1
vote
1answer
40 views

How would you describe category $\mathsf{Rel}$?

I encountered two definitions for a category denoted by $\mathsf{Rel}$: Objects are pairs $\left(A,R\right)$ where $A$ is a set and $R$ a relation on $A$. Arrows in ...
0
votes
0answers
35 views

What's the right way to write big-O?

I always write $\mathcal{O}(n)$ (\mathcal{O}(n)). But I frequently see $O(n)$ (O(n)), probably because it's shorter and more ...
0
votes
0answers
32 views

Terms for particular equivalence relation and partition?

Let $T$ be a set of sets. Let $\equiv$ be an equivalence relation on $\bigcup T$ defined by the formula $$a\equiv b \Leftrightarrow \forall X\in T:(a\in X\Leftrightarrow b\in X).$$ Let $S$ be a ...
0
votes
0answers
21 views

The space of alternating multilinear forms

I was just wondering if there is a standard (or even just usual) notation for the space of alternating $k$-linear forms on an $F$-vector space. I know that this space is naturally isomorphic to the ...
0
votes
1answer
99 views

Does “arbitrarily small” mean very close to zero or very negative?

In mathematical writing, does “arbitrarily small” mean very close to zero (like $0.000001$) or very negative (like $-1000000$)? Are there better phrases to distinguish these two cases?
0
votes
0answers
43 views

Hyperbolic sinc function

Cardinal sine function or sinc function is defined by: \begin{equation} \mathrm{sinc}x=\begin{cases}\frac{\sin x}{x}, & x \neq 0,\\ 1, & x = 0,\end{cases} \end{equation} Is there any ...
1
vote
0answers
30 views

In regards to metric spaces, does $d^\star$ have an accepted name, or notation? Do any authors use it?

(I write $\omega$ for the set $\{0,1,2,\ldots\}$.) Let $X$ denote a metric space with metric $d$. Define a function $d^{\star} : X^\omega \times X^\omega \rightarrow [0,\infty]^\omega$ by writing ...
0
votes
0answers
24 views

Is there accepted notation and/or terminology for the smallest cover of $S$ with cells from $P$?

Let $X$ denote a set. Then for $S \subseteq X$ and $P$ a partitioning of $X$, define $P \diamond S$ as the smallest cover of $S$ with cells from $P$. Explicitly: $$P \diamond S = \bigcup\{Q \in P ...
0
votes
2answers
59 views

Very simple notation question

What notation is it called when a number is represented as a series of additions, for example: 124 = 100 + 20 + 4 This is a very simple question obviously but I don't remember what it's called! ...
21
votes
3answers
683 views

Who named “Quotient groups”?

Who decided to call quotient groups quotient groups, and why did they choose that name? A lot of identities such as $$\frac{G/A}{B/A}\cong \frac{G}{B}$$ suggest that whoever invented the notation ...
1
vote
1answer
33 views

The origin labelled on a graph: $0$ or O?

When one draws a graph, say in the x,y plane, we label the origin with a circular/elliptical symbol. Now is this a $0$ (zero), or is it O (for Origin), or simply just a circle/ellipse? Can it be ...
3
votes
1answer
53 views

Is there a way in matrix math notation to show the 'flip up-down', and 'flip left-right' of a matrix?

Title says it all - is there an accepted mathematical way in matrix notation to show those operations on a matrix? Thanks.
0
votes
1answer
90 views

What does $\mathbb{Z}_2$ mean?

Wich number space is ment by: $\mathbb{Z}_2$ (I know that $\mathbb{Z}$ stands for Integer)
3
votes
1answer
1k views

How do we pronounce this symbol?

I would like to know how to pronounce in english this symbol $\nabla \phi$ It is something phi ... ? thank you
3
votes
1answer
90 views

$f_{n+1}(x)=f_n(x+1)-f_n(x)$ functional equation and “classification of functions”

Doing a quiz I found a question of this kind "given $a_0, a_1, a_2, ...,a_n$ find $a_{n+1}$" In order to find the $f$ such that $f(a_n)=a_{n+1}$ I tryed for a function like $f(x)=k+x$ ...
0
votes
2answers
59 views

$\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ notation

Define $\mathcal N$ $\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ Does $\mathcal N$ has a special name and standard notation?
0
votes
0answers
41 views

Is there a traditional name for the “eigenspace” function?

Let $A$ denote a field, $X$ denote an $A$-vector spaces, and suppose $\varphi : X \rightarrow X$ is a linear transformation. Is there a traditional name for the corresponding "eigenspace" function? By ...
0
votes
1answer
11 views

An indexed family of filters and their elements

Let $X$ is an indexed (by some set $n$) family of filters (on some poset $\mathfrak{A}$). Is there any standard notation/terminology for the set $\{ y\in \mathfrak{A}^n \,|\, \forall i\in n:y_i\in ...
18
votes
4answers
2k views

Is there a way to denote the calculation $1+2+3+\dots+n$? [duplicate]

Since $n!$ represents $$1\cdot2\cdot3\cdots n,$$ I am wondering if there is a way to represent $$1+2+3+\dots+n?$$ What are some usual notations for the computation of some common sequences? Any other ...
1
vote
1answer
28 views

Notation/terminology: Existence of a nonleast element which is less of any element of a set

Let $A$ is a subset of a partial order $X$. Are there any name and/or notation for the following predicate $P(A)$? $P(A)$ iff there is a non-least element $x$ of $X$ which is a subelement of each ...
1
vote
2answers
40 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 ...
0
votes
0answers
104 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 ...
5
votes
1answer
151 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 ...
0
votes
2answers
125 views

Is “zed” a valid name for $\emptyset$?

I've always known that $\emptyset$ is called an empty set or null, until recently, when I heard someone calling it zed. I looked it everywhere but couldn't find this naming. Is "zed" a valid name ...
2
votes
1answer
22 views

What is the name for the property that a subset of a set follows the same rules as the set?

I have a set that follows a certain property and I want to say that the subsets of this set also follows the property. What is this called? I know that closure under an operation means that performing ...
0
votes
0answers
58 views

Identity relation of many variables

The identity relation on a set $A$ is $\operatorname{id}_A = \{(x;x) \,|\, x\in A\}$. This can be generalized for any (possibly infinite) index set $N$ as $\{(\lambda i\in N: x) \,|\, x\in A\}$ (here ...
0
votes
2answers
247 views

Probability of a Min/Max

I am studying probability for an exam and I am finding hard to understand the notion of $P(\min(X_1,X_2))$ and $P(\max(X_1,X_2))$, where $X$ is a discrete or a continuous variable. I have found in my ...
0
votes
1answer
50 views

Is there a name for this theorem about the convergence of a function?

Let $f(x)$ be a continuous function over $\mathbb{R}$ such that for all $a < b$, we have $a < f(a) < b$. Then, for any $x < b$, the sequence $\{t_n\}$ defined by $t_0 = x, t_n = ...
1
vote
2answers
62 views

Basic Cartesian prodcuts

I am having some issues grasping basic ideas of Cartesian products. I am reading a PDF my professor gave us explain sets/Cartesian products. If $\mathbb{R}\times \mathbb{R}$ can be written as ...
0
votes
1answer
37 views

Notation for permutation corresponding to the action of a group element

Let $G \times X \to X,\ \ (g,x) \mapsto g.x$ be an action of $G$ on $X$, i.e., $e.x = x$ for all $x \in X$; $gh.x = g.(h.x)$ for all $g \in G$, $x \in X$. For a fixed $g \in G$, how should I refer ...
1
vote
1answer
82 views

From $\mathsf{O}$ to $\mathsf{I}$ via $\infty$

The following is not true mathematics, but a little imaginary story about mathematical symbols. I wonder if there is - in parts - a true (etymological) story behind it. Once there was a symbol ...
1
vote
3answers
88 views

Is there a notation for $((n!)!)!$?

I wonder if there is a notation for repeating factorials such as $((3!)!)!$. Without the parentheses, $(3!)!$ could be confused with the double factorial $3!!$. Is there is no such notation known, ...
0
votes
1answer
44 views

How to correctly write this ring theoretic thing?

Im unsure how to write this thing below in a formal way : For an integer $n>2$ Let $F_n(x) = a_0 + a_1 x + a_2 x^2 + ... + a_{n-1} x^{n-1}.$ Also we have $x^n = 1$ and $1 + x + x^2 + ... + ...
1
vote
2answers
89 views

Notation and terminology for functions, interpreting $f(y)$

It seems to me there are two different interpretations of a symbol $f(y)$. I will explain what I mean: Suppose I have a function $f(x) = x$. (I took the identity map to have a simple example). Also ...
1
vote
1answer
104 views

Name for a category

Is there any name or notation for this category? Let $U$ be a set. By "function" I will mean a function $U\rightarrow U$. objects are functions; morphisms from a function $A$ to a function $B$ are ...
2
votes
1answer
46 views

Notation for translating vectors

I'm completely new to vector geometry and recently encountered some new notation (and wholly unfamiliar) for the translation of vectors. $$T:Z \mapsto A + Z$$ The above is described as A ...
0
votes
1answer
50 views

We refer to X for standard notations and definitions from Y

I'm having problems with my mathematical English, so I'd like to ask for your help! Is it correct to write something like "Unless stated otherwise, we refer to [1] and [2], respectively, for standard ...
2
votes
2answers
181 views

Is there a proper term and/or symbol for an “agnostic” conclusion?

My question stems from the material conditional: $p \rightarrow q\\p\\\therefore\space q$ However, if $\bar p$ then the conditional is silent. I would like a way to represent this fact using, if ...
0
votes
0answers
42 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 ...
0
votes
2answers
34 views

What is the term to make one matrix from two or more?

I am looking for the proper term for the operation of creating one block matrix from two or more for example $[AB]$ from $A$, $B$. And what is the correct notation to denote such a matrix. Do we use a ...
3
votes
0answers
51 views

Curve of centers of curvature

I really can't find the English name of the curve of the centers of curvature of a curve. Formulated more precisely: Suppose $\alpha$ is a regular curve in $\mathbb{E}^2$ and $||\alpha(t)'||=1$. How ...
1
vote
1answer
70 views

Cartesian Product

Given sets $A_1,A_2,\ldots, A_n$ how do I describe its Cartesian product $$C = A_1 \times A_2 \times \ldots \times A_n$$ in a succinct fashion? An example would be $C = \times_{i=1}^n A_i$ or $C = ...
5
votes
4answers
219 views

What is a suitable name for numbers like $a + b\sqrt{c}$

The motivation for this is to find a succinct name for a data type in a Python module. Suppose I choose an integer $c$ and I want to talk about the set of numbers of the form $a + b\sqrt{c}$, where ...
2
votes
1answer
92 views

A few basic questions about the arithmetical hierarchy, mostly about terminology.

I was reading about the arithmetical hierarchy, and I have a few questions, mostly notational. For completeness, here's the definition given over at Wikipedia. The classifications $\Sigma_n$ and ...
2
votes
3answers
69 views

Notation for definition and equivalence

I would like some clarification about the usage/meaning of $:=$ and $\equiv$. I have been using $A := B$ to denote "Let $A$ be defined as $B$." This is akin to assignment ...
1
vote
1answer
138 views

A name for set of disjoint intervals

What's in a name? That which we call a rose by any other name would smell as sweet. William Shakespeare I'm looking for a short name for the phenomenon collection of disjoint intervals. I ...
2
votes
2answers
89 views

What is the notation of 'a single term in the DFT'

I have a notation/terminology question: I am writing a paper in not-quite-my-area and can't figure out the right way to phrase/notate the following: I have a discrete function $p[x]$, of which I can ...
1
vote
1answer
102 views

What is a finite partial function from $\mathfrak c$ to $D=\{0,1\}$

While I reading a paper, there is a notation is called finite partial function. I searched by google, I cannot find its definition. So I post it here as a question: What is a finite partial ...
2
votes
2answers
118 views

What does it mean to “identify” points of a topological space?

I was recently reading about circle rotations (a basic example in dynamical systems) and got confused by some notation. It said consider the unit circle $S^{1} = [0,1]/{\sim}$, where $\sim$ indicates ...
0
votes
1answer
49 views

Formal notation when using the axiom of specification

The axiom of specification states formally that for every property $\varphi$ holds $\forall X\exists Y\forall x(x\in Y\longleftrightarrow x\in X\wedge\varphi(x))$. Since from the axiom of ...