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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2
votes
2answers
61 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) = ...
1
vote
1answer
66 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 ...
0
votes
2answers
54 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 ...
-1
votes
3answers
116 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 ...
3
votes
2answers
143 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 ...
1
vote
0answers
49 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 ...
0
votes
1answer
322 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?
0
votes
0answers
30 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
69 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
votes
2answers
49 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
125 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
votes
1answer
187 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 ...
3
votes
3answers
124 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 ...
1
vote
2answers
168 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
vote
1answer
51 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
vote
1answer
70 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
278 views

Mathematical Notation - Arrow Sign

What does the $\Rightarrow$ arrow mean when showing working out in maths? How do we use it appropriately?
1
vote
0answers
256 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
124 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
votes
1answer
71 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 ...
2
votes
0answers
37 views

Notation in derivation theorem

Can you explain what does $ \frac{\partial}{\partial x^i}$ means?
0
votes
1answer
49 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 ...
4
votes
0answers
1k 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
66 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
vote
3answers
39 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 ...
1
vote
0answers
37 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
vote
2answers
28 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
79 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
votes
1answer
50 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 $A_i \in M_n(\mathbb{R})$, ($i=0,1,2,\dots$) ...
5
votes
3answers
253 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
vote
0answers
49 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
votes
1answer
95 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
64 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
votes
0answers
79 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
vote
1answer
55 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
113 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
votes
1answer
223 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
76 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 ...
1
vote
2answers
154 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
48 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
64 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
votes
2answers
57 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, ...
3
votes
2answers
43 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
votes
0answers
41 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
415 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
35 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
votes
1answer
86 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
1answer
145 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
39 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
22 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 ...