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Questions tagged [notation]

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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Mixed Fractions and Multiplication (with Variables)

I stumbled over this expression: $3 \frac{1}{x^3}$. How should you interpret something like that? While you could see that as implicitit multiplication ($3 * \frac{1}{x^3}$), you could also argue ...
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1answer
45 views

Soft question - are these two set notations correct?

Do these sets equal the interval notation given? \begin{align} T&=\{t\in \mathbb{R}:t^2\lt{2}\}=(-\sqrt{2},\sqrt{2})\\ S&=\{s\in \mathbb{R}:s^2\leq{2}\}=[-\sqrt{2},\sqrt{2}] \end{align}
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0answers
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Notation for the operator that transforms sets (unordered) into tuples (ordered)?

Take a set $\mathcal{A}\equiv \{a_1,a_2,a_3\}$ of real numbers. Is there any specific notation in math for the "operator" that transforms $\mathcal{A}$ into the 3-tuple (ordered) $$ (a_1,a_2,a_3) $$ ...
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1answer
29 views

Suggestion for notation of a sequence

What could be a good notation for a sequence $(x_n)$ chosen from a vector space $\displaystyle V= \bigcup_{n\in \mathbb N} f_n(V_n)$ where all $V_n$ are vector spaces and $f_n$ are linear maps.
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1answer
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How to properly get the sum of products for all elements of a set

I'd like to express the following: Sum up all products of a and b of all elements in a set. To be a little more specific: Let's says we have employees that have a certain rate and worked a certain ...
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1answer
75 views

Can this “new” notation for Maclaurin expansions be useful? [on hold]

Here is a notation for Maclaurin expansions that I made up: \begin{align*} sin(x) &= \sum \{alt(+); \frac{x^n}{n!}; \text{ n odd $\in$ $\mathbb{N}_0$} \} \\ cos(x) &= \sum \{alt(+); \frac{x^...
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1answer
16 views

How can I notate the assignment of each variable in a tuple to a specific value?

Assume I have a tuple of variables, i.e. $\mathcal{T} = (x_1,...,x_n)$. Now I would like to assign each of those elements in the tuple to the same value $c$. How I can I denote this in a formally ...
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0answers
27 views

Understanding minimum/maximum and minimal'maximal elements in a partial order.

I don't understand, are "minimal/minimum/maximal/maxium" elements properties of a partial order or properties of base sets of partial orders? Given any partial order $(X,\leq)$ from what I can gather,...
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1answer
52 views

Is there a notation for least/greatest element of partially ordered set?

Definition. Let $P=(S,\leq)$ be a partially ordered set. If it is true that $$(\exists s_0\in S)\ (\forall s\in S)\ \ s\leq s_0$$ then $s_0$ is said to be a greatest element of $S$. Of course, ...
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1answer
44 views

Integral d notation

Is the following notation somehow wrong (or rather can it produce wrong results)? $$\int{f'(x)dx} = \int{df(x)} = f(x) + C$$ As far as I know this is pretty standard notation in many Russian textbooks....
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1answer
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Prove $\sum 3^k = O(3^n)$

Prove $\sum_{k=0}^n 3^k = O(3^n)$. Below there is a picture from my text that contains the proof. My question pertains to the notation and/or assumptions in the proof. I don't need help with basic ...
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0answers
47 views

Define a subset from another set

I have a closed disc $D$ \begin{equation} D=\{(x,y) \in \mathbb{R}^{2}: (x-a)^{2}+ (y-b)^{2} \leq R^{2} \} \end{equation} centred at the origin $(a,b)=(0,0)$ and with radius $R=15$ [m]. I have ...
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0answers
47 views

Can anyone explain the following slash notation?

This notation can be seen made use of in equation 1.5 of https://arxiv.org/pdf/1311.5200.pdf Roughly speaking, $$\left. I = \int f(z) \prod_a \frac{dz^a}{z-z_a} \middle/ d\omega \right.$$ where $$d\...
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2answers
27 views

How to interpret notation $X: [0,T] \times \Omega \rightarrow R^d $ for a stochastic process?

How to interpret notation $X: [0,T] \times \Omega \rightarrow R^d $ for a stochastic process, where $T$ is time, $\Omega$ is a set of outcomes and $R^d$ denotes real numbers in $d$ dimensions? Is $\...
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1answer
49 views

Scalar Multiplication of a Set

I am aware of how one can represent the Cartesian product of two sets, say $A$ and $B$. However, is there are standard way to represent the scalar product of a value and a set/multiset? As a simple ...
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4answers
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Should one use “tends to” or “equals” when dealing with infinity?

Is this perfectly valid: $$\lim_{x\to0}\frac{1}{x}=\infty \tag{1}$$ or should I use: $$\frac{1}{x}\to\infty\quad\text{as}\quad x\to0 \tag{2}$$ or likewise: $$\lim_{x\to0}\frac{1}{x}\to\infty \tag{3}$$ ...
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2answers
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Euclidean division? ( $16=5\cdot 3+1$ vs $16=3\cdot 5+1$)

Is the equality $16=5\cdot 3+1$ the euclidean division of $16$ by $3$ or not ? This question is a point of discord between teachers where some them state that the divisor must be written in the first ...
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1answer
44 views

Notation question: Is there a difference between centered dots and lower dots?

In mathematical notation, do the "lower dots", i.e. $A, B,\ldots , K$ have a different meaning than the "centered dots", i.e. $A, B, \cdots, K$? For instance, is it the case that lower dots are used ...
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0answers
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Expression for maximum column index of every row in matrix

Let $H$ is $(k \times j)$ matrix. How can one describe "for every maximum column of each row in $H$"? Can I write $\underset{j}{\text{argmax}} (H_{kj}), {k = 0,\ldots,K}$? I feel something is wrong ...
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1answer
42 views

What is $P(A\mid B)(C\mid D)$? Is this the same as $P(A\mid B) \times P(C\mid D)$?

I'm curious about the general case but also need to understand if $P(A|B)(C|D)$ is the same as $P(A|B) \times P(C|D).$ In equation (7), it states Is this the same as $P(u|f,s) \times P(f|s)$ ? The ...
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1answer
45 views

What are the different symbols used for denoting an angle?

This is not a question involving numbers and stuff, but suddenly had this basic question in mind: What are the different symbols that different people use for denoting an angle? (I mean, we usually ...
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0answers
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How to note several transformations at once like 2x-4=0 | +4; :2

I have a long equation in a TeX document and want to show help the reader to see clearly the transformations. On the other hand I do not want to repeat the equation for every little perhaps trivial ...
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1answer
34 views

Confusion about the notation of empty interval

Currently, I'm studying about intervals. I got the basic understanding and knowledge about them but while reading the page about intervals in Wikipedia, under the classification of intervals tab, I ...
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1answer
54 views

How to Write This Properly in Set Theoretic Notation? [closed]

Using set theoretic notation, how do you write a set A that contains 4 letters of the alphabet that precedes x (i.g. 'b')?
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1answer
27 views

Is value in the matrix notation

Given an $m\times n$ matrix $A=\begin{bmatrix} a_{1,1}&...&a_{1,n} \\ \vdots&\ddots&\vdots \\ a_{m,1}&...&a_{m,n} \\ \end{bmatrix}$, say that I wanted to describe a set ...
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1answer
44 views

What is the difference between “divides” and “divides exactly”? [duplicate]

Maybe this is the sort of question I could find the answer myself if I just knew the right search terms. I've gotten a whole bunch of search results and quite a bit of sidetracks. In my handwritten ...
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2answers
45 views

what does the notation $x^{(n)}$ mean?

What does the notation $x^{(n)}$ where $x$ is a matrix and $n$ is an integer? $$\|W^T\mathbf{x}^{(n)}+b-y^{(n)}\|_2^2$$
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0answers
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Appropriate terminology for classifying some assumptions

I would like your help in order to choose the appropriate terminology for classifying the assumptions below. Consider a random vector $X\equiv (X_1,X_2,X_3)$. Let $\Delta X\equiv (X_1-X_3, X_2-X_3, ...
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0answers
62 views

Naming a sum such as $\sum\limits_{x=1}^{n}{x}=\frac{n(n+1)}{2}$

If we let consider a simple sum such as the following: $$\sum_{x=1}^{n}{x}=\frac{n(n+1)}{2}$$ Would it be correct to name the function that equals $\sum\limits_{x=1}^{n}{x}$ for a given upper bound,...
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1answer
23 views

Wedge and common notation for “a line between two points”

I'm using a somewhat old presentation from 2011 that covers twistor geometry. It uses the notation "$L = Z_1 \wedge Z_2$" to suggest that the line $L$ is the "join of the twistors $Z_1$ and $Z_2$, ...
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0answers
32 views

What does $\sim_k$ mean

I am reading the following lecture notes:(http://www.math.ucla.edu/~tao/247b.1.07w/notes8.pdf) regarding stationary phase integrals, specifically concerned with their asymptotic behavior and there is ...
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1answer
31 views

C-like type declaration.

In most math books declaring an object along with its type is done with the type after a colon after the object, and the definition of this object is done in another expression. E.g. $$ \begin{align} ...
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1answer
39 views

Is there a notation for the unique value that satisfies a predicate?

Let's say that we have a predicate $\phi$ such that $\exists!x.\phi(x)$. Is there a notation for denoting the unique value of $\phi$? Of course you can just say "let $x$ be the unique value such that ...
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0answers
43 views

What is the meaning of this ampersand and exclamation mark?

On the top of page 4 of this paper Direct Construction of Minimal Acyclic Subsequential Transducers, there is an expression $$\forall r \in S\ \forall a \in \Sigma\ \forall \sigma \in \Sigma^*\ ((\...
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1answer
30 views

Confusion about the tensor product and matrix multiplication

This is a question I came across looking at special relativity and tensor products. For example, we have the metric tensor and its corresponding matrix representation $$ g_{\mu\nu} = g^{\mu\nu} =\...
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2answers
69 views

Difference between $[a,b]\in \mathbb R$ and $[a,b]\subset \mathbb R$?

What is the difference between the following? Are they both mathematically correct? \begin{align} [a,b]\in \mathbb R \tag 1 \\ [a,b]\subset \mathbb R \tag 2 \end{align} And also, which one should I ...
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1answer
32 views
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1answer
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A raised star (asterisk) in an entropy formula

I am reading a section in a book about translation. The formula below is given as a mathematical way to calculate word translation entropy. So for a source token s ...
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1answer
40 views

Origin of infix notation

Wondering where the infix notation of things like 1 + 2 came from, when roughly it came about, and if it was before/after prefix or postfix notation. I know the ...
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0answers
40 views

Standard Unicode symbols for logic operations

There are these logic gates symbols, but I am looking for the more low-level math-like symbols such as those found here, but for all the logic operations. There doesn't seem to be a central place for ...
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1answer
39 views

What does $D^{\alpha}$ usually mean?

$\alpha = (\alpha_1,\cdots,\alpha_n), \, |\alpha| = \alpha_1 + \cdots + \alpha_n,$, and this is how $D^\alpha$ is defined in the notes I’m using to study distribution theory: $$D^{\alpha} = \left(\...
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0answers
54 views

Notation for using a relation as a function from an element to set?

Let $R \subseteq X \times Y$ Is there a commonly used term/notation for the functions $f:X\rightarrow \mathcal{P}(Y)$ and $g:Y\rightarrow \mathcal{P}(X)$ defined as follows?: $$f(x) = \{ y \mid (x, ...
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1answer
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What is an asymptotically nonnegative function?

I was reading up on the definition of theta- notation and came across this, The definition of $\Theta(g(n))$ requires that every member $f(n) = \Theta(g(n))$ be asymptotically nonnegative, that ...
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0answers
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Generalise to any dimension some notation

I would like your help to generalise to any dimension and in the most simple way the following piece of notation (written for dimension $3$). Step 1: Consider the 3 dimensional random vector $\...
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1answer
21 views

Understanding the meaning of the notation $([x_{i-1},x_i],t_i)$

When learning about tagged partitions I'm introduced to the notation $([x_{i-1},x_i],t_i)$. Is this referring to all numbers y such that $x_{i-1}<y<t_i$ ? Or does it mean something else? Cheers
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2answers
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What is the difference between “$=$” and “$\equiv$”?

I was recently thinking about some of my past math classes, and depending on the context I recall my professors would sometimes use the "$\equiv$" symbol in places where I'd feel "$=$" to be more ...
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2answers
15 views

Notation for a Point being between two Other Points

Let $x$, $y$ and $z$ be real numbers. Is there any notation that means that $x$ is between $y$ and $z$? If $y$ is less than or equal to $z$, then the notation $y \leq x \leq z$ can be used, and there ...
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0answers
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How do I find what common notations stand for?

I am reading a paper that defines a Gelfand triples. The paper states: "We define the Gelfand triple of Hilbert spaces $V \subset H \subset V^*$ by $$H= (L^2(D), <\cdot, \cdot>, ||\...
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2answers
39 views

What is the base of this exponent?

Given the following, what is the value of $ 2b^5 $? $$ b = 5 $$ $$ 2b^2 $$ I'm confused as to whether the exponent applies to $ 2b $ or just $ b $. Thus, does $ 2b^2 $ equal 50 or 100? What is the ...
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1answer
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“nothing” in boolean algebra

Is there formal notation for saying "there is no x for which P(x)" or is it simply something like $( \neg \exists x) P(x)$?