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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36 views

Help with understanding the definition of operation

I'm having trouble understanding this excerpt from Wikipedia, which defines an operation: Mainly, I don't understand what is meant by $V \subset X_1 \times...\times X_k$. Why does an operation ...
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2answers
34 views

Notation question: defining a matrix as $P=\sum_{i=1}^{k}v_{i}v_{i}^{T}$

I've seen in a paper the following sentence: Let $V$ be a $k$-dimensional subspace of $\mathbb R ^d$ and let $v_1 ,...,v_k$ be an orthonormal basis of $V$. Define ...
5
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2answers
83 views

is there any history at all for this notation of partial anti-derivatives?

i have searched but can not find examples of any published book or online articles that use this notation: $$\int f(x,y) \partial x$$ seems it would be useful for example here: $$\int_I\int_J ...
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4answers
64 views

Surprised over notation in fundamental theorem

So I'm looking into the fundamental theorem of calculus and I'm a bit weirded out by the notation used in part two. $$ \int_{a}^b f(t) dt = G(B)-G(a)$$ Why don't we say $F(b)-F(a)$? We are just ...
2
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5answers
99 views

Chain Rule: Is the notation $\frac{dy}{du} \cdot \frac{du}{dx} = \frac{dy}{dx}$ accurate?

My question is if it is okay / mathematically rigorous to write the Chain Rule like that (the Leibniz way). I thought that $dx$, etc. do not follow the rules of algebra and cannot be treated as such. ...
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1answer
37 views

How to verify if an element is inside an ordered pair?

The notation to verify if an element belongs to a set is $e \in E$. But which notation should I use to verify if an element is part of an ordered pair? Is $a \in (a,b)$ valid (e.g., $1 \in (1,2)$)? ...
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2answers
48 views

Is $\mathbb{Z}_+ = \{ 0, 1, 2, \dots \}$ or $\mathbb{Z}_+ = \{ 1, 2, \dots \}$?

Is there complete consensus on which of these is true?
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1answer
17 views

Notation query: matrix projection

I've used the following notation in a report: $G\boldsymbol{w}\in\mathcal{H}_2\,\forall\boldsymbol{w}\in\mathcal{H}_2 $ In other words $G$ projects $\boldsymbol{w}$ back into the same set. But this ...
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2answers
46 views

function application order

In traditional mathematics, when we post-compose $x$ by $f$ we write $fx$ or $f(x)$, that is we prefix writing things right to left. I realize some might be used to it, and it is absolutely trivial, ...
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2answers
38 views

Is the maximum-likelihood estimation notation formally correct?

I just saw from the Wikipedia's entry on Maximum likelihood, http://en.wikipedia.org/wiki/Maximum_likelihood , the formula $\mathcal{L}(\theta\,|\,x_1,\ldots,x_n) = f(x_1,x_2,\ldots,x_n\;|\;\theta) = ...
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1answer
31 views

meaning of subscript notation $\ 1_{a=a'}$

I'm not familiar with the meaning of the 1 with the subscript notation $\ 1_{a=a'}$ and $\ 1_{b=b'}$, where (a,a') and (b,b') are simply coordinates of a matrix. Could anyone explain this to me ...
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2answers
49 views

Infinite primes and notation

While reading a book about algebraic number theory, the symbol for a rational prime $p$ $$p^\infty$$ often occurs and I was wondering, what the exact definition of this is. Also, what is the ...
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3answers
55 views

Set theory symbol

I'm studying very basic set theory for a module and have come across this symbol: | quite a few times, although I have no idea what it means, can someone explain what it is and how it makes sense in ...
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0answers
52 views

About Kernel and the coimage of a function

Introduction I was serching for a concept of "equivalence relations" induced by an arbitrary function in a "natural" way and I found the concept of Kernel. But I'm not sure that I understand it and ...
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2answers
127 views

Usage of $\cdot$ in calculus

I often find myself caught in the dilemma of whether or not to use the symbol $\cdot$ in calculus. Take for example, the chain rule: $$\frac{dy}{dx} = \frac{dy}{du}\cdot\frac{du}{dx}$$ Is the ...
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0answers
43 views

Even, Odd, Congruent

Im new in math world, i know the modulo congruence in order to defining odd and even. But I don't know if i can write Even is $$x \equiv 2x$$ Odd is $$x \equiv 2x + 1$$ If it's not that, can you ...
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1answer
20 views

Vector notation of all entries 1

Is there any notation describing a vector with all components being 1? Or whether the bold-face one $\mathrm 1$ is publicly acknowledged as it?
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0answers
27 views

Notation from nowhere - $V(T_A)$

This is a poor question I have. In an exam question, $T_A$ is a linear map. What is $V(T_A)$ ? It is not stated in the question. And I have not seen it before. Maybe some help to figure it out, he ...
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1answer
62 views

Is there any advantage to the $a \equiv b\;\;(\mathrm{mod}\;c)$ notation?

Congruences modulo equivalence classes other than those defined by division remainders are ubiquitous in contemporary mathematics. It is not uncommon for a single mathematical argument to refer to ...
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2answers
32 views

About the definition of fixed-point combinators

I am reading this wikipedia page to understand Fixed-point combinators: In computer science, a fixed-point combinator (or fixpoint combinator[1]) is a higher-order function y that satisfies the ...
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4answers
75 views

Notation for “all integers less than $n$”

Is there a short mathematical notation for all integers less than $n$ where $n$ itself is some integer? The only thing that comes to mind is $$\mathbb{Z} \cap (-\infty, n),$$ But this is pretty ugly ...
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1answer
130 views

On proving $n = \sum_{d\mid n}\varphi(d)$

$\def\nset{\{1,\dots,n\}}$ I'm trying to work out my own proof1 of Euler's classic formula $$n = \sum_{d\mid n}\varphi(d)\;.$$ I'm looking for some pointers to the standard terminology and/or ...
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3answers
83 views

Why are there so many notations for differentiation?

There are so many notations for differentiation. Some of them are: $$ f^\prime(x) \qquad \frac{d}{dx}(f(x))\qquad \frac{dy}{dx}\qquad \frac{df}{dx}\qquad D f(x)\qquad y^\prime\qquad D_x f(x) $$ Why ...
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2answers
137 views

discrete math: is there a difference between $\subseteq$ to $\supseteq$

I have a question which asks if $X \supseteq I$. Is it just the same as $I \subseteq X$? Because I never saw it the other way around or learned about it, I'm confused.
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1answer
41 views

Generally speaking, how should one read notation?

I became a better reader when I stopped sub-vocalizing (hearing the words in my head). I still do that when I read math. I tried not to do that when I read an expression today. I felt less confident ...
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1answer
51 views

How to 'show your work' with game theoretic notation

Everything I've read on game theory seems to describe the game in notation and solves it in natural language. How do you work with notation in game theory? Could you recommend a straight-forward ...
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1answer
41 views

Mathematical Notation - Arrow Sign

What does the $\Rightarrow$ arrow mean when showing working out in maths? How do we use it appropriately?
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0answers
68 views

What do two number on top of each other in square brackets mean?

Im currently going through "Universal Portfolios with Side Information" by Cover and Ordentlich [96]. Near the end of the paper, they provide a formula for calculating weights of a Universal Portfolio ...
0
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1answer
21 views

Symbol or notation for quotient operator

I'm trying to describe an algorithm in pseudocode where I've used the integer division operator. In VB.NET, the language I'm using, the operator used is "\", but I don't know if this is unambiguous to ...
0
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1answer
49 views

What do vertical bars with an index mean?

A fairly basic notation question: what do the vertical bars in the following mean? x = $_{k=0}^{3}\big|\;f(k)\;\big|$ I've never seen vertical bars with an index before and I can't seem to find the ...
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0answers
30 views

Notation in derivation theorem

Can you explain what does $ \frac{\partial}{\partial x^i}$ means?
0
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1answer
34 views

Summation notation rule

Sorry if this sounds elementary, but I have problems with the following in a text I am reading: $$ \left(\sum_{k=0}^{n} C_k\phi_k(x)\right)^2 = \sum_{k=0}^{n}\sum_{l=0}^{n}C_k ...
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0answers
49 views

The best symbol for non-negative integers

I mean to specify the set {0, 1, 2, ...}, i.e., non-negative integers in an engineering conference paper. Which symbol is more preferable? $\mathbb{N}_0$ $\mathbb{N}\cup\{0\}$ $\mathbb{Z}_{\geq0}$ ...
2
votes
1answer
42 views

Abstract Algebra Math notation, kernel

So I defined $$\theta:R \rightarrow R\backslash I$$ by $$\theta(x) = [x]_I$$ and $$\phi: R[x]\rightarrow (R\backslash I)[x]$$ by $$\phi(a_nx^n +\dotsb+a_1x+a_0) = ...
1
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3answers
27 views

Notation for function compositions/derivatives

When given $(f \circ g)'(0)$, does it mean to compose the 2 functions first, then take the derivative of the composed functions and evaluate it at $0$, or take the derivative of $g$ first and evaluate ...
0
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0answers
15 views

argmax over set membership probability

I'm trying to find the argument which maximises a function, where the variables are set membership relations: $\{\in ,\notin \}$. This is how I'm doing it now (a simplified argmax): $$ ...
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0answers
19 views

Girard's System $F$ (also named Polymorphism)

I have been studying Girard's Polymorphism and a question came to my mind: why is it (also) called system $F$? Where does the $F$ come from? (i searched it online but didn't get any luck...)
1
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2answers
21 views

Notation Question regarding Ring-mod-Number and Ring-mod-Some Kernel

I'm having trouble linking the notation of something like $\mathbb{Z}/n$ and $R/H$ where $n \in \mathbb{Z}$, $R$ is a ring, and $H$ is the kernel of some homomorphism from that ring to another. In ...
2
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2answers
64 views

What does this mean? $K_n \boxtimes K_n$

I have to show that $K_n \boxtimes K_n = K_{n^2}$. Where $K_n$ is a complete graph. What does the operator "$\boxtimes$" do?
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1answer
58 views

Confusing Notations in a Paper

From : "Multicast Routing and Design of Sparse Connectors" by Andreas Baltz and Anand Srivastav, Springer 2009: http:\\link.springer.com/chapter/10.1007%2F978-3-642-02094-0_12 In 2-Copy Method, ...
0
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1answer
21 views

Product Notation for Multiplication in Reverse Order

Is there a standard notation for multiplication in reverse order? For example consider the problem $$x_{k+1} = A_k x_k$$ where $x_i \in \mathbb{R}^n$ and $A_i \in M_n(\mathbb{R})$, ($i=0,1,2,\dots$) ...
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3answers
184 views

Why do statisticians like “$n-1$” instead of “$n$”?

Does anyone have an intuitive explanation (no formulas, just words! :D) about the "$n-1$" instead of "$n$" in the unbiased variance estimator $$S_n^2 = \dfrac{\sum\limits_{i = 1}^n ...
1
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0answers
36 views

Notation to refer to all the n element subsets of a set?

Is there a notation to refer to all the n element subsets of a set? I know the power set denotes all of the subsets.
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1answer
40 views

Question about identity of Dirac delta function [duplicate]

I am trying to understand an identity of the $\delta$-function written on this Wikipedia page: \begin{equation} \int \mathrm{d} x \; f(x) \delta[g(x)] = \sum\limits_i \frac{f(x_i)}{\left| ...
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1answer
37 views

What is the convention for using unconventional notation?

I am new to writing mathematics papers, and often times I have the need to express an idea for which there is no standard mathematical convention (or if there is, may be too tedious to do formally). ...
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0answers
18 views

What is the notation for X has a truncated inverse gamma distribution?

I am writing a paper and have a random variable with a truncated inverse gamma distribution. I have seen notation for X having a truncated normal distribution before, such as ...
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1answer
44 views

Notation for “set of all possible unions”

For a set $S$, for "all possible subsets of $S$" you have $\mathcal{P}(S)$. For a set $S$ consisting of sets, for "the union of all sets $T\in S$" you have $\bigcup_{T\in S}T$. Is there a notation ...
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0answers
23 views

Notation for pointwise versus “setwise” stabilizers

Suppose one is working with both pointwise and setwise stabilizers of sets under a group action. Are there common conventions for notationally distinguishing these two notions? How common are they? ...
0
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0answers
10 views

Notations in Oka family definition

Definition. An ideal family $F$ in a ring $R$ with $R \in F$ is said to be an Oka family (strongly Oka family) if, for $a \in R$ and $I$, $A \lhd R$, $(I, a), (I:a) \in F \Rightarrow I \in F$ ...
0
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1answer
65 views

Is there a symbol for “dependent”?

For random variables $A$ and $B$, $A \perp B$ is sometimes used to denote "A in independent of B". Is there a symbol that is commonly used to mean "A is not independent of B"?