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
45 views

what does this summation mean?

I apologize if this question has been asked. I know several similar ones have been asked but I cannot find one answering this in particular. I want to know what this summation means: ...
2
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1answer
34 views

Is there any good reason against referring to employed equations over the relation sign when establishing a new relation?

I need to write down a complicated proof for a paper, for which I need to employ equations that I established earlier for almost every new relation I show. I would consider it best for the reader, if ...
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1answer
18 views

How to mathematically describe a loop over a set with two indexes.

I have a set of sets $G = \{D_{0,0}\,D_{0,1}\,D_{0,2}\,D_{1,0},...,D_{n,0}\,D_{n,m}\} $ What I know want to express is a constraint that for each set in $ G $, if $ x \in D_{0,0} $ then the statement ...
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1answer
61 views

What is varpi in Zhang's notation?

In his video from this summer at the IHES on bounded gaps between primes, T.Tao uses the $\varpi$ notation as shown here : When asked what his notation means in this context, he answers that he ...
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2answers
20 views

How to mathematically describe the number of Element x in a set

I am trying to formulate the following. I have a Set A={x, y, z}, I also have a Set B, C and D, which all are subsets of A. It is not exactly defined which elements are in B, C and D. I only want to ...
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2answers
42 views

Have I properly used $\,\exists !\,$ in this statement?

I want to express the following in logical notation. For every natural number, there is a unique natural number that succeeds it. Does the following statement express that proposition? ...
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0answers
17 views

Function Notations

Let $f:X\to Y$ be a function and let $x\in X$. For the image of $x$ under $f$, a popular notation is $f(x)$; while some author prefers $(x)f$. To me, $(x)f$ is far more natural as if we apply a ...
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1answer
51 views

suggest a topic about history of mathematics

Can you suggest a topic (the history of mathematics) concerning the evolution of a given concept from a document written in English from varied scientific resources What do you think of the ...
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2answers
31 views

Why $E^2$ instead of $\Bbb R^2$

I was reading a paper earlier where whenever the author would discuss vectors in polar coordinates, he'd call the space $E^2$. He'd even give a function of vectors in that space as $f:E^2 \to \Bbb ...
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1answer
37 views

Interpretation of hint for Exercise 2.19b of Eisenbud

I am doing exercise 2.19b of Eisenbud's Commutative Algebra with a View Towards Algebraic Geometry. Here we have an $R$-module $M$ and elements $\{f_i\}$ which generate the unit ideal. The exercise ...
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1answer
21 views

Clarification on notation

For a graph $G$, put $δ(G) = \text{min}\{\deg_{G} (v) : v \in V\}$ (the minimum degree of $G$). Prove $χ(G) \leq 1 + \text{max}\{δ(G ) : G' \subseteq G\}$, where $G' \subseteq G$ means that $G$ is a ...
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21answers
9k views

Most ambiguous and inconsistent phrases and notations in maths

What are some examples of notations and words in maths which have been overused or abused to the point of them being almost completely ambiguous when presented in new contexts? For instance, a ...
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1answer
48 views

Incomplete statement of commutativity of summation in Concrete Mathematics?

My text (p. 30, eq. 2.17) states the "commutative law" for sums as $$\sum\limits_{k\in K}{a_k} = \sum\limits_{p(k)\in K}{a_{p(k)}}$$ where $p$ is a permutation and $K$ is a set of integers. While ...
2
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1answer
39 views

What does single parentheses mean?

I see look at Changing a number between arbitrary bases, Math Gems answer and see such annotation : 1⋅6+2=10)6=60)+1)=61)6=446)+3=451 What does 10)6 mean? What single ")" mean? Mathematics teacher ...
2
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1answer
65 views

What is the purpose of the symbol $\int f(x)dx$? [closed]

In elementary calculus I was taught that given $x\in\mathbb{R}$ (or $\vec x\in\mathbb{R}^n$) if the limit $$\lim_{\delta\to 0}\sum_{i=1}^n f(x_i)\Delta_i\ \ \ \ (\ \text{or }\lim_{\delta\to ...
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1answer
27 views

about $\nabla^{4}\Phi=0$, write down this equation in terms if Cartesian Coordinates

$\nabla^{4}\Phi=0$, write down this equation in terms if Cartesian Coordinates(x,y). I am a bit confused here, the question doesn't tell you if $\Phi$ is scalar or vector, but i think it is a vector, ...
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3answers
39 views

Does every element of the empty list posses every property?

Suppose we have a list of elements $v_1, v_2, \ldots, v_n$. Then, as I've understood, setting $n=0$ above results in the empty list $v_1, v_2, \ldots, v_0$ of no elements (please correct me if I'm ...
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0answers
27 views

Need help in a question related to Matrix notation

Can anyone please help me with this question?
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4answers
42 views

Let $S$ be a set. How is $f(S) = S$ different from $f(s) = s$ for all $S$?

Usually, $f$ denotes a function, $f(x)$ is an image of $x$ under $f$. But what's $f(X)$ if $X$ is a set? edit: Please, disregard the body of this question. I had to put something here to be able to ...
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0answers
21 views

Intersection of Elements from Sets of Sets

Say I have 2 sets of sets: $$ X = \left \{ \left \{ 1,2 \right \}, \left \{ 3,4 \right \} \right \} $$ $$ Y = \left \{ \left \{ 1,3 \right \}, \left \{ 2,4 \right \} \right \} $$ I want to express ...
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1answer
33 views

How correctly define the pixel intensity of an image?

Let's do easy: I have an image IM and p(i,j) is the discrete intensity value of a pixel in the image IM (not necessarily 2-dimensional)..... How can I mathematically correctly define this? Thank you ...
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3answers
50 views

“sup” in an equation

I am currently reading through JC Lagarias' "The $3x+1$ Problem and its Generalizations" and have come across some notation reading : $$\sup_{K \ge 0} T^{(K)}(N)$$ Now I assume that this means ...
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1answer
43 views

What does $Du$ mean in a differential equation?

I'm very interested in the following work: http://maths-people.anu.edu.au/~andrews/HSU_Survey141105.pdf . Unfortunately, the author uses (in this and other papers I'm interested in) the notation $Du$. ...
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2answers
39 views

Can I say that a fixed constant is less or equal infinity?

Mathematically speaking, given $c\in\mathbb{R}$, can I say that: $c\leq\infty$? E.g., is $10 \leq \infty$ a correct mathematical statement? I know this comparison is true in computer arithmetic, ...
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0answers
41 views

Analytic Functions: Notation? [duplicate]

Analytic functions are usually denoted by $\mathcal{C}^\omega$. What does the $\omega$ stand for? (The infinity symbols of a colleague of mine really look like omegas...)
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0answers
27 views

In logic is there a concise way to express the quantity of things that a predicate applies to?

I have $Fxy$, where F stands for 'falls on'. I want to express the number of such relations in the world. How would I notate this in formal logic?
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2answers
28 views

Help me evaluate this equation in Scientific Notation

How do i solve this using Scientific Notation? $$ \frac{3\times 10^8}{4\times 10^{-5}} $$ I have been trying for hours now! Help please
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0answers
33 views

Notation for a sum product

I'm struggling with notation for a sum product. Let $f:Z^+\rightarrow Z^+$. I am interested in a sum where each term is the product of functions whose sum of arguments equals $n$. For example if $n=3$ ...
13
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1answer
196 views

Did Einstein introduce anything new to mathematics? [duplicate]

Newton introduced calculus, so I am wondering, did Einstein introduce anything important to mathematics?
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0answers
15 views

What is the mathematical notation for the mode of a distribution?

Am writing an economics paper wherein defining a dummy variable as a taking the value one if the value of one variable is greater than the mode of another. What would be the best way to write this ...
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3answers
90 views

In logic, do the $\Longrightarrow$ and $\rightarrow$ signify different things?

In logic, do the $\Longrightarrow$ and $\rightarrow$ signify different things? Are there contexts where one is more appropriate than the other? I had believed that the $\Longrightarrow$ was for ...
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1answer
39 views

How to write notation for this function?

Say $X=(x_1,x_2,x_3,..,x_n)$, and there is a function of $X$, which is $f(X)=g(h(c,X))$ where $c$ is constant. Now in my case, given a $X_0$,there will be a function $i_1(x_1)$, which takes $x_1$ in ...
0
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1answer
15 views

How do you use mathematic logical notation to notate a function whose output positively correlates with the input?

Suppose the amount of weight John gains from a meal is a function of the number of calories he eats, and that John will gain X weight, such that X>A, if he consumes Y calories, such that Y>B, where A ...
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1answer
20 views

Question about Set Notation and Minimization: $\colon, \mid$

I see many different notations in context of sets, minimization. For example $$\min_{x \in X} f(x),$$ $$\min \{ f(x) \mid x \in X \}$$ $$\min \{ f(x) \colon x \in X\}$$ and so on.. Is there any ...
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0answers
17 views

What does the notation [v]_{\times}^2 mean in this answer?

I was reading this answer http://math.stackexchange.com/a/476311/191081 I don't understand the notation in the second equation (given below) $$R = I + [v]_{\times} + [v]_{\times}^2{1-c \over s^2},$$ ...
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0answers
9 views

notation question: what is $|f|_{\mathcal C^0(I\times J)}$

For $I=[\xi,\xi+a], J=[\eta-b,\eta+b]$ and $f(\cdot ,\cdot )\in\mathcal C^0(I\times J)$ where $a,b>0$, how do we define $|f|_{\mathcal C^0(I\times J)}$ ? Is it $$|f|_{\mathcal C^0(I\times ...
1
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2answers
31 views

Derivative notation?

I am getting a bit confused with the primed notation for derivatives, does $$f'(g(x))$$ mean the first derivative of $f$ with respect to the spacial coordinate $x$ or with respect to $g(x)$. If it is ...
1
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0answers
28 views

Proper notation for a generalization of the Liouville $\lambda$ function

Can someone suggest good notation for a simple generalization of the Liouville Lambda function, $\lambda(n) = (-1)^{\Omega(n)}?$ I would like to express that $\lambda_{k,r}(n) = 1$ if ...
0
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1answer
33 views

Arithmetic operations on sets

Is there a formal definition for a system where you can perform arithmetic operations on sets, for instance, $2 \cdot \mathbb{Z}$ = the set of even integers? If there is, what is it called? What ...
1
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0answers
16 views

Why is the sample set notated with $\chi$ in statistics?

My professor of statistics based his lesson notations on H. Georgii's work 'Stochastics'. The sample set is thereby notated as $\chi$, instead of the usual $\Omega$. I don't really understand the ...
0
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1answer
22 views

notation for precision or number of decimals

If you have a formula like $x = y+2.1234$, is there a way to specify $y$ should have no more than 2 decimals? So if $y = 12.1234$ then you should use 12.12 when using this formula. Same for the ...
0
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1answer
23 views

Mathematics Notation Help: For each elements within a dataset, count all elements within and space time window

So for every element in the current data set DC, has a space property i(s), and time property i(t). For each of these elements, I count of elements with the space window (SW) and time window (TW). ...
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1answer
15 views

Difference in the function (Game Theory)

I was hoping to know the difference between equation (1) and equation (2). Would they be considered equal or is equation (2) less strict compared with equation (1)? Let the correspondence ...
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0answers
28 views

How to read an expression that is ambiguous?

(1) How should I parenthesize $\log n \log \log n$? Also: (2) What general rule/rationale is used to do this parenthesization? To elaborate; I see why $\log\log n$ is unambiguous, but $\log n \log ...
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2answers
46 views

Question about set notation regarding removal of elements

Consider the sets \begin{align*} \mathcal{A} &= \{1,2,3,5,7\}\\ \mathcal{B} &= \{2,4,6,8\}\\ \mathcal{R} &= \{2,5\} \end{align*} I want to remove the elements in $\mathcal{R}$ from ...
2
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2answers
36 views

What is the mathematical notation for a random number in a certain range?

In school, I was taught to denote a random variable like so: $$R=\{_{0}^{1}$$ This only goes for a random choice between two integers, like a coin flip. How do I write a variable that is equal to a ...
2
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0answers
38 views

When is iterated exponentiation used and how is it defined?

I was thinking of ways to define an iterated exponentiation operation. The nice thing about addition and multiplication is that they're associative and commutative, which makes defining the sum and ...
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0answers
29 views

How to denote the set of non-negative rationals?

How would you denote the set of rationals greater than or equal to zero? I was thinking $Q^+$ but I don't think that's quite right.
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0answers
65 views

Subgroup notation on Wikipedia

Surfing wikipedia about finite groups, I see a lot of notation similar to that found in this section (image below). Its meaning is not clear to me and I didn't find an explanation on wikipedia. Could ...
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1answer
29 views

How to mathematically note down “sum of all elements / numbers of elements”

I have 1-n elements and I sum them up (I1+I2+I3...In)/N. Also for 5,5,8 the result is 6. I am not sure about the mathematical notation of the formula.