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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2answers
74 views

Notation in commutative algebra

I am doing some exercises on commutative algebra and came along the following expressions, which were not elaborated on. Is someone familiar with them? The first is for $p$ a prime number ...
0
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2answers
76 views

What is $\operatorname{syt}$?

I came across the following definition of the set on this web page But what is $\operatorname{syt}$?
0
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0answers
28 views

if $F_{\bullet}$ is a complex and $r$ an integer, what is $F_{r-\bullet}$?

While reading the paper Some results and questions on the Castelnuovo-Mumford regularity, by Marc Chardin, I encountered in the proof of Theorem 5.1 the notation $F^N_{r-\bullet}$. To provide some ...
1
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1answer
24 views

Omitting the refference to a particular logarithmic base - order notation

How can I prove by using the Order notation definition that we can conventionally refer to an algorithm taking "log time", without referring to a particular logarithmic base?
1
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1answer
20 views

Notation for arbitrary indexing of summation, integration, and derivation

Suppose I have a multivariate function $f(x_1, x_2, \dots, x_n)$ and I'd like to divide the arguments of this function into two groups. The indices of these groups can be represented by two sets. ...
0
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2answers
96 views

How do I notationally write 6 and -6 are the only solutions of the equation $x^2=36$?

I would like to notationally write ''$6$ and $-6$ are the only solutions of the equation $x^2=36$'' using double turnstiles. Is it something like this? $$⊨ x∈{-6,6} ↔ x^2=36$$
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1answer
26 views

Can I write this statement like this?

Can I write the statement "$\varphi$ is a well-formed formula of PA" as $$\varphi \in PA$$
0
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2answers
77 views

What does the function f: x ↦ y mean?

I am doing IGCSE Maths, and am having a few problems with function notation. I understand the form f(x). What does the form f: x ↦ y mean? Could you also give one or two examples? And, if possible, ...
0
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1answer
29 views

Where do matrices of real numbers lie?

I have a question on the space where matrices of real numbers lie. Suppose I have a vector $x$ of real numbers with dimension $p\times 1$. I usually write $x\in \mathbb{R}^p$. Consider now a matrix ...
0
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1answer
30 views

How do I denote the set of all the elements of a cyclic group?

For example, can I simply write $\langle a\rangle$? (from Wikipedia) And furthermore, is there some notation involving the representative symbol/name of the group, like $\underline{G}$ or ...
2
votes
1answer
74 views

Inferring $d$ in $dx$ as derivative?

For few problems now, I've made substitutions by inferring $d$ in $dx$ as derivative. An example is in the proof of $$\int_a^bf(a+b-x)dx=\int_a^b f(x)dx$$ where one notes that "if we infer $d$ as ...
0
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1answer
15 views

Applying a vector of functions on vectors

Is there an adequate mathematical representation (operator $\star$) to apply a vector of functions to another vector of values, element by element? Something like the following: $$ \left[ f_1, ...
0
votes
1answer
11 views

Notation to define an element with maximum occurrence in a set

I have a set of sets of natural numbers which is as follows: $A=\{ \{1,1\},\{1,2\},\{3,1\}\}$ . I want to express the natural number with maximum occurrence. For example, 1 has the highest ...
0
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0answers
17 views

Is there a notation to designate a random variable given it's distribution and vice versa?

Most of the times, I find it unnecessary and tedious to name the corresponding random variables of a given bunch of probability density functions. For example, one must write things like this even ...
0
votes
1answer
30 views

Difference in Notation for Vectors in Linear Algebra & Multivariable Calculus

Often in Linear Algebra we see vectors depicted either in Column or Row Form as : Linear Algebra : Vector in Row Form $$ \vec{V}^{\,} = \left[x_1,\ldots,x_n\right]$$ OR Linear Algebra : Vector in ...
1
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0answers
28 views

L2 Norm: Unfamiliar notation

In this article that I am reading, I am given a non-negative spectral function $w(\lambda)$ which is "interpreted as a weight function determining the scalar product of two functions $f(\lambda)$ and ...
1
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1answer
30 views

Notation for equivalent equations

What is the notation for showing that equations are equivalent by rearranging terms? For example, for the arc length formula: $$s=r\theta$$ I sometimes solve for $r$ and write it as ...
0
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0answers
30 views

What notation can I use to indicate probabilities of probabilities?

What notation should I use to describe a uniform probability conditional upon a binomial distribution? In addition, I would like to describe the range of the uniform distribution and that each sample ...
0
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0answers
18 views

Question regarding congruence notation [duplicate]

I have a question regarding notation in modular arithmetic and congruence classes. I am used to the notation $a \equiv b$ $(\mod n)$; it simply means n divides a-b But I've seen a similar notation ...
1
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3answers
55 views

What does an exclamation point raised to a power, with no preceding number, mean?

In the OEIS sequence A049210, I noticed an odd notation I haven't seen before: a(n) = (8*n-1)(!^8), n >= 1, a(0) = 1. What does the ...
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3answers
48 views

Is there another notation for this set-theoretic formula? [closed]

I am writing a book. In my drafts there are formulas like $\prod_{X\in S} X$ or $\{ \operatorname{im} P \mid P\in\prod_{X\in S} X \}$. If there are other way to write the same expressions, I should ...
1
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0answers
28 views

What would be the meaning of the following expression?

If I have a function r(s). Then I could write down( in principle): $\dfrac{d}{dr} (r'(s))$ But I have troubles understanding what this would mean and how to work with it. Using leibniz notation I ...
0
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1answer
19 views

Correct notation with composite function & characteristic functions.

I have the functions $p: \mathbb R \to \mathbb R; \quad p(x) = \frac12 x + 1$ $q: \mathbb Z \to \{0, 1\}; \quad q(x) = \begin{cases} 1 & x \geq 1 \\ 0 & x \leq 0 \end{cases} $ I know that ...
0
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0answers
19 views

Riemann integral notation

I came across many notations for a Riemann integral of $f$ on the interval $[a,b]$, such as $$\int_{[a,b]} f,~~~~ \int_a^b f,~~~~\int_a^b f(x)~dx$$ Where does this multitude come from? Should I stick ...
0
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1answer
21 views

Symbolize a finite set by $\in \mathbb{N}$

Lets say that $A$ is a set. I looking for a way to show that $A$ is finite. I thought about a way and I'd like to know if this way is correct: $$|A|\in \mathbb{N}$$ or, there is a better (or ...
0
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0answers
41 views

What is $\stackrel{d}{=}$?

What does $\stackrel{d}{=}$ mean? I see it in this sort of context: $$ \operatorname{Var}_x\omega \stackrel{d}{=} (1/x)\sum_{n\le x}(\omega(n)-\bar\omega_x)^2 \sim \log\log x $$ which in this case ...
0
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2answers
30 views

Confirming some notation regarding Ring of Polynomials

Hi I just want to clear up some confusion regarding some notation. If $R$ is a ring and $\mathfrak p$ is a prime ideal in $R$, does $(R/\mathfrak p)[x] = R[x]/\mathfrak p[x]$? (or perhaps they ...
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0answers
13 views

What's the proper symbol to use in a statement containing both exact and approximate results?

I am having a pretty simple question regarding the notation of approximative and exact results on the same line. Let's use linear approximations as an example. Let's say that we have ...
2
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2answers
28 views

Natural logarithm power notation

I am trying to understand how to use Dirichlet's test for convergence and saw an example here (example 2). Show that $\displaystyle\sum_{i=1}^\infty \frac{2^{2n}n^2}{e^n\,n!}\frac{1}{\ln^2n}$ ...
0
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0answers
28 views

Can anything equal DNE?

I've come across several references where a person has shown a limit equal to DNE. Something like $\lim_{x\to 0}\frac{1}{x}=DNE$. Is it ever reasonable to say that something is equal to something ...
1
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0answers
123 views

Is this translation into symbols correct?

Me and my friend came up with a cool game - we take turns in taking some mathematical theorem stated in English and turn it into a symbolic statement. The rules are this: you are only allowed to use ...
0
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0answers
17 views

What is the notation for the mean of a percentile range?

I am trying to figure out the notation of the mean for all numbers in a set, A, up to the xth percentile of A. From what I have been reading, the percentile should be noted $P_x(A)$, but I believe ...
2
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0answers
38 views

Why is \mathsf{} used for formal systems?

A lot of times I have seen well-respected members of this community edit posts (including mine) changing things like "ZFC" into "$\mathsf{ZFC}$". It kind of makes sense, because formal systems like ...
0
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0answers
24 views

Simplest way to say “$\varphi$ is a wff of formal system $\mathbf{F}$”?

What is the simplest way to say "$\varphi$ is a well-formed formula of formal system $\mathbf{F}$" in symbols? The only thing that comes to mind is: $$\varphi \in \mathbf{F}$$ Am I right? I.e., ...
1
vote
1answer
40 views

Question about notation in group theory

If you click on the link below you will find a theorem from Daniel Gorenstein's book "Finite Groups". I am not sure what is the meaning of the i'(x). What does the ' mean? http://prnt.sc/as5413 ...
0
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1answer
21 views

Elements of the range of a random variable that are transformed into the same element

Let $X$ be a random variable and $Y = g(X)$. Then, the range or support of $Y$ can be written as $R_Y = \{g(x) \mid x \in R_X\}$. My question is whether there is a name (or standard notation) for ...
4
votes
1answer
85 views

Why isn't '&' used for logical conjunction?

There is a beautiful and well-established logogram for "and" that is known to virtually every more or less educated person in the world - it's the ampersand '&'. It's completely unambiguous, as ...
0
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1answer
35 views

Building a set of sets with different sizes

Let $n$ be a positive integer and $N$ be a set of ordered sets that meet some condition, whose size goes from $1$ to $n$. My question is how to write this downs by using set-builder notation. Here go ...
0
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0answers
34 views

Question about the following notation (groups and homomorphism)

So I was reading a paper on homomorphic encryption, and it in turn introduces some concepts that I didn't know much about before (primarily groups). I have a few questions but I'll first post the ...
0
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1answer
31 views

What does $[n=0]$ mean?

Namely, in the context of a recursively defined sequence: $a_n=a_{n-1}+b_{n-1}+a_{n-2}+[n=0]$ where b is an element of another sequence.
1
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0answers
37 views

How to denote a variable is an argument to a function.

How would one write "x is an argument to the function f" in set notation. For instance here is a piece of logic I'm trying to write as set notation: For all x where x is an argument to the function ...
0
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0answers
17 views

Is $f\in \mathcal{O}(g)$ then is $h\circ f \in \mathcal{O}(h \circ g)$.

Let be $f,g,h:\mathbb{N}\to\mathbb{N}$ strict increasing. Is the following statement true: Is $f\in\mathcal{O}(g), $ then is $h \circ f\in \mathcal{O}(h\circ g). $
0
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0answers
16 views

Subscript plus and negative sign

What is the precise mathematical definition of the positive and negative subscript signs as in the following function? $f(\mu) = \displaystyle\sum_{i=1}^n \alpha (x_i - \mu)_{+} + (1- \alpha)(x_i - ...
1
vote
2answers
85 views

Why polynomial functions f(x)+g(x) = (f+g)(x)?

Why polynomial functions f(x)+g(x) is the same notation as (f+g)(x)? I've seen the sum of polynomials as f(x)+g(x) before, but never seen a notation as with a operator in a prenthesis as (f+g)(x). ...
0
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0answers
27 views

Does the “truncation function” $\langle a,b\rangle : \mathbb{R} \rightarrow \mathbb{R}$ have an accepted name or notation? [duplicate]

Given real numbers $a$ and $b$ satisfying $a \leq b$, define: $$\langle a,b\rangle (x) = \mathrm{min}(b,\mathrm{max}(a,x)) = \mathrm{max}(a,\mathrm{min}(b,x))$$ (These numbers are equal because $a ...
6
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3answers
544 views

Different arrows in set theory: $\rightarrow$ and $\mapsto$ [duplicate]

Can someone explain the difference between symbols: $\rightarrow$ and $\mapsto$ Thanks.
1
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1answer
23 views

question on vector calculus notation

I just have a question about the vector calculus notation: $$(u \cdot \nabla)u$$ Is that the same as $( \nabla \cdot u)u$?
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0answers
23 views

Short notation for mapping to a family of sets

I want to write a function of which the output is a family of sets over the domain. Is this a correct notation? $ f: A \rightarrow \{ A' | A' \subseteq A \} $ Is there a way I can shorten this, the ...
1
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1answer
16 views

How to specify a function with flexible domain but same range?

As an example, I could be interested in functions that operate on $\mathbf{R}$ and $\mathbf{R}^2$. One way to say this is "all functions $f:\mathbf{R} \to \{0,1\}$ and all functions $f: \mathbf{R}^2 ...
0
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2answers
47 views

What is the Order (Big O) of this polynomial?

$$\frac{2n^{14} + 7 n^8 - 3}{3n^8 - n^4 + 3}$$ If this division is $p(n)$, I have to write $p(n) = O(n^k)$ I guess the answer is $n^6$, but how can i solve it step by step?