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
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
40 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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0answers
11 views

Point-free notation for (not direct) sums of functions over products of spaces.

I am writing a paper, and there are lots of expressions containing integrals of form: $$\int_{X \times Y} \phi(x) + \psi(y) d\alpha(x,y) $$ where $\phi$,$\psi$ are abstract functions and $\alpha$ is ...
0
votes
2answers
26 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 ...
1
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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
votes
2answers
27 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
25 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
71 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 ...
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0answers
15 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
votes
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 ...
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0answers
23 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
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1answer
38 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
20 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
82 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
34 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 ...
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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
30 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.
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0answers
36 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 ...
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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
13 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 - ...
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2answers
84 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
519 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
21 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
22 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
votes
2answers
44 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?
2
votes
1answer
16 views

Different use of approximate equality symbols

I have been wondering for a long time whether there is a unequivocal way to define and use the symbols commonly adopted for an approximate equality between two quantities. I am a physicist, and I ...
1
vote
1answer
21 views

What does $L^2((1+|\xi|^2)^sd\xi)$ mean?

In the most elementary contexts of Lebesgue measure, $L^2$ is the space of the lebesgue measurable functions $f$ such that $\int|f(x)|^2dx<\infty$. For a general measure $\mu$, $L^2(\mu)$ is the ...
2
votes
1answer
89 views

What's the real life purpose of Knuth arrows?

I recently read about Knuth's Arrows. Didn't even know those operations existed. My questions is: Do they have real-life applications? Most of the times a mathematical development follows a real-life ...
0
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1answer
13 views

notation for excluding an element from a sequence

I'm working on a question wherein I need to show that $y=Sup\, x_{n}$ but without the element $x_{1}$. Can I just write $y=Sup\, (x_{n}/x_{1})$?
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0answers
15 views

How do I describe the set of all sets that are the result of a given number of changes to a given set?

Let $k$ be the number of elements that are allowed to change in a set with fixed size $n$. How would one formally describe the set of all possible sets that are a result of changing $k$ elements of ...
1
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0answers
17 views

Is there notation for an open OR closed interval?

Is there a notation for indicating that an interval could be open or closed, (similar to the $\pm$ symbol meaning the operation could be $+$ or $-$)? I am looking for an equivalent, less cumbersome ...
0
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0answers
15 views

In bivariate probability: How do I denote different cases at the same time?

I have two random variables $X$ and $Y$, each of which can take on the values $1$ or $0$. I was browsing other questions for examples of notation, but couldn't find any. In particular I want to know ...
-2
votes
1answer
29 views

author2vec angle between vectors notation [closed]

Reading the latest "author2vec" paper (Author2vec publication), I stumbled upon equations (1): $h_C^{(x)}=v_u \odot v_p$ and (5): for the sake of this question consider it exactly as (1), where ...
0
votes
1answer
49 views

What's the difference (if any) between writing $(n-1)/2$ and $\frac{n-1}{2}$?

This might be a very basic question, but I've always wondered if there's any difference between these two forms, and under what circumstances may one be preferable to the other?
0
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1answer
27 views

What does the notation $\overline{ \operatorname{span} M}$ represent?

What does the notation $\overline { \operatorname{span} M}$ represent? For example $M$ is total in $X$ if and only if $\overline { \operatorname{span} M}=X$
1
vote
1answer
26 views

Is there a shorter way to show the union of many sets?

Let $\space H_n \space$ be a set such that: $$H_{n} = \{ h^2\in \mathbb{N} : n \leq h \leq n^2 \}$$ Where of course $\space n \in \mathbb{N}$. Now if I wanted to specify the union of (for example) ...
1
vote
1answer
27 views

Difference quotient in little-$o$ notation

I understand that, in the following definition of the derivative, $$f'(x_0)=\frac{f(x_0+\delta x)-f(x_0)}{\delta x}+\frac{o(\delta x)}{\delta x},$$ The term $o(\delta x)$ denotes a remainder. And ...
0
votes
1answer
51 views

What does the overline symbol mean?

So I have got a question in an old exam paper for Fourier Analysis. Let $f:I\to C$ be an integrable function. Prove that$\int_I \overline{f(x)}= \overline{\int_I f(x)}$. The problem is that I ...
0
votes
2answers
57 views

What is the meaning of the notation $A :\Leftrightarrow B$?

This is the text from my book: To define a statement $A$ so that it is true whenever the statement $B$ is true, we write $$A :\Leftrightarrow B$$ and say '$A$ is true, by definition, if $B$ is ...
1
vote
1answer
27 views

What is the definition of a single valued function

this is potentially a dumb question but I am a touch confused about some terminology. I'm reading Ahlfor's complex analysis, and I am in a section on integrals of harmonic functions. I may be being ...
0
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1answer
24 views

What does it mean for a subgroup $H$ of an abelian group $G$ to be less than or equal to $G$?

I am reading through some linear algebra lecture notes and have come across the following notation: $$K \leq G,$$ where $G$ is an abelian group and $K$ is a subgroup of $G$. What does this notation ...
1
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1answer
45 views

Notation and Proof: Sets [closed]

List all eight subsets of the set $$A=\{3,5,7\}$$. Let $$A=\{j,m,h\}$$ Explain why $\{A\}$ is not a subset of $A$. We notice that the given set $A$ is finite. It contains three elements: 3, 5 and 7. ...
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vote
3answers
32 views

Definition of surjective - understanding notation

In Measures, Integrals and Martingales by René L. Schilling surjective (or onto) is defined as: $$f(X) := \{f(x) \in Y\,:\,x\in X\} = Y$$ I think I understand the concept of surjective in a function ...
2
votes
1answer
24 views

Partition $\lambda/\mu$ notation?

When talking about two partitions $\lambda$ and $\mu$, what does the operation $$\lambda/\mu$$ mean? When Macdonald introduces partitions in the first chapter of "Symmetric functions and Hall ...
0
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0answers
20 views

Are scalar/vector fields basically just “multi-valued” functions?

Not really familiar with terminology in higher Mathematics, so I will try to use python to express my ideas instead. From Wikipedia: a scalar field associates a scalar value to every point in a ...
0
votes
1answer
16 views

Classes of exponent

I found this terminology in an a paper (link) and did not understand it's meaning. Here is the set of lines that I am talking about: For each prime $p \le g$, we remove all residue classes $\mod p$ ...
2
votes
1answer
56 views

Is there a mathematical symbol for “once”?

I've found a couple symbols that include the concept of once, like "the list of values which appear only once" and stuff like that. Is there a symbol that just means "once" or "one repetition" or ...
2
votes
1answer
30 views

If a word starts with a number, does capitalization apply to the first letter?

If a mathematical word begins with a number and a hyphen, such as "4-dimensional" or $3-manifold," and this word occurs at the beginning of a sentence, should you capitalize the first letter? For ...