# Tagged Questions

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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### Notation Question for summations

I came across this notation in a textbook of Algebra. With respect to the definition of linear independence in a Vector Space $V$. We define a subset $S = \{\alpha_i \ | \ i \in I\} \subset V$ as ...
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### Is there a name for this theorem about the convergence of a function?

Let $f(x)$ be a continuous function over $\mathbb{R}$ such that for all $a < b$, we have $a < f(a) < b$. Then, for any $x < b$, the sequence $\{t_n\}$ defined by $t_0 = x, t_n = f(t_{n-1})$...
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### Multiplying subscripts

I'm not too good with math, but once in a while I like to fiddle around with it. But one question has been bugging me lately. Let's say I have $x_{1} = 1$, $x_{2} = 2$, etc, $x_{352} = 352$. Is there ...
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### Is there another notation for a characteristic of a domain of a measurable function?

Let $(X,\Sigma,\mu)$ be a measure space and $E\in\Sigma$. In measure theory language, one can prove that $\int_E f d\mu = \int \chi_E f d\mu$. Here, $\chi_E$ is not a function, but it merely means ...
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### Why do we make a distinction between derivatives and partial derivatives?

The definition of a partial derivative is the "derivative of a multi-variable function relative to a single variable when all other variables are held constant". But isn't the regular derivative (for ...
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### why the square root of x equals x to the one half power [duplicate]

Could someone explain how/why the square root of $x$ equals $x$ to the one half power? I know by definition it does, but is there any mathematical process we can go through to get from one to the ...
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### whats the difference between $|v|$ and $||v||$?

$v$ being a vector. I never understood what they mean and haven't found online resources. Just a quick question. Thought it was absolute and magnitude respectively when regarding vectors. need ...
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### What is this form of 'notation' called?

I was reading some of Max Tegmark's lecture materials and I found this little thing. Is there a name for it? Specifically, I am talking about $S_1$ R $S_2$ & $S_1$ R $S_2$ and the matrix. Is ...
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### What's the difference between ]a,b[ and (a,b)?

Is there any difference between $]a,b[$ and $(a,b)$? If there is no difference, what would be the motivation of using $]a,b[$ over $(a,b)$?
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### What is meant by this notation?

I found the following question: Let $\large f(x)=e^{x^2}$. Find and simplify $\large{f^{(3)}(x)}$. Is it asking to find the third derivative of the function? Which rule is used to find the ...
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### Notation Question (Meaning of double inclusion symbols)

What does the notation $\subset \subset$ mean? In my class notes, our prof writes $\Omega \subset \subset \mathbb{R}^{n}$ to mean that "$\Omega$ is a convex subset of $\mathbb{R}^{n}$". Is that all ...
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### What does $a$ mean in Taylor series formula?

I'm trying to code the Taylor summation in MATLAB, being Taylor's formula the following: I've also seen $a$ denoted as $x_0$ in distinct bibliography. Problem is that I'm not sure how should I ...
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### Regarding the notation $f: a \mapsto b$

While I have come to understand that $f:a\mapsto b$ means that for input from the set $a$, the function will return a value from the set $b$, I am curious as to how far one may "drag" this notation. ...
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### Ambiguity in Reverse Polish notation

Given the infix form: 1 * 2 * 3 What is the Reverse Polish notation? As I see things, two valid answers are: ...
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### Tensor product symbol and convolution

The convolution of $f$ and $g$ is sometimes written as $f\ast g$ and sometimes as $f \otimes g$. Is convolution denoted by both of these symbols because the operations are related, or is it just ...
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### Notational Question : (a) = (b)

What does the notation (a) = (b) mean? For context, a and b are elements of a ring. I have tried to find an answer by googling, but it's difficult to do this since I am not sure what to call it.
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An answer to one question claims that if it is true that $B=\{a,b\}, G=\{\{a,b\}, \{c,2\}\}$, then it is also true that $\{B\}\subseteq G$ But wouldn't $\{B\}=\{\{a,b\}\}$ and there is no $\{\{a,b\}\... 0answers 73 views ### What is the correct notation for defining norms in measure spaces? For a function$f \in L_2(R)$, we can define its norm as $$\|f\|_2^2 = \int f^2(x) dx$$ If I use a different measure$\mu$, I can in turn define the norm as $$\|f\|_2^2 = \int f^2(x) \mu (x) dx ... 1answer 135 views ### Explain the symbol \bigvee in “Adventures in Stochastic Processes” What does the symbol \bigvee mean in statement 1.5.1.2? Thank you. 2answers 132 views ### Notation for quotient ring I'm wondering where the notation for the quotient of a ring by an ideal comes from. I.e., why do we write R/I to denote a ring structure on the set \{r+I: r\in I\}, wouldn't R+I be more natural?... 3answers 71 views ### In set notation, why does the meaning of A differ from the meaning of {A}? If the identity of a set depends on what the set contains, then wouldn't a set represented as A contain the same entities a set represented as {A} contains? 1answer 124 views ### What is the proper notation for integer polynomials: \Bbb Y=\{p\in\Bbb Q[x]\mid p:\Bbb Z\to \Bbb Z\}? I would like to write down some of my thoughts on "the set of polynomials p\in\Bbb Q[x] which map the integers to the integers" and I would like to know what the proper notation is for discussing ... 5answers 743 views ### What does this symbol “\gg” mean I was reading a paper and came to a symbol as follows: "\gg" (e.g. x\gg 5). What does that mean? Is it larger than or has more information to mention? Thanks. 2answers 43 views ### Help with notation: \triangle_{\gamma}\arg f? What is denoted by the term \triangle _{\gamma} \arg f , where f is analytic in region of complex plane and \gamma is any curve in the region. Can anyone explain me this notation with example? ... 2answers 142 views ### Is there a factorial for factorials? Is there a more succinct way to notate this?$$(n!)((n-1)!)((n-2)!)\cdots(2!)(1!)$$for clarification, if I had asked a similar question, how to succinctly notate:$$(n)(n-1)(n-2)\cdots(2)(1)$$I ... 1answer 207 views ### Use set notation to define vector or matrix? I'm looking for a concise way to define the following (horizontal) vector:$$\mathbf{x} = [x_{-k}, \dots ,x_{k}]$$where x_k = \mathrm{i} if k is odd and zero otherwise, and |k| \le K . So ... 1answer 60 views ### Comparison of notation for sets Different authors use different notation, no question here...but doesn't this make the study of maths a little more difficult, always chasing different definitions of how a set is represented? I ask ... 0answers 156 views ### What is a common symbol for angles and what are semantic differences? I've just seen that LaTeX offers at least three symbols for denoting angles: \text{\sphericalangle}:\sphericalangle ABC \\\text{\measuredangle}:\measuredangle ABC\\\text{\angle}: \angle ABC I ... 1answer 127 views ### Comma after equation ps: I have asked this question on http://tex.stackexchange.com/ (here) but is regarded as off-topic. So I moved it here. I have seen different ways in papers to put comma after equation. right ... 2answers 289 views ### Difference between two inequality symbols I have come across the symbol \leqq in a paper I am reading. Is there any difference between this symbol and the symbol \leq ? 1answer 1k views ### Notation: using dot instead of argument Is there any difference between: f\left(\cdot , \theta \right) is continuous in x for each \theta f\left(x , \theta \right) is continuous in x for each \theta 1answer 53 views ### Notation for permutation corresponding to the action of a group element Let G \times X \to X,\ \ (g,x) \mapsto g.x be an action of G on X, i.e., e.x = x for all x \in X; gh.x = g.(h.x) for all g \in G, x \in X. For a fixed g \in G, how should I refer ... 2answers 2k views ### What does the 'triple line equals' sign with a strikethrough mean? I understand that the triple equal sign can mean "identical to" or "defined to be equal to", so intuitively, I assume that the triple equal sign with a strikethrough means "is not identical to" or "... 1answer 63 views ### Notation for quadratic form My book states the following for a generalisation on \mathbb{R}^k: \displaystyle\sum_{i,j=1}^{k} a_{ij}x_ix_j Is this the same notation as \displaystyle\sum_{i\leq j=1}^{k} a_{ij}x_ix_j or is ... 0answers 121 views ### Lucas Number Equivalent of the Pisano Period? I'm doing some work with the Pisano Period, and it's leading to also talk about the Lucas numbers mod \ m, and their period. Is there a specific notation already designated? Sticking with using a ... 1answer 43 views ### notation for equations solving I have some notation questions on the following equation solving: 2+x=5\iffx=5-2\iffx=3 Would you read the above as "two plus x equals five if and only if x equals five minus two if and only if ... 1answer 44 views ### Is there a name for this structure? I don't know what branch of math best characterizes what I'm thinking of, so I'll use a concrete example. Suppose you have four boxes, A, B, C, D Box A is an empty box Box B contains Box A ... 1answer 84 views ### What does the notation Dx(a-bi-x) mean? Sorry for completely newbie question, but could not the answer anywhere else. On the Wikipedia page about "Steiner inellipse" there is the following notation equating roots of cubic polynomial and ... 1answer 958 views ### Double left-right arrow meaning While reading Hilbert's Tenth Problem (English version of a talk by Y. Matiyasevich) at page 3 I found: ...On the other hand let$$D(x_1,...,x_m) = 0 \quad (3)$$be an arbitrary Diophantine ... 2answers 461 views ### Notation for summing all elements under the diagonal of a square matrix I have a simple question: What is the notation for summing all elements under the diagonal of a square matrix? I appreciate your help. 4answers 988 views ### The origin of the function$f(x)$notation What are the historical origins of the$f(x)$notation used for functions? That is when did people start to use this notation instead of just thinking in terms of two different variables one being ... 1answer 57 views ### Other than$\models$, is there standardized notation for semantic consequence? It is common practice to use$\models$both for the satisfaction relation between models and sentences, and for the corresponding semantic consequence relation. Question. Suppose I don't want to use$...
I was taught that if $G \simeq H \ltimes K$, then (by convention) $H$ is the subgroup that is normal, but I see on Wikipedia and elsewhere that other people use the convention that the above indicates ...