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
50 views

How would you describe category $\mathsf{Rel}$?

I encountered two definitions for a category denoted by $\mathsf{Rel}$: Objects are pairs $\left(A,R\right)$ where $A$ is a set and $R$ a relation on $A$. Arrows in ...
8
votes
0answers
82 views

$\sin$ vs. $sin$ - history and usage

One thing newcomers to TeX or MathJax often get wrong is that they write something like $sin(x)$ instead of $\sin(x)$ - the point being that common mathematical functions with names consisting of ...
0
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0answers
13 views

Counts symbol in mathematical notation

Is there specific symbol rather than Sigma, that I can show counts of an element ? Here I would like to say "g" contains elements of type "e", and "T" for all "e" are equal and the number of "e" ...
0
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1answer
29 views

What is the meaning of E and d in this formula?

I am trying to learn the information bottleneck method. On slide 15, they give this equation. I think I understand that X is a random variable (but do not understand the meaning of the exponent, n). I ...
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0answers
25 views

How to show proper set inclusion/exclusion? Please don't give me the solution.

I found this problem from an online source. I've just got two question 1) I think there is a typo in the solution, it should be $(x_n) \in \ell_1$ right? 2) I am guessing $c_0 \subsetneq ...
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0answers
10 views

Notation for expansion of multivariable functions

Let $ f: \mathbb{R}^2 \rightarrow \mathbb{R} $ be some analytic function. I want to say something like, as $ x, y \rightarrow 0 $, the taylor expansion looks like: $$ f(x,y) = a x^2 + b y^2 + ...
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1answer
25 views

Notation regarding the continuity equation for conservation of mass

I have the following equation for the net mass flow out of a control volume through a surface $S$ - $$\int \int_S p \overrightarrow{V} \cdot \overrightarrow{d}S$$ (Actually there should be an ellipse ...
2
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1answer
16 views

Can I write $[x_{i,j}]$ for the matrix whose $\{i,j\}$-th element is $x_{i,j}$?

Is it a general way to write $[x_{i,j}]$ for the matrix whose $\{i,j\}$-th element is $x_{i,j}$? Thanks.
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1answer
36 views

What does this notation mean for Expectation and Variance?

Let $f: \{-1,1\}^n \rightarrow \mathbb{R}$ Then the influence function of $x_i$ is defined by $$ \text{Inf}_i(f) = \mathbb{E}_{(x_1,...,x_{i-1},x_{i+1},...,x_n)}[\text{Var}_{x_i}[f]]$$ What does ...
6
votes
3answers
1k views

Ambiguity of notation: $\sin(x)^2$

Several people have told me that $\sin(x)^2 = \sin(x^2)$. However, on several computing platforms, such as the TI-84 and Wolfram|Alpha, $\sin(x)^2 = \sin^2(x)$. Can I safely conclude that the notation ...
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votes
1answer
41 views

function notations

can you explain how you get this answer? and explain the answer? the distance in feet $d(t)$ a dropped object falls in $t$ seconds is given by the function $d(t)=16t^2$. suppose you drop a ball from ...
3
votes
2answers
96 views

What does$ \|x\|_{\infty}$ mean?

In one of my homework-assignments in analysis, I have stumpled upon $ \|x\|_{\infty}$. I know x is a vector, but what does the infinity-symbol imply? The whole problem is actually this: $\| ...
0
votes
3answers
83 views

How to formulate “The $n$ smallest”

I know how to formulate the set of all $x$ with minimal distance to $y$ with $d(x,y)$ being the distance function: $\{x \mid \arg\min d(x,y)\}$ But how do I formulate the set of the $n$ closest $x$ ...
1
vote
3answers
82 views

Set notation and mappings question

Good evening. I have a question. Suppose I have two sets, $A=\{1,2,3,4\}$ and $B=\{5,6\}$. I want to write the notation for a function that takes each element in $A$ and assigns to it a value in $B$. ...
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2answers
51 views

Is there a symbol, or abbreviation for coefficient of x

Doing some binomial expansions with algebra where I need to equate different coefficients together but don't know what to write: [Coefficient of $x^3$] = _ $k=+1.5$
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2answers
36 views

Notation for writing down products of sets of combinations

I am writing a paper in which I come across an expression analagous to; $$ \prod_{k=0}^{n} (x-r_k) $$ I wanted a nice way of writing down how the $r_n$ relate to the coefficients in the resulting ...
3
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2answers
86 views

Weird integral symbol : $\mathrel{\int\!\!\!\!\!-}$

What does this integral sign mean ($\int$ with line going through the middle)? $$ \mathrel{\int\!\!\!\!\!\!-} $$ (It had something to do with the Beckenbach-Radó Theorem)
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1answer
53 views

Notation for a functor between comma categories

Suppose we have two categories $D$ and $S$, as well as two functors $K,L:D\to S$ and a natural transformation $\varphi:K\to L$. Given another category $C$ and a functor $Y:C\to S^D$, is there a nice ...
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2answers
46 views

Einstein Summation - does the following equality hold: $a_{ij} x_i y_j = a_{ij} y_i x_j$

Does equality hold when $x_i = y_i$ and $x_j=y_j,$ and $ i, j = 1, ..., n $.
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2answers
31 views

Einstein Summation: How do I show $a_{ij} (x_i + y_j) \not= a_{ij}x_i + a_{ij}y_j $?

Einstein Summation: How do I show $a_{ij} (x_i + y_j) \not= a_{ij}x_i + a_{ij}y_j $?
3
votes
0answers
44 views

Notation $(a,b)$ for $]a,b[$.

Is there any logic or justification for the notation $(a,b)$ to represent $]a,b[$? To me this notation is very ambiguous and confusing because it looks like a couple of numbers and not an interval. ...
2
votes
2answers
96 views

Some notation regarding “::”

I'm reading through some geometry proofs, and I can see something like $AB^2:PM\times EB::BC^2\ :CD\times PQ$ So I understand that $A:B$ is equivalent to $\frac{A}{B}$, but what does the $::$ mean?
2
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2answers
30 views

Notation on partial deriviatives

If I need to find $$\frac{\partial ^{2}g}{\partial u \partial v}$$ Then do I want to perform $$ \frac{\partial} { \partial v}\ \big( \frac{\partial g}{\partial u} \big) $$ or $$ \frac{\partial g} ...
0
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1answer
25 views

What's the domain of this function?

$$f(x,y,z) = \frac{1}{x-z}$$ I see two possible domains: $$D = \{x,y,z \in \mathbb{R}\mid x \neq z\}$$ or $$D = \{x,z \in \mathbb{R}\mid x \neq z\}$$ Is it equally valid to say the function has ...
2
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0answers
18 views

How to explain Borel sets and Stieltjes integral to beginner maths student?

The problem is that I know by the definition what Borel sets and Stieltjes integral are but I'm not good to explain in layman terms what they are. Is there easier answer that "write down the ...
0
votes
1answer
34 views

Notation symbol $x$ for functions

On the Modern Stream Ciphers slide #6, the following expression is used: $$ \{0,1\}^s × R ⟶ \{0,1\}^n$$ What does $×$ mean? I've seen $×$ used in a few other contexts, and I suspect it means ...
1
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1answer
19 views

wedge product with and without a second pair of vectors

I am starting to study wedge products, and am stuck on notation. The Bachman book on differential forms says $$ \omega \wedge \nu ( v_1, v_2 ) $$ "gives the area of the parallelogram spanned by ...
2
votes
0answers
160 views

Vector space basis change: is this “index-free” notation correct?

There are already quite a number of questions on basis change in a vector space. Nevertheless, to fully grasp the underlying idea I made up the following notation and I have some doubts on it (note: ...
0
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2answers
45 views

What does this mean exactly?

I am having trouble understanding the following notation, which I encountered studying combinatorics: \begin{equation} \sum_{A \subseteq \left[ n \right]} \prod_{a\in A}x_a \end{equation} where ...
0
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0answers
37 views

What's the right way to write big-O?

I always write $\mathcal{O}(n)$ (\mathcal{O}(n)). But I frequently see $O(n)$ (O(n)), probably because it's shorter and more ...
0
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0answers
21 views

Distributed to symbol for frequency distributions

How would you write down that some random variable $X$ is distributed to a frequency distribution. For the normal distribution e.g. I often see sth. like that: $X\sim \mathcal{N}(\mu,\sigma^2)$. Is ...
0
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0answers
32 views

Terms for particular equivalence relation and partition?

Let $T$ be a set of sets. Let $\equiv$ be an equivalence relation on $\bigcup T$ defined by the formula $$a\equiv b \Leftrightarrow \forall X\in T:(a\in X\Leftrightarrow b\in X).$$ Let $S$ be a ...
6
votes
1answer
120 views

What is the mathematical truth behind the Leibniz notation in differentiating twice or more?

So $f: \mathbb{R} \to \mathbb{R}$ is $n>1$ (or more) times differentiable. The notation of the first derivative makes perfect "sense" with regard to what's going on: $$\lim_{h \to 0} ...
1
vote
2answers
48 views

Partial derivative in two dimensions

I am struggling with section 3.3 of the following thesis https://smartech.gatech.edu/xmlui/bitstream/handle/1853/29610/grigo_alexander_200908_phd.pdf. Page 21 is fine, then the problems occur in ...
1
vote
2answers
48 views

What do $\Bbb N^*$ and $\Bbb Z(p^n)$ mean in this paper?

There is a theorem: in this paper: http://journals.cambridge.org/download.php?file=%2FJAZ%2FJAZ78_01%2FS1446788700015548a.pdf&code=2ffd5c5100675caf83c2e95bce65491e But there is no explanation ...
0
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1answer
32 views

Are several equality operators okay to use in mathematics?

For example, is it okay to say: $x=y=z=1$ if $x,y,z$ all equal $1$?
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0answers
28 views

What is an open property?

From an academic paper, "the existence of elliptic or hyperbolic 2-periodic orbits is an open property". I have never seen the term "open property" used before, moreover the paper gives no ...
3
votes
2answers
61 views

Is it proper to write $\int \partial x$

For single variable function, you write $\int dx$ But for multivariable function, can you write $\int \partial x$?? I've never seen the latter, can someone explain why?
3
votes
2answers
51 views

Notation for “should be equal to”

Suppose I have some (possibly complicated) expression depending on one or more parameters, and a value which this expression should have for the solution I'm interested in. How do you write that, in ...
1
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1answer
29 views

Notation for repeated composition of functions

I have a repeated composition of functions ${T_n}(z) = {\tau _0} \circ {\tau _1} \circ {\tau _2} \circ \cdots \circ {\tau _n}(z)$ By analogy with $\sum\limits_{i = 1}^n {} ,\prod\limits_{i = 1}^n ...
0
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1answer
32 views

How are the essential upper and lower limits defined?

What means \begin{equation} \operatorname*{ess\,lim\,inf}_{x\to x^*} F(x) \end{equation} and \begin{equation} \operatorname*{ess\,lim\,sup}_{x\to x^*} F(x)? \end{equation} Sorry I also do not know in ...
0
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2answers
36 views

Are 400 and 45 correct for CD and VL in roman,respectively?

can VL and CD be roman numerals for 45 and 400 respectively? By the way,I already tried CCCC for 400.
0
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2answers
46 views

What is the notation for the number of elements in a set?

Let's say S = {1, 2, 3}. There are 3 elements in S. How do I express this in notation? I tried using google but I could not find what I was looking for.
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1answer
32 views

Notation for proof with Tensors

I'm working on proving For a second order tensor $\mathbf{A}$,$\mathbf{u}\cdot\mathbf{A}\cdot\mathbf{u}=0$ for all vectors $\mathbf{u}$ if and only if $\mathbf{A}$ is skew symmetric. Now, I ...
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0answers
11 views

Notation question about scalar products and bilinear forms

Quick notation question. Is it necessary to distinguish between a scalar product and say a bilinear form $A: V \times V^* \rightarrow \mathbb{R}^n$. Would it be recommended that say you define ...
3
votes
1answer
137 views

Problem with notation in a thesis

I am struggling with section 3.3 of the following thesis https://smartech.gatech.edu/xmlui/bitstream/handle/1853/29610/grigo_alexander_200908_phd.pdf. Page 21 is fine, then the problems occur in ...
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1answer
22 views

Is there a notation for incomplete quotient

If $n, m > 0$ are integers and $m \nmid n,$ how to denote the incomplete quotient this division?
1
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1answer
39 views

What does this function notation mean?

My text tells me that the general term of a sequence can be looked at like a function: $ f:\mathbb{N}\rightarrow \mathbb{R} $ What does that mean translated into common english?
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1answer
32 views

Question About Group Theory Notation

I am having trouble understanding what "Universal Cover of $\mathbb{Z} \times \mathbb{Z}$" mean exactly. Thanks
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1answer
58 views

How to find the domains of functions $f(x) = x-5$, $g(x) = \sqrt{x-5}$, and of their sim?

I've been studying on Study Plan Practice, on MyMathLab for my College Algebra class. We're going over the Algebra of Functions right now and several things don't make much sense. The question is: ...