Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [terminology]

Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

0
votes
0answers
7 views

Does the phrase “sparse bundle” mean anything?

This question is of no real consequence, it just popped into my head and I am curious about it. Apple uses a file format called the .sparsebundle for Time Machine backups on network drives. A ...
4
votes
1answer
42 views

Looking for a terminology for “sameness” of functions

Consider the situation described in the following diagram, namely: $A$, $A'$, $B$, and $B'$ are sets. $\alpha:A\rightarrow A'$ and $\beta:B\rightarrow B'$ are bijections. $f:A\rightarrow B$ and $\ f':...
1
vote
1answer
22 views

What does the word “extend” mean in the context of model theory?

Consider the following two problems: (1) Let $L=\{E\}$ be a language consisting one binary relation symbol. Let $T$ be the $L$-theory saying that $E$ is an equivalence relation with infinitely many ...
0
votes
0answers
26 views

Greek symbol for bit?

Symbols / greek letters are used in mathematical notation for variables, functions etc. and commonly informs the reader that it is definied within a conventional accepted range. What is the most ...
1
vote
2answers
23 views

Denoting Like Inequalities

I wish to assert that the equivalence of ordered pairs (a,b) and (c, d) is contingent upon the common direction of their inequality. a could be less or greater than b but (c, d) could be considered ...
3
votes
0answers
23 views

Matrices with positive permutation products

Let $A=(a_{ij})$ be a $n\times n$ real matrix such that $$ \operatorname{sign}(\sigma) \cdot a_{1,\sigma(1)} a_{2,\sigma(2)} \ldots a_{n,\sigma(n)}\ge 0 $$ for all $\sigma\in S_n$. Is there a name ...
3
votes
0answers
50 views

Is there an English term for a function which is locally linearizable?

In Italian we have the notion of derivabilità and differenziabilità. In one dimension they are equivalent; in more dimensions, instead: A function is derivabile it is differentiable, that is, if ...
7
votes
1answer
254 views

What is the term for this family of improper integrals?

What is the name of the integrals of this form? $$\int_{0}^{\infty} \frac{\sin\left(\frac{x}{1}\right)\sin\left(\frac{x}{3}\right)\cdots\sin\left(\frac{x}{2n + 1}\right)}{\left(\frac{x}{1}\right)\...
1
vote
0answers
18 views

Is there a name for an integral of the form $\int d \vec{r} \int d \vec{r}\,'\, f(\vec{r})\, K(\vec{r} - \vec{r}\,')\, f(\vec{r}\,')$?

Is there a special name for an integral of the form $$\int d \vec{r} \int d \vec{r}\,'\, f(\vec{r})\, K(\vec{r} - \vec{r}\,')\, f(\vec{r}\,')\; ?$$ Here $\vec{r}, \vec{r}\,' \in R^d$, and the ...
2
votes
1answer
47 views

Coefficients of the expansion of $\prod_{i=1}^k(x+i)$

This seems to be something well known, but I couldn't find any reference. Suppose that we wish to expand the product $\prod_{i=1}^k(x+i)$ as $a_0x^k+a_{1}x^{k-1}+\ldots+a_{k-1}x+ a_k$. The ...
2
votes
0answers
41 views

Terminology for free variables

Suppose you have a proof along the lines of $$\begin{array} {rc} \text{Assume:} & x > 2 \\ & \vdots \\ & \text{Some logic stuff} \\ & \vdots \\ \text{Conclude:} & x > 1 \\ \...
0
votes
0answers
14 views

how to name a set which subset is not vertex-cut set

Sorry, this question sounds stupid because it's just like a basic term, but it's difficult for me, as my mother language is Chinese. Now, i write my paper about graph theory in chinese, and editor ask ...
2
votes
0answers
46 views

Definition of “Integration”

Can I call it "Integration" if I solve a Riemann integral by calculating the area under the curve using the areas of known geometrical shapes (assuming they exist for such a curve)? Or can I only call ...
1
vote
0answers
28 views

Powerset without subset with more than k elements

I am looking for something very similar to the powerset concept but i don't know how to search for it. This is what I found: Wikipedia defines the powerset as follow: In mathematics, the power set ...
0
votes
0answers
15 views

What do the terms “special form” and “general form” mean in reference to an equation?

What do the terms "special form" and "general form" mean in reference to an equation? Is the "standard form" the same as the general?
0
votes
0answers
20 views

Is there a name for the vectors produced by the vee operator?

The $\vee$ (vee) operator is defined in Chirikjian's Stochastic Models, Information Theory, and Lie Groups, Volume 2, page 20. It maps elements of a Lie algebra to a vector: $$ \left(\sum_{i=1}^n x_i ...
3
votes
1answer
28 views

Is there a word for “nodes that can reach every other node and itself again”?

This graph is a sub-graph of a larger one. But this sub-graph contains all nodes with a special characteristic. You can start at any point of the graph. You can reach every other node from there AND ...
2
votes
2answers
53 views

How do we formally define “j-th smallest element”?

Let $A$ be a nonempty finite subset of $\mathbb{R}$. Firstly, let me write down how to define the term "the smallest element of $A$" formally. Suppose 'for every $x\in A$, there exists $y \in A$ ...
0
votes
1answer
38 views

What is a poset?

I know the standard definition, but are there any alternative definitions? In particular, I distinctly remember seeing a remark that the definition given by John Kelley in his classic text on General ...
0
votes
2answers
34 views

How to refer to a set of lines where each line is either parallel to $x$-axis or $y$-axis

Suppose that there are $k$ lines on the plane that are parallel to $x$-axis along with $m$ lines parallel to $y$-axis, not necessarily spaced equally. Is there a technical term for these kind of line ...
1
vote
1answer
13 views

Is there a specific format for writing “where variable x represents/is”

For instance, I have the equation y = mx, where m is the slope. Is there a concise and mathematical way to write "where m is the slope"?
0
votes
0answers
27 views

What does evenly distributed mean?

I, repeatedly, find this expression used in many places, especially when talking about probabilities. I am interested in understanding the meaning of the expression in a $2$-dimensional and $3$-...
1
vote
0answers
30 views

Is there a name given to a group of symbols which are multiplied together?

If I have several terms (is that the right word?) multiplied together, is there a name for such a group? E.g. $a \times b \times c + d \times e=z$ What would you call the groups $a \times b \times c$...
8
votes
8answers
444 views

Is induction something we take on faith?

I understand that in mathematics and logic we can continue to reduce things to simpler axioms, principles, and so on, and we have to "stop" at some point otherwise we're just going on forever. We ...
0
votes
0answers
6 views

uniform convergence on segments

A google search for “uniform convergence on segments” yields only one hit: https://www.encyclopediaofmath.org/index.php/Shift_dynamical_system in which ‘the topology of uniform convergence on ...
3
votes
1answer
50 views

Distinction between “fuzzy” and “confused with.”

In the terminology of game theory, "fuzzy" and "confused with" signify different things. How are their associated concepts alike and distinct? EDIT: My initial encounter with the terms was here: ...
1
vote
0answers
25 views

Is there a name for a direction vector scaled by its directional derivative?

Given a direction vector $\hat{v}$, of unit length, and a gradient $\nabla f$, and that the directional derivative $\nabla f\cdot \hat{v}$ is equal to the magnitude of the gradient vector projected/...
0
votes
1answer
35 views

Convention for $(-1)^x$ in closed form expressions ($x\in \Bbb{R}$)

I'm trying to find the closed form expression from a question but I'm debating whether I should include $(-1)^x$ in it, which would make the question significantly easier. My problem with the question ...
0
votes
2answers
29 views

Is there a term for numbers like 1001, 2002, 3003 or 1010, 2020, 3030

If I am speaking to somebody about 4 digit numbers in specific format where the second and the third digits are the same or where the first and the third digits are the same what would be the term for ...
0
votes
1answer
10 views

Adjective that describes a proper cumulative distribution function that may be discontinuous

If $f(x)$ is a non-atomic probability distribution function, then its integral $F(x) := \int_{-\infty}^{x}f(y)dy$ is a continuous function. However, if $f(x)$ has atoms then $F(x)$ may be ...
1
vote
1answer
38 views

Help to translate mathematical definitions [closed]

I'm from a non speaking english country so many concepts I learn are translated to my native language and most of them I can easily translate or find them but these one I can´t seem to: (I will post ...
0
votes
1answer
31 views

When, if ever, are subsets elements?

A very basic question on terminology that I have not seen addressed despite some searching: are any sets (such as subsets) considered elements? My understanding is that the empty set is a subset of ...
0
votes
0answers
50 views

Which mathematical property prevents reducing equations to 0 = 1?

Which mathematical property prevents taking an equation, this one for example: $r = -0.5\cdot a \cdot t^2$ and moving all terms to one side to make it equal to zero... $\Longrightarrow 0 = -r - 0.5\...
2
votes
0answers
31 views

In a congruence are the numbers remainders or residues?

If we have $a \equiv b \pmod{n}$ then $a$ and $b$ are congruent to each other modulo $n$, correct? What do we "call" $a$ and $b$? Because sometimes these numbers can be negative. Would they be ...
2
votes
0answers
38 views

Term for removing a graph's node while preserving paths

I am looking for standard terminology for the following operation on a directed graph $G=(V,E)$. Intuitively, the operation removes a node $v$ while preserving paths via $v$, by adding edges that ...
0
votes
2answers
46 views

Name for the set of unique $\{a, f(a), f(f(a)), … \}$?

Is there a name for the unique values produced by recursive function calls? Something like $f(x) =$ (recursive applications of) $(x \cdot 2) \mod 6$ $f(1) = \{1, 2, 4\}$ Thank you.
-1
votes
1answer
36 views

What is the relation between these two meanings of “theory”?

In this introduction on Satisfiability modulo theories, it is explained that by a "theory" $T$, it is meant a tuple $(\Sigma, I)$ where $\Sigma$ is a signature (i.e. a set of non-logical symbols), and ...
0
votes
0answers
24 views

Terminology of function; $f(n)=(4^n-2) / 7$

Let $n\in\mathbb{N}$, and I define the function: $$f(n) = \frac{4^n - 2}{7}$$ Is this $f(n)$ called a quartic function? Is $f(n)$ a polynomial function of degree four? Can a polynomial be restricted ...
1
vote
2answers
57 views

Is $\iint f(x,y)\; dx\;dy$ called an iterated integral or iterated integrals

In my Calculus 4 class we are learning about finding double and triple integrals. For example, one finds a double integral $$ \iint_E f(x,y)\;dA $$ by writing it as $$ \int_a^b\int_c^d f(x,y)\; dx\;...
2
votes
0answers
27 views

The Name of a Special Matrix Whose Entries $A_{ij} = j^i$

I heard that the matrix A whose entries $A_{ij} = j^i$is a special one and has a name. Could you please help with its name? Below is an example of a 4x4 matrix of this special type: \begin{bmatrix} 1 ...
3
votes
1answer
44 views

Rings without associativity.

Is there a specific terminology for rings in which we do not require associativity on the multiplication ? Like, for example we say semiring for a ring where we do not require the additive inverses. ...
5
votes
0answers
32 views

Name of a particular matrix with $M_{ij}=t_{\min(i,j)}$?

I'm looking to see if there's a name for a particular type of matrix $M_{ij}=t_{\min(i,j)}$, ie.: \begin{bmatrix} t_1 & t_1 & t_1 & t_1 \\ t_1 & t_2 & t_2 & t_2 & \cdots\\ ...
2
votes
1answer
26 views

What does “carry a quadratic into a reduced one” mean?

I was reading A. Adrian Albert's Modern Higher Algebra (1938). On p.30, there is such an exercise (emphasis mine): Let $\mathfrak F$ be a field of characteristic $2$ and $x^2+ax+b=0$ be a quadratic ...
0
votes
1answer
25 views

If $a \in X$ we can say “$X$ contains $a$”. Is there a corresponding verb for the relation $A \subset X$?

Obviously I can say "$X$ has $A$ as a subset" or "$A$ is a subset of $X$", but I'd like a more concise way of putting this.
1
vote
1answer
55 views

Can we say two morphisms to be isomorphic?

The definition of subobject in Wikipedia is this: let $A$ be an object of some category. Given two monomorphisms $u : S\to A$ and $v : T\to A$ with codomain $A$, we write $u\le v$ if ...
0
votes
1answer
45 views

Terminology question: $\sigma$-algebra generated on the codomain

Let $X$ and $Y$ be two non-empty sets and $f:X\to Y$ a function. Furthermore, let $\tau$ be a topology and $\Sigma$ a $\sigma$-algebra, respectively, on $X$. It is easy to see that \begin{align*} f(\...
3
votes
2answers
49 views

We know there are beta distribution and gamma distribution. Why not alpha distribution?

We know the well-known beta distribution and gamma distribution. I am just wondering why don't we have alpha distribution? I am guessing there must be a reason for this but couldn't find it elsewhere. ...
0
votes
0answers
30 views

'If' or 'Suppose' in a mathematical statement

One of three characters used to define probability measure $\mathbf{P}$ on $(\Omega,\,\mathcal{F})$ where $\mathcal{F}$ is a set algebra (NOT a $\sigma$-algebra), is that if (or suppose) $(A_i)_1^{\...
2
votes
2answers
35 views

Are Laurent series called polynomials?

Traditionally, polynomials cannot have negative exponents. So what gives? Inspired by this.
0
votes
0answers
22 views

What is parameterization in general?

Consider the set of all infinite arithmetic sequences of real numbers: $$\forall f,d\in\mathbb R\ (f,f+d,f+2d,\cdots,f+id,\cdots)$$ Most people would say that the set of all of these sequences is ...