For example, consider that the height of a tree (“H”) is my parameter and the property is the tree’s ...
0
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3answers
73 views

What is $X^{\omega}$ where $X$ is a set?

I fail to find a duplicate. If it exists, please link me in the comments and I will delete the question. In my recently bought topology book, they use $X^{\omega}$ where $X$ is a set. However, this ...
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0answers
15 views

Probabilistic Graphical Model Diagram Notation, what does the box mean?

I'm just learning about probabilistic graphical models, I know the circles represent random variables, shaded being observed and unshaded being latent variables. But what does the box mean?!
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2answers
53 views

How to denote that an equation is true?

If I have a simple equation such as this: $$x+5-1=x+4$$ how can I denote that this equation is true? More specifically, if I refer to that equation as P(x), then is there a mathematical notation for ...
0
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0answers
23 views

Notation for parametric family of joint densities

This is copied from my textbook; Assume that the statistical model for the MVR $\textbf{Y}=(Y_{1},Y_{2},\ldots , Y_{n})^{T}$ is given by the parametric family of joint densities: $$\{ ...
0
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1answer
34 views

Notation for vector space of polynomials of bounded degree

Is there standard notation for the vector space of polynomials in $n$ variables with coefficients in a field $F$ and with degree at most $D$? Without bounding the degree, it is $F[x_1, \ldots, x_n]$. ...
0
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0answers
16 views

Notation for mimimal sum when choosing elements from two sets

I'd be grateful for any pointers on the following I am wondering if there is any standard notation (or neat suggestions) for the following. I have two sets $\{t_1, t_2, \ldots , t_k\}$ and $\{s_1, ...
0
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0answers
20 views

Notation of axis

I have a graph where I rescaled the axis by dividing by 10. In the label on the axis, should I put "(x10)" or "(/10)"? I don't know the correct semantics of these labels in graphs.
6
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2answers
396 views

Meaning of a set in the exponent

Let $ D = 2^\mathbb{N} $, i.e., D is the set of all sets of natural numbers. What's the meaning of this definition? Intuitively, I would suggest that $ D = \{1,2,4,...\} $ but the explanation ...
7
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1answer
86 views

What does $\frac12(D_{2p}\times D_{2p})$ mean in group theory?

Reading a thesis, I have come across the (unexplained) notation $$\frac{1}{2}(D_{2p}\times D_{2p})\cong (p\times p):2,$$ where $D_{2p}$ is a dihedral group. What does this "$\frac12$" notation mean? ...
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0answers
25 views

Statistical symbols: should greek letters be used for population or for a sample?

When finding mean and the stansard deviation, do you use the Greek symbols for a population, or a sample. When do you use "s" and xbar, for a population, or a sample? (I am taking AP Statistics)
2
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1answer
73 views

Why we use $\mathbb{R}^{m \times n}$ notation instead of $\mathbb{R}^{n \times m}$?

I just realised, that I use all the time the notation $\mathbb{R}^{n \times m}$, and all books and papers use $\mathbb{R}^{m \times n}$. $\mathbb{R}^{n \times m}$ is more sympathetic for me, because I ...
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1answer
42 views

Integral notation

I have encountered the following integral: $\int_{x-d}^{x+d}f(y)dy$ I am trying to figure out what is the role of $d$ in this integral. Is the $d$ at the beginning of the integral the same as the ...
2
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3answers
184 views

Basic question: what does the notation $[A,B]$ mean?

If $A$ and $B$ are both matrices, what is $[A,B]$? I understand that it is a commutator and that $[A,B]=AB-BA$, but since I don't know what a commutator is, none of this information is telling me ...
3
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0answers
12 views

Equivalent to proportionality sign for additive constants

Short question Is there an equivalent to the proportionality sign $\propto$ for additive constants? The proportionality relation $y\propto x$ implies that $y=kx$ for some constant $k$. Is there a ...
7
votes
5answers
484 views

Functional Notation.

I have some doubts regarding function notation: First If I present a function I write:$f(x)$ If I write it's inverse:$f^{-1}(x)$ So why doesn't$f(f(x))=f^2(x)$ Second If $\frac{df(x)}{dx}=f'(x)$ ...
2
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0answers
37 views

notation for minimum and maximum?

I'm trying to figure out the correct notation for this situation for use in Machine Learning. I have various ratings (for texts): ...
1
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1answer
46 views

Standard Notation For The Set of All the Morphisms Of A Category

Let $\mathscr C$ be a category. Let $\text{Ob}(\mathscr C)$ be the set of all the objects of $\mathscr C$. Is there a standard notation for $\bigcup_{A,B\in\text{Ob}(\mathscr C)}\text{Mor}(A,B)$? ...
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1answer
40 views

Just a translation issue.

I'm italian and my professor of spectral theory wrote the list to the arguments to be studied in italian. The problem is that all the literature is in english and often the translation are a bit ...
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9answers
1k views

Is there an interval notation for complex numbers?

Just as $$\{x \in \mathbb{R}: a \leq x \leq b\}$$ can be written in the more-compact form $[a,b],$ is there an analogous notation for $$\{z \in \mathbb{C}:z=x+yi, x \in[a,b], y \in[c,d]\} \quad ?$$ ...
0
votes
1answer
95 views

Does “arbitrarily small” mean very close to zero or very negative?

In mathematical writing, does “arbitrarily small” mean very close to zero (like $0.000001$) or very negative (like $-1000000$)? Are there better phrases to distinguish these two cases?
5
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2answers
77 views

What is this notation for a function? I've never seen it written like this before.

What does this mean? $$ f=\{ (x,y): y= x+2 \}$$ I don't understand what "$(x,y):$" means in regard to the problem. Also why is the $y$ inside of the $f(x)$ function. Isn't it supposed to be outside? ...
2
votes
0answers
98 views
+50

Meaning of notation $\operatorname{ord}_Q(g)$ in “Algebraic Curves” by Fulton

I didn't understand this notation in the chapter 7 page 93 of Fulton's algebraic curves book: What the author means by $\text{ord}_Q(g)$? Maybe he would like to say $\text{ord}_Q(G) := ...
1
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1answer
37 views

Lerch transcendent

While messing around with something I got a result on WolframAlpha with a notation like this $$\text{LerchPhi}^{(0,1,0)}\left(\frac{1}{2}, 0, 2\right)$$ I know that ...
0
votes
1answer
31 views

What notation to use for a sequence of integers that end with digit 5?

I need to solve a low high school home work and I ask a question about the most correct notation. The problem is to build a set of circles with $r$ and $d$ such that $d=5, 15, 25, 35,...d_{+_1}$ and ...
3
votes
0answers
176 views

Identities for Sieve of Eratosthenes collisions.

Edited to define the last two tables Three Questions: 1) Is all notation correct? 2) Is there a symbol for flatten? 3) How would we prove the identities: the sum of the divisors in the symmetric ...
2
votes
1answer
57 views

Understanding the notation of a book when derivating

I'm trying to understand the notation that the book uses. The book says $(1)$ $y=a\cdot \sin x$ and then the derivate of $(1)$ is $(2)$ $\frac{d^2y}{dx^2}=-a \cdot \sin x$ I don't get what to do ...
0
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1answer
211 views

What are the $\succ$ and $\prec$ operators for when used with matrices?

I understand that $A\succ0$ means that "A is a positive definite matrix" (i.e.; all of the eigenvalues of A are positive). But what does it mean when the right hand side is a different value than ...
4
votes
1answer
258 views

Derivative $\Delta x$ and $dx$ difference

This may seems like a dummy question but I need to ask it. Consider the definition of derivative: $$\frac{d}{dx}F(x) = \lim_{\Delta x->0}\frac{F(x+\Delta x) - F(x)}{\Delta x} = f(x)$$ Also: ...
2
votes
2answers
51 views

Writing solutions of inequalities: $3<x$ versus $x>3$

My son wrote a solution to a number line graph as 3 < x instead of what his teacher said was the correct answer of x > 3. When he brought his paper back in to bring it up he was told that the ...
41
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10answers
2k views

Have there been efforts to introduce non Greek or Latin alphabets into mathematics?

As a physics student, often I find when doing blackboard problems, the lecturer will struggle to find a good variable name for a variable e.g. "Oh, I cannot use B for this matrix, that's the magnetic ...
2
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3answers
196 views

Why are variables in integration by substitution so counter intuitive?

Integration by substitution is defined as something like $\displaystyle\int_a^b f(\phi(t))\phi'(t)dt = \int_{\phi(a)}^{\phi(b)} f(x)dx$ But for my taste, the variables $x$ and $t$ are exactly ...
3
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0answers
51 views

Etiquette for proper usage of Greek letters and other notation

I've progressed to the "output" point in my mathematics career and have run into a slightly embarrassing problem while writing a paper. Clearly, certain Greek letters are suitable for some situations ...
0
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1answer
85 views

Why is the symbol ζ sometimes used in a complex function?

I just flipped through a book on complex analysis and found some functions being written as f(ζ) instead of f(z). It did not state why this is so. Can someone help enlighten me? Thank you.
0
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0answers
67 views

What does $X:Y\to x(t)$ mean?

Relatively new into math and working my way into it. I need some help understanding the statement below. X:Y -> x(t). Can someone please help me with what does it mean? So just to clarify I have a ...
2
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1answer
13 views

Consider a symmetric matrix $X$ with eigendecomposition $X=UVU^T$, how to call $\sum_{v_{k,k}>0}v_{k,k}u_ku_k^T$?

Consider a symmetric matrix $X$ with eigendecomposition $X=UVU^T$ How do people call $\sum_{v_{k,k}>0}v_{k,k}u_ku_k^T$? Sum of positive components of $X$? The positive semi definite part of $X$? ...
0
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2answers
26 views

Sigma notation: number columns with sum > 0 of binary matrix

I'm trying to formulate a Sigma notation formula which would yield the count (sum) of columns which themselves have a non-zero sum. $\begin{bmatrix} 1 & 0 & 0 & 0 & 0\\ 1 & 1 ...
2
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3answers
260 views

Notation: subscript vs. superscript for coordinate vector fields

Some books write the coordinate vector fields with a subscript as $$\frac{\partial}{\partial x_i}$$ while some write it with a superscript as $$\frac{\partial}{\partial x^i}.$$ Is there a conceptual ...