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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0answers
44 views

On a Probability notation - $\mathbb{E}[X(.)|\mathcal{F}]_G$

What could mean this notation : $\mathbb{E}[X(.)|\mathcal{F}]_G$ ? where G : $\Omega \rightarrow \mathbb{R}$ is a random variable on a probability space $(\Omega,P, \mathcal{F})$. X could be a ...
0
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1answer
10 views

Notation: square brackets with a unique scalar?

my question is purely about notation. I am reading papers in computer science and I see that people use the following notation $[x]$ to denote $\{1,2,\ldots,x\}$. Is that correct? Or does it mean ...
1
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1answer
24 views

How to interpret scientific notation?

I'm having a problem understanding scientific notation. What is the difference between the following: $$\text{5e2, 5e-2, -5e2, -5e-2}$$
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1answer
21 views

The sum of $V=U+W$ of a vectorspace V and subspaces $U$, and $V$

I know what the sum of two subspaces is and how we notate but is it ok to write a minus to denote what I hope should be obvious is meant. So we have $V=U+W+Y$ where $V$ is a v.space and $U,W,Y$ ...
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0answers
37 views

Is the notation $\mathbb{P}(X \cap Y) = \mathbb{P}(X,Y)$ common?

For two random variables $X,Y$, is the notation $\mathbb{P}(X \cap Y) = \mathbb{P}(X,Y)$ common? In a probability class last year we had always used $\mathbb{P}(X \cap Y)$. This year in a stochastic ...
2
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1answer
74 views

Uniform norm $ \|u\|_{C(\overline{U})}$ in PDE

Let $U\subset \Bbb{R}^n\to\Bbb{R}$ be an open set (not necessarily bounded) and $u:U\to\Bbb{R}$ be a bounded continuous function. In Evans's PDE textbook, the author defines a norm $$ ...
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1answer
13 views

Clarification of Direct sum meaning with $\geq 3$ subspaces

Let $V$ be a vectorspace and $U_i$ subspaces of V. In the definition of $\oplus_{i \in I} U_i$ it is said that is does not suffice for $U_i$ to be pairwise disjoint. Instead we must have the stronger ...
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1answer
16 views

Explanation Notation Union Probability

Could somebody explain how to create intuition for the probability/union notation below? I don't know how to read it. And is this a situation where events are disjoint, but dependent?
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1answer
30 views

Big O notation $O(\epsilon)$ [on hold]

What does it mean to say that $\tau=O(\epsilon)$? Where $\epsilon$ is small, meaning that $\epsilon \ll 1$.
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2answers
88 views

Origin of the notation for statistical divergence

The unusual notation $D(P||Q)$ seems to be universally used for statistical divergences (e.g. KL divergence). What is the origin of this notation, and do the double bars (pipe symbols) have any ...
0
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0answers
16 views

Topology; difference between open subsets of $X$ containing $x$ and open neightborhood od $x$?

I see my lecture notes and some texts alternate between the two. What is the difference in saying that "an open subset of $X$ containing $x \in X$" and an "open neighborhood of $x \in X$"?
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4answers
45 views

Mathematical Notation of Sequence of Functions

Let's say I have a finite set of functions $F=\{f_1,f_2,f_3,...,f_n\}$ and I want to show a recursive function that is constructed by an arbitrary sequence of applications of functions in $F$ to input ...
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2answers
58 views

Notation in commutative algebra

I am doing some exercises on commutative algebra and came along the following expressions, which were not elaborated on. Is someone familiar with them? The first is for $p$ a prime number ...
2
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1answer
374 views

Confused about notation and derivatives inside integrals

EDIT: To make what I am asking more clear. I've simplified it and have a more direct question. Let's say I am writing out an expression, and I want to write: $$\int_0^xF'(y)\,dy$$ However, for ...
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1answer
41 views

In sequent calculus, what's going on with sequents with multiple formulae in the succedent?

The sequent proof systems I learned only allowed one formula on the right hand side of the sequent, and $\phi_1, \ldots, \phi_n \Rightarrow \psi$ (or ... $\vdash \psi$) is understood as saying that ...
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1answer
17 views

Are these two notations equivalent?

I've seen both $\forall a,b$ and $\forall a\forall b$ of these being used in various posts and wondered if they are equivalent or if there is a subtle difference between the two.
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1answer
28 views

How can I write a set of equations in summation form?

I have a system of equations as follows: \begin{align} & A_1^{11} + A_1^{12} + A_1^{13} + \cdots + A_1^{1n}=X \\[8pt] & A_1^{21} + A_1^{22} + A_1^{23} + \cdots+ A_1^{2n}=X \\[8pt] & ...
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1answer
12 views

Notation To Define A Mapping From A Set to a Relation Between Two Elements Of That Set

Say I had a set $S=\{s_1,\dots, s_n\}$, and each $s_i$ denotes an outcome. If I wanted to define a function, $f$ which takes two elements of $S$, $\{s_i, s_j\}$, and maps it to a relation, either ...
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0answers
10 views

reference request: $C^k(\overline\Omega)$ as restriction of $C^{k}$ functions on $\Omega$

Let $\Omega\subset\mathbb{R}^d$ be an open set. $C^k(\Omega)$ is defined as the space of functions $f:\Omega\to\mathbb{R}$ such that $\partial^nf$ is continuous for $0\leq|n|\leq k$. There are ...
1
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1answer
25 views

Symmetric Simple Random Walk - Definition Clarification

I'm finding conflicting answers everywhere, including in my own notes. In the phrase "symmetric simple random walk", which part, "symmetric" or "simple" refers to having a probability of $0.5$ to go ...
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1answer
40 views

Notation for kernel object

When $f: A \mapsto B$ is a morphism in some category with a zero object and limits, we can use $\ker(f)$ to refer to an equivalence class of morphisms to $A$ which satisfy a particular universal ...
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0answers
26 views

How to formalise a procedure involving Cartesian products of sets of vectors and transformation in matrices?

I am asking for an help to formalise with the correct notation the following procedure. Let $n\in \mathbb{N}$. Let $\{0,1\}^{n-1}$ be the set of vectors of dimension $(n-1)\times 1$ with each ...
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0answers
43 views

Why isn't the identity/unit matrix upright?

I realize this is more of a typesetting problem then a mathematical one. I've already tried the TeX stack exchange and the question got canned. In ISO 80000-2:2009, variables and running numbers are ...
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0answers
21 views

Conventions for named equations [on hold]

In the document I'm writing, I find myself referring back to a small number of equations often enough that it makes sense to give them a name; perhaps some sort of initialism. (I hate when texts ...
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0answers
18 views

Slow time variable

If I have a time variable $t$ such that $t \in[0,5]$ and I introduce a new variable $\tau$ st $\tau =\epsilon t$, where $\epsilon <<1$. Why is $\tau$ called a 'slow time variable', when $\tau ...
0
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1answer
17 views

Basic set notation in combining different ranges of numbers

What is the proper way to specify a set which contains all even numbers between 1 and 10, and all odd numbers between 11 and 30? Would this work? $$ U = \{n, m\ |\ n \ \text{is even},\ 1 \le n \le ...
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1answer
48 views

Notation and Quantifiers

I was wondering what is a natural way to write certain formal expressions, without make them look too cumbersome. In particular, what I learned from various books is that, when we deal with the ...
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0answers
47 views

in spanish do you have to do the upside down exclamation marks before a number for factorials? [on hold]

for example $4! = 4 \times 3 \times 2 \times 1 = 24$ if you were to write this in spanish would you have to write $¡4! = 24$ ? a quick google search doesn't give me anything
104
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22answers
11k 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 ...
0
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2answers
37 views

Is this element-of_{ij} - looking symbol the Levi-Civita symbol?

I'm reading this formula: from a page Is the symbol that looks like an element-of symbol with two indices i and j the Levi-Civita symbol? Mathematics is my weak-side so I'm not sure. Actually I ...
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7answers
2k views

Why do we (mostly) restrict ourselves to Latin and Greek symbols?

99% of variables, constants, etc. that I run into are named for either a Latin character (like $x$) or a Greek character (e.g. $\pi$). Sometimes I twitch a little when I have to keep two separate ...
1
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1answer
24 views

Write the series using sigma notation: $f(x)= 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! +\cdots$

$$f(x)= 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + \cdots$$ I don't know how to get the signs to work like negative, then positive. I have tried to make it like the following: $(-1)^{n-1} \frac{x^{2n-1}}{ ...
2
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1answer
44 views

Notation for sets of unordered pairs

Let $A$ be a finite set of unordered pairs, e.g., $$A = \{\{1, 2\}, \{1, 3\}, \{2, 3\}\} \enspace .$$ Which of the following is proper notation for "the element $\{1, 2\}$ belongs to $A$"? $\{1, 2\} ...
0
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0answers
21 views

Question about notation for a statement about conditional probability distribution

Consider the random variables $X,Y$ defined on the same probability space $(\Omega, \mathcal{F}, P)$. Suppose $Y$ is a discrete random variable with support $\mathcal{Y}\subset \mathbb{R}$. Suppose ...
1
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6answers
7k views

Is there a mathematical symbol for unknown?

I'm searching for two symbols - considering they exist - (1) unknown value; (2) unknown probability. Note: I thought that $x$ was used in a temporary context, whenever I see it, it remains unknown ...
0
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1answer
21 views

Set builder notation: defining the number of elements

I have a set L and I have a subset S which is part of L and contains three elements A, B and C. Finally, each of these elements are subsets that consist of their own elements: $A=\{a_1...a_n\}$ ...
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0answers
27 views

Question regarding terminlogy and wording of the derivative

When doing calculus, we typically say that we "take the derivative of a function f(x)." However, rigorously, f(x) is not a function but rather the value of the function f evaluated at x. Thus, in ...
4
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2answers
22k views

What does ! mean in sequences?

I'm doing a sequences problem where I have to write the first five terms of a sequence. It looks normal, but there is an exclamation mark on the denominator: $$a_n = \frac{1}{(n + 1)!}$$ & ...
2
votes
2answers
104 views

What does the notation $C(\bar U)$ mean for $U\subset\Bbb{R}^d$ open?

Let $U$ be an open subset of $\Bbb{R}^d$. In Evans's PDE book, $$ C(U)=\{u: U\to\Bbb{R} \mid u\ \hbox{continuous}\} $$ and $$ C(\bar U)=\{u\in C(U)\mid u\ \hbox{ is uniformly continuous on bounded ...
2
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1answer
61 views

Why don't we use “dx” as the limiting variable when teaching the definition of the derivative with respect to x?

For a function $f(x)$ that is differentiable at $x$, the derivative of $f$ with respect to $x$ at the point $x$ is usually given as $$\frac{df(x)}{dx} = \lim_{h\to0} \frac{f(x+h)-f(x)}{h}.$$ I think ...
0
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0answers
13 views

Notations of conditions

Assume I have the Mean Square Error: $\mathcal{L}(X, Y) = \frac{1}{\lvert X\rvert}\sum_{i=0}^{\lvert X\rvert}\left(f(\mathbf{x}_{i}) - \mathbf{y}_{i}\right)^2 \space \space ,\space \space \lvert ...
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3answers
489 views

What is the amalg symbol?

I saw this formula: $A \amalg B$, where $A$ and $B$ are sets. I searched for the name of the symbol, "amalg", but haven't found a definition. What is the meaning of this symbol?
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2answers
5k views

What does $×$ mean in this context

I have two definitions, from real analysis - Metric Space: Given a set $X$, a function $d:X×X→\mathbb{R}$is a metric on $X$ if for all $x, y∈X \dots $ Function: Let $A,B$ be two sets. A function ...
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0answers
22 views

representing a periodic circular shift for a vector formally

I'm writing an algorithm in which the operation of circular shift to a given vector $x=[1 \ 0 \ 0\ ... 0]$ is needed on periodic basis i.e. every $\Delta t$ a circular shift will occur. How this ...
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1answer
55 views

Can I ask about copyright here? [closed]

I don't know it is okay if I post about copyright here. If there is any problem, please leave a comment. I will delete this post. Thank you. I am a graduate student studying engineering and ...
0
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1answer
24 views

Levi civita and kronecker delta properties?

I'm trying to grasp Levi-civita and Kronecker del notation to use when evaluating geophysical tensors, but I came across a few problems in the book I'm reading that have me stumped. 1) ...
1
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0answers
48 views

Falling Factorial Notation

If $(x)_{n}$ refers to $$x(x-1)\cdots(x-n+1)$$ then what does $(xy;x)_{n}$ refer to? Is it $$xy(xy-1)\ldots(xy-n+1)?$$ Thanks. The notation in question is used on page two of this paper.
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1answer
22 views

FUNCTIONS : Theoretical Doubt

I am currently learning calculus of one variables , and i have come across a symbol $$f(x,y).$$ Can anybody explain the meaning of this ? Thanks!
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0answers
9 views

Understanding falling factorial notation with semicolons.

I have a question about the following notation: $$\prod_{j=1}^{k/d}(z^dt^{dj}q^d;q^d)_{\infty}$$ I'm confused as to what I do with $q$ and the other variables especially when the semicolon is ...
4
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2answers
56 views

Difference in use between $d$, $\partial$, $\operatorname d$, $\varDelta$ and $D$ for derivatives.

While reading different sources on implicit differentiation (and thereafter differentiation in general), I came across many different "d's" being used for (or similar to) the familiar ...