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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0
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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 ...
6
votes
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 ...
0
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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 ...
1
vote
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 ...
5
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1answer
128 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 ...
2
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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 ...
0
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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.
1
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1answer
40 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 ...
1
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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 ...
1
vote
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
66 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
votes
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 ...
1
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0answers
30 views

Notation in derivation theorem

Can you explain what does $ \frac{\partial}{\partial x^i}$ means?
0
votes
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 ...
0
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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
41 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): $$ ...
1
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0answers
17 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...)
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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
votes
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?
0
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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
votes
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 $A_i \in M_n(\mathbb{R})$, ($i=0,1,2,\dots$) ...
4
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3answers
183 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 ...
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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.
0
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1answer
39 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| ...
0
votes
1answer
36 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). ...
0
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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 ...
1
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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 ...
1
vote
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"?
4
votes
1answer
63 views

Why $dt/t$ in Mellin transform

I've noticed that often when people write the Gamma function $\Gamma(s) = \int_0^\infty t^{s-1}e^{-t}\,dt$, that they write it like $$ \Gamma(s) = \int_0^\infty t^s e^{-t}\,\frac{dt}{t} , $$ where ...
0
votes
0answers
20 views

$\sigma_{ji,j}+ F_i = 0$ - explain notation

''...Cauchy stress tensor in every material point in the body satisfy the equilibrium equations'' $\sigma_{ji,j}+ F_i = 0.$ Also there is this notation, which I don't fully understand: ...
1
vote
2answers
116 views

What does the following notation mean? (ODEs)

I saw this notation many times, but I don't understand why the $y$ variable is missing in the first term of the first equation below. $$ \frac{\mathrm{d}y(x)}{\mathrm{d}x} = f(x,y) $$ It just mean: ...
2
votes
0answers
14 views

Notation of List other than Set, and related operations?

we all know that a single capital letter (e.g., $S$) usually represent a set (containing non-duplicate objects) and we can write a number of operations on set such as $|S|$, $|S|$ union $|S'|$ etc. ...
1
vote
1answer
53 views

Subscript before a function symbol?

Does anyone know what the subscript before the function means? $$ _pf_p $$ It's part of a definition for selfish routing in networks: Let $N = (V,E)$ be the network, which is a directed graph. ...
0
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2answers
49 views

A question about notation

Earlier this week, a friend asked me what the most complicated equation I could think of was that was equal to $1$. The answer I gave was this: Let $G_n$ denote the n$th$ number in the grandi series, ...
0
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0answers
15 views

chained max notation

I'm confused on how to implement a quality indicator for multi-objective optimization. I don't understand the following notation. $$I_{\epsilon} (A,B)=\max_{z^2 \in B} \min_{z^1 \in A} \max_{1 \le i ...
3
votes
2answers
39 views

Notation when evaluating an integral at infinity

Using a trivial example to illustrate the question - $$\int_0^\infty 2 dx$$ $=2x \mid_0^\infty = 2(\infty) - 2(0)$ Can we actually say $2(\infty)$? It doesn't seem valid me.
0
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0answers
19 views

Notation help: “linearizing” multidimensional indices

I have an algorithm that makes use of a multidimensional data structure, e.g. $A(i,j,k)$, $1\le i,j,k\le n$. I am looking for a simple notation that enables me to refer to the $\ell$'th elements of ...
0
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0answers
34 views

Standardizing the terminology of graph theory

I took a course in graph theory many years ago and remember being frustrated that the terminology was not at all standardized (or didn't seem to be). Various sources used vastly different words or ...
3
votes
2answers
193 views

How do commas and brackets affect the meaning of quantifiers?

My logic class didn't introduce us to multiple quantifiers. I've seen a few variations that seem to have distinct meanings: $$ \forall x, \forall y(...) $$ $$ \forall x \forall y(...) $$ $$ \left( ...
0
votes
1answer
19 views

Notation for describing half-planes

In a 3D space, if I want to describe a half-plane of the plane $X=Y$ where $Z\geq{X}$, is there some concise notation for that? Also, what is the notation for saying a point $P$ is on that ...
0
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1answer
39 views

Large Operators?

Large operators have always seems strange to me, sometimes their meaning is based on the symbol and other times it has no correlation. For instance, the summation (sigma) has no relation to the ...
4
votes
2answers
79 views

What are different notations used by mathematicians and physicists?

One can find many cases that mathematicians and physicists use different notations for the same concepts. Here is a few cases I find. Inner product of vectors: Mathematicians use $(a,b)$ or ...
2
votes
0answers
28 views

How should I interpret this function notation?

I'm trying to implement an FDGD Algorithm from a paper and I'm a little stuck how to interpret a piece of function notation. See page 7, equations 2 and 3 in this document: In there we have ...
0
votes
1answer
16 views

How to mention a specific member of a set?

I know there are other questions like this, but they are yet to satisfy me. How would would go about mentioning specific members of a set. For instance, if I wanted to mention the third element from ...
12
votes
9answers
579 views

Strangest Notation? [closed]

While this may be a fruitless pursuit of anecdotes, I still ask: what is the strangest (or most blatantly wrong (at least in the eyes of common notation)) mathematical notation you have ever seen?