# 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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### What is the difference between disjoint union and union?

If $S = A \cup B$, then $S$ is the collection of all points in $A$ and $B$ What about $S = A \sqcup B$?, I think disjoint union is the same as union, only $A, B$ are disjoint. So the notation is a ...
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### What do we call the set of elements fixed by an involution of the second kind?

If $A$ is an algebra over a field $F$, and $\sigma:A\rightarrow A$ is an involution of the second kind, then it seems natural to talk about the set $S=\{a\in A\mid\sigma(a)=a\}$. I am not finding any ...
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### Never seen this notation before: $\int (y-f(x))^2 Pr(dx,dy)$

I have never seen an integral like this: $$\int (y-f(x))^2 Pr(dx,dy)$$ What is that? More precisely what is $Pr(dx,dy)$? And how is that integral defined? I found it in Elements of Statistical ...
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### Notation for Line Segment vs. Directed Line Segment

This may be nit-picky, but I noticed inconsistencies in a high school math text I was reading, and I'm curious what the world thinks. For the most part throughout this textbook, notation is used as ...
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### What is the standard notation for the Banach space of functions that vanish at infinity?

Given a topological space $X$ and a real (or complex) valued function $f$ on $X$, we say that $f$ vanishes at infinity if for any $\varepsilon>0$ there is a compact $K \subseteq X$ such that ...
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### $L^1(0,T;(L^1_{loc}(\mathbb{R^N}))^N)$ - Confused about notations used for space and time dependent vector fields

I found this notation - $L^1(0,T;(L^1_{loc}(\mathbb{R^N}))^N)$ - in a paper of DiPerna and Lions concerning vector fields space and time dependent, "Ordinary differential equations, transport theory ...
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### What is the e notation regarding to decimal numbers?

Say the following number: $\text{1.4E-46}$. What is the e meaning? I'm not talking about euler number. Thanks in advance.
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### Why are contravariant vectors denoted with a superscript (and not a subscript)?

I wonder whether the choice of denoting contravariant/covariant vectors with a superscript/subscript is arbitrary (and could have been made the other way around), or whether there is a specific reason ...
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### Notation: Vectors in a Matrix

In my lecturer's notes, he made use of the notation $$\begin{pmatrix}|&|&|\\\mathbf u&\mathbf v&\mathbf w\\|&|&|\end{pmatrix}$$ to denote a matrix which is made up of the ...
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### Is it correct to say $\frac{\text{d}}{\text{d}x}[F_{X}(x)] = f_{X}(x)$ or $\frac{\text{d}}{\text{d}x}[F_{X}] = f_{X}$?

Is it correct to say $\dfrac{\text{d}}{\text{d}x}[F_{X}(x)] = f_{X}(x)$ or $\dfrac{\text{d}}{\text{d}x}[F_{X}] = f_{X}$? This notation question comes up in probability, where $F_{X}$ is a CDF of a ...
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### Index notation convention for 'all the elements in this dimension'

I am writing a paper that involves several matrix operations. An example an be: $$\sum_i^N Y_{k, i} \cdot V_k$$ The equivalent matlab notation is ...
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### Functional difference between d(total) and partial

edit 2(final answer in terms of python) ...
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### What do the square bracket signify in $\int [\text{d}\pi]f(\pi)$

I am reading this paper which repeatedly includes integrals such as, $$P_M(\phi \to \phi') = \int [\text{d}\pi][\text{d}\pi'] P_G(\pi)\delta((\phi, \pi) - (\phi'', \pi''))$$ Note ...
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### Can't understand notation of formula

The notation in the image features a straight line after the first fraction with some sort of parameter (?) given below. What does this mean in English exactly?
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### Math notation (filling in values)

I got the following formula: $$\text{D}=e^{-\pi\frac{|\lambda|}{|\omega|}}$$ When I solve $|\omega|$ I get: $$|\omega|=-\frac{|\lambda|\pi}{\ln\left(\text{D}\right)}$$ Now, how can I ...