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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76 views

(x)f=y is more natural than y=f(x)

Has anyone ever considered the notation such as $(x)f=y$ that specifies the argument $x$ of the function first and then the function itself? I have never seen anyone use it but it seems more natural ...
0
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0answers
54 views

Embedding vs restriction

Embedding is the morphism $( A ; B ; \operatorname{id}_A)$ of the category $\mathbf{Rel}$ for sets $A \subseteq B$. I call restriction the morphism $( A ; B ; \operatorname{id}_B)$ for sets $A ...
3
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0answers
74 views

How do you type such nice solutions with all the different mathematical notation here on Math.stackexchange? [closed]

I am totally lost as to how this is done. I have never used a computer to type solutions nicely. What do I need to download? I want to learn how to type nice solutions like some of the people on this ...
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1answer
65 views

Clarification on use of sigma notation

I find the use of sigma notation quite arbitrary. Sometimes the counters and limits are defined, sometimes they aren't. And sometimes, I just can't comprehend what it means. For example, in my ...
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1answer
58 views

Integrals with infinite bounds sometimes written as limits, sometimes not?

When I saw Wikipedia's notation for the inverse Laplace transform, I became curious if there was a reason behind it. Is there a reason why Wikipedia writes the inverse Laplace transform as this ...
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1answer
48 views

What is the $\lVert v\rVert$ sign mean in the context of vectors?

Suppose $V$ a inner product space, $u, v \in V$. I need to prove this identity: $$\lVert u+v\rVert^2 +\lVert u-v\rVert^2 = 2\left(\lVert u\rVert^2 +\lVert v\rVert^2\right) $$ what is the $\lVert ...
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0answers
2k views

Bar Mean vs Bracket Mean

I know that the standard representation for the average of a data set: $$ \bar{x} = \frac{1}{N} \sum_{i}^N{x_i} $$ I have also ran into an average denoted as $\langle x \rangle$. This notation is ...
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1answer
33 views

Value expressions

What is the value of the expression: $\sum_{k=0}^{d}b^{k}\left[\begin{array}{c} d\\ k \end{array}\right]\prod_{i=0}^{k-1}\left(c-b^{i}\right) $ for $ k = 0 $? In particular, what is then the value ...
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3answers
97 views

What do exponents of $\mathbb{R}$ denote?

An equation in my machine learning class says $$ x= \begin{bmatrix} x_0 \\ x_1 \\ \vdots \\ x_n \\ \end{bmatrix} \in ℝ^{n+1} $$ I'm reading this as "x ...
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1answer
117 views

Graph theory notation

Just a quick question on graphs: how do I read the notation in this question for the edge set? I can't find any explanation in my notes or online. ... specifically that first half of the union. I'm ...
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3answers
3k views

What is the equal sign with 3 lines mean in Wilson's theorem?

I'm reading up on Wilson's Theorem, and see a symbol I don't know... what does an equal sign with three lines mean? I'm looking at the example table and I still can't infer what they are trying to ...
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3answers
181 views

$x^{y^z}$: is it $x^{(y^z)}$ or $(x^y)^z$?

Of the following, why is a usually considered true, and for what reason other than "tradition" and "more convenient"? a: ${x}^{y^z} = x^{(y^z)} \neq {(x^y)}^z$ b: ${x}^{y^z} = {(x^y)}^z \neq ...
3
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2answers
74 views

degree of commutativity

What is the exact definition of the degree of commutativity of a $p$-group? When we use notations $d(G)$ and $c(G)$ for other concepts, what is the best notation for degree of commutativity of $G$?
2
votes
1answer
60 views

Can objects repeat in commutative diagrams?

Are objects allowed to repeat in commutative diagrams? This seems to be necessary when representing endomorphisms such as the morphism $f : X \to X$ in the category $\mathbf{Set}$, such as when $f$ is ...
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0answers
34 views

Restricting binary relations by composing with an “inclusion binary relation”

If $X' \subseteq X$ then we may define an inclusion map $\iota : X' \to X$ where $\iota(x) = x$. One use of $\iota$ is that we can express the restriction of some $f : X \to Y$ to $X'$ as $f|_{X'} = f ...
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2answers
134 views

Notation of logarithm and its exponent

I am little confused about this notation, $\log^3 n$. Does it mean $(\log n)^3$ or $\log (\log (\log n))$?
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1answer
278 views

Big Omega Notation Proof

Can someone show me how to start this off? I need to prove it, but I'm not sure how I would prove Big Omega. Prove that $f(n)=\sum_{i=1}^ni^k\in\Omega(n^{k+1})$. Thank you for the help!
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2answers
94 views

“Preimage” of a binary relation

Consider the binary relation $R \subseteq X \times Y$. Is there a standard name and notation for the set $X' = \{x\ |\ (x, y) \in R\}$? ProofWiki calls $X'$ the preimage of $R$, denoted as ...
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1answer
48 views

A notation problem of partial derivatives

I have a notational problem of partial derivatives: Let $z=f(x,\phi(x))$,and let $\phi(x),f$ be a differentiable functions.What is the difference between $\frac{\partial z}{\partial x}$ and ...
2
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3answers
81 views

A notation for a morphism in a thin category

Consider a thin category with objects $A\leq B$. There exists a unique morphism $A\rightarrow B$. Is there a standard notation for this morphism (given $A$ and $B$)?
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0answers
32 views

Clear notations when working with random variables

I have a set of random variables $X_1,X_2,...,X_n$ each variable $X_i$ has a set of possible values $\Omega_{X_i}$ and a function associated with it $f(X_i)$. An assignment $\bf x$ for a subset of ...
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4answers
72 views

Expressing how many of $a,b,c$ can be zero

My scenario is that I need to express with mathematical syntax the following condition: There are three integers: ${a, b}$ and ${c}$. Case 1: two of the three can be zero. Case 2: only one can be ...
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1answer
41 views

Notation for Permuting Sets

If I have some arbitrary sets $A_i : i \in I$ and I want to permute their intersections pairwise, how would I write such a permutation? Would I use some permutation tensor? Essentially I want to ...
2
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2answers
115 views

How to prove $x-y = x+(-y)$ in ring theory.

Okay, I have talked with a lot of people about this silly question. And I have thought about this way longer than is good for me. Everybody seem to disagree with me, and that is the reason I think I ...
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1answer
497 views

Mathematical notation to represent all combinations of three variables?

This is a fairly simple question involving mathematical notation which is outside of my expertise. I'm looking for the correct representation of a matrix M which shows all combinations of three ...
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1answer
43 views

Vector field of functions equalling real numbers

We consider the set $\mathbb{N}^{\mathbb{R}}$ (i.e. all functions $f\colon\mathbb{N}\to\mathbb{R}$). I've been asked to prove that this forms a real vector space (that is, a vector space over ...
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2answers
46 views

Is this notation correct?

I am writing a paper and I have an expression something like this: $$\begin{equation} \notag x = \text{large_expression} + \begin{cases} y & \text{if } a<b \\ z ...
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1answer
179 views

Symbol for “if any”

I am looking for a symbol if any for the following equation in my algorithm This is to find closed pattern where $p_i$ is longer than $p$ and $p$ is a sub-pattern of $p_i$ and $support(p) = ...
3
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3answers
91 views

What are the sets V and ON?

Are there any known classes called "V","ON" in the subject of ordinals? I have seen it in a few places but can't find the definition in wikipedia.. Thank you!
0
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1answer
42 views

notation for numeral concatenation

I have a set, I need to represent in a form: $\lbrace f(x) \ | \ x \in A \ \& \ P(x)\rbrace$. However, have not been able to find the right mathematical notation for numeral concatination. What is ...
0
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1answer
88 views

$\sigma$-algebras, containment, and the notation used.

I'm proving the following proposition taken from Royden 4th Edition, Let $\mathcal{F}$ be a collection of subsets of a set $X$. Then the intersection $\mathcal{A}$ of all $\sigma$-algebras of subsets ...
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0answers
48 views

Notation for linear transform where only a subspace of the domain is used

I posed this question (sort of) here: A 2x2 matrix $M$ exists. Suppose $M^3=0$ show that (I want proof) $M^2=0$ Suppose I have a linear transformation over a field $K$ $T:K^3\rightarrow K^3$ ...
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6answers
2k views

A 2x2 matrix $M$ exists. Suppose $M^3=0$ show that (I want proof) $M^2=0$

I'm sure I've done this before in abstract algebra. Regardless it's escaped me now. I have proved that for $T:U\rightarrow V$, with $dim(U)=m$ and $dim(V)=n$ that $rank(T)\le m$ which is obvious, ...
0
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2answers
84 views

Let $R$ a commutative ring and let $a\in R$. What does $aR$ mean?

Let $R$ a commutative ring and let $a\in R$. What does $aR$ mean ? I would think it means $\{ar : r \in R \}$ as that was the meaning in group theory. The thing that confuses me is that in group ...
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1answer
135 views

understanding 'p∈ (n, succ)'

I understand that this may be a stupid question to some, but I've come to my wit's end trying to understand this condition: if p ∈ (n, succ) then I keep ...
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3answers
3k views

What is the symbol $\triangleq$?

I came across this new symbol while reading a document about writing proofs, and I have never seen it before.
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2answers
123 views

can someone explain this notation to me?

$$ dz_t \sim O\left(\sqrt{dt}\,\right) $$ $z$ is a Brownian motion random variable, for reference. I just don't understand what the $\sim O$ part means. I've looked up the page for Big O notation ...
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0answers
44 views

Nested log notation

As a complement to this question: What's the correct notation for log squared? What is the correct notation for $\log (\log \log ( ... \log((n))))$? By analogy, with the $n$th derivative of ...
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2answers
265 views

Meaning of NOT all but finitely often

Can someone clarify for me the meaning of the statement "NOT all but finitely often"? It's driving me crazy. I'm not able to break it up. Thanks.
1
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1answer
74 views

Is this absolute value notation or something else?

In this document, in Figure 1 (second to last page) there are several uses of $\| \;\;\|$: Is this another notation for absolute value, or is this a notation for something to do with ...
2
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1answer
68 views

Seeking advice on copying Peano's notation

Can anyone give me advice, or a URL for advice, on simulating the notation of Peano's Formulario in LaTeX? or in Word?
0
votes
1answer
188 views

What is the dot product between a vector of matrices?

There is a notation used in many sources (e.g. Wikipedia: http://en.wikipedia.org/wiki/Exponential_family) for the natural parameters of exponential family distributions which I do not understand, and ...
1
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3answers
741 views

Standard notation for the set of integers $\{0,1,…,N-1\}$?

I was wondering if there exist a standard notation for the set of integers $\{0,1,...,N-1\}$. I know for example $[N]$ could stand for the set $\{1,2,...,N\}$ but what about the former, i.e. ...
5
votes
3answers
187 views

How to write $\frac{k}{k}$ using $\sum$ notation?

I want to use $\sum$ notation for this:$$\underbrace{\frac{1}{k}+\frac{1}{k}+\ldots +\frac{1}{k}+\frac{1}{k}}_{k\text{ times}}$$ I guessed$$\sum_1^k\frac{1}{k} ,$$but it equals ...
0
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1answer
62 views

Question about notation in differential equations.

In general, an ordinary differential equation is in the form $$ \begin{cases} x'(t) = f(t, x(t)) \\ x(t_0) = x_0 \end{cases}. $$ When proving the existence and uniqueness theorems, an operator $T$ was ...
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1answer
55 views

Limit Comparison Test Defined entirely in symbolic notation

Is it possible to define the limit comparison test entirely with symbols (no textual explanation), or with as little textual explanation as possible? How? My latest best attempt: ...
0
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1answer
75 views

Notation question in linear algebra problem

I am confused by the symbol $\mathcal{L}$. What do $\mathcal{L}(V)$ and (especially) $\mathcal{L}(\mathcal{L}(V),\mathcal{L}(W))$ in b) mean? Let $T:V\to W$ be an isomorphism. For each ...
0
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1answer
197 views

What does $R^+$ mean?

I'm not sure if it's statistics related but I came over this in my stats related computing assignment. Does $R^+$ (looks like R to the power of plus) mean all positive real numbers? Does it include ...
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1answer
99 views

What is the definition of $\sum\limits_{0\leq i\leq m,\text{ }0\leq j\leq n}a_{ij}$

I understand the concept of double summations, at least intuitively, but I'm trying to understand it formally. So, to begin with, I have a question: Is this double summation equality true by ...
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2answers
40 views

Simple notation question

Let A = {2, 3, 4, 6, 7, 9} and define a relation R on A as follows: For all x, y ∈ A, x R y ⇔ 3 | (x − y). Then 2 R 2 because 2 − 2 = 0, and 3 | 0. What does the ...