Questions tagged [terminology]

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

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Definition of increment

As feedback on a project about stochastic processes, I was asked to give the definition of "Increment". However I can't seem to find a well written definition anywhere. Would the following ...
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Understanding the term “double roots” of a quadratic equation [duplicate]

We know that when a quadratic equation $ ax^2 + bx + c = 0 $ has zero discriminant value, then the quadratic equation has only "one root". But why do some mathematician call it "double ...
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Question About the Definition of a Preorder

Given a set $\{a,b,c,d\}$, does the set of relations $\{a\leq b, b\leq c,c\leq d,d\leq a\}$ give rise to a preorder? If so, what does a preorder have to do with the notion of ordering if $a$ can be ...
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What is the meaning of this sentence? “The right side of $a\equiv b \pmod c$ is less than or equal to the left side.”

Let us consider a congruence of the form $$a\equiv b \pmod c$$ What is the meaning of the following sentence? $$\text{The right side of the congruence is less than or equal to the left side.}$$ For ...
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Name for cuts which result in shapes that are rotatable images of one another

I'm looking for the technical term to describe any line that cuts through a shape such that the two pieces are a rotation of one another. Obviously any line of reflective symmetry fulfils this ...
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Question regarding the given definition of algebra

Rereading the notes of a proof based course I took last year I encountered the following exercise: Let $\phi\neq C\subset P(E)$. $C$ is called and algebra if it satisfies: $$\forall A,B\in C ~[A\cup B\...
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Is UFD an integral domain?

Let $R$ be a ring. Does part of the definition of $R$ being UFD contain that it is an integral domain, or does conditions of $R$ being a UFD forces $R$ being an integral domain? If latter, why is it ...
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Terminology for functions with preimage of finite cardinality?

I'm dealing with a class of continuous functions $f:[0, 1] \to \mathbb{R}$ such that the preimage of any $y \in f([0, 1])$ is of finite cardinality. I wonder whether there is a common terminology of ...
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What is the terminology for a product of a ring with a group (like the quaternions) or (more generally) with a monoid (like a polynomial ring)?

I don't think there is much for me to elaborate beyond the title question: "What is the terminology for a product of a ring with a group (like the quaternions) or (more generally) with a monoid (...
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Box Topology Name

To put it simply, why is the box topology on an infinite product of topological spaces called the box topology? What is "boxy" about it?
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Are there single words for being within two bounds exclusive and non-exclusive?

When $a <= b <= c$ is there a single word that describes $b$ being between $a$ and $c$ (inclusive)? Is $b$ within $a$ and $c$? Similarly, when $a < b < c$ is there a single word that ...
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“Big ear” of polygons: proper nomenclature

I've developed a polygon triangulation algorithm which uses a process similar to the "Graham Scan" to remove convex "portions" of a concave polygon. I couldn't find the proper ...
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Tridiagonal matrix with extra diagonals at sides

I'm struggling with the construction of a matrix given below. I need to find a pattern to later on code it in Python and then solve a linear system of equations involving that matrix. Does that kind ...
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Is there a name for the multiplicity of each eigenvalue in the minimal polynomial of a linear operator?

We know that when the characteristic polynomial of a linear operator $f$ can be written in the form: $$ \chi_f = \prod_i (x - \lambda_i)^{\mu_i}, $$ the number $\mu_i$ is called the algebraic ...
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Is there a common name for the numerator and denominator

For instance, prefixes and suffixes can be collectively called adfixes. Adfixes themselves are a subset of affixes. Is there a common name for the numerator and denominator? (The inspiration came ...
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Question regarding terminology used in a lemma

I was reading my calculus notes and found the following lemma: Lemma: Let $f:I\to\mathbb{R}$ be continuous on $I$ and differentiable on its interior $I^•$. Then $f$ is increasing (strictly increasing)...
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Adding edges with the Breadth-First Search algorithm

I was reading a paper about extending trees to unicyclic graphs and it had the following statement: Critically, an edge (x, y) can be added to a tree T if and only if when applying Breadth-First ...
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What is an infinite set with increment operation called?

What is an infinite set with a unary increment operation (along with the inverse, decrement) called? For example, the set of integers, $\mathbb{Z}$, along with an increment operation (f: x -> x + 1)...
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When can we say that two representations of an island's shore line are topologically equivalent? Is Luzon an instructive case?

Under this answer to "Is this 'satellite photo' the only representation of the shape of Gilligan's Island?" is a short discussion of the degree of similarity between drawings of a famous but ...
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There are two rocks in front of your hourse. True or false: There is one rock in front of your house [closed]

I say true because there is indeed one rock in front of your house (it is also reasonable to say that there are two rocks). However, my teacher is claiming that the statement is false and sees the ...
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Compound variables? Is this the correct term?

I asked this yesterday in Cross-validated (the statistics equivalent of here) but got few views and no answers. So I thought that I would ask it here. I am looking for a term to describe the concept ...
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What is an inclusion of a subgroup?

I have to find all the inclusions of the subgroups of $\mathbb{Z}_{48}$ but I don´t know what is that. What is an inclusion?
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Proper Terminology for Difference via Subtraction vs. Division

When comparing normalized data sets, I'm struggling to find the correct terminology for $X_1-X_2$ vs $ X_1\div X_2$. Often I see the word "Difference" used interchangeably. Is there a most ...
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Why is it called the “congruence class”, not “congruence set”?

Stupid question, why do we call it the congruence class, not congruence set? Is there any scenario when the congruence class is not a set?
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On matrices satisfying $T^* J T = - J$

Let $J\in\mathbb{C}^{n\times n}$ be a fixed matrix and let $T\in\mathbb{C}^{n\times n}$ be a matrix such that $$ T^* J T = -J $$ where $T^*$ denotes the conjugate transpose of $T$. Do matrices $T$ ...
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Is a square a special case of a diamond (rhombus)?

Is the diamond shape (rhombus) necessarily different from the square (sides not perpendicular, different lengths of the diagonals), or is the square a special case of a diamond? Sometimes I see a ...
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Is there a term for a graph data structure in which a graph node can contain another graph?

A hypergraph is a graph in which an edge can connect more than two nodes. Is there a term for a "nested graph" - a graph whose nodes can "contain" arbitrary graphs? I have seen ...
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Why is a geometric theory called “geometric”?

In topos theory, the notion of “being geometric” often comes up. Some examples are: geometric morphisms, geometric logic, and geometric theories. For instance, here's a quote from Steve Vickers' ...
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What is difference between jordan curve and Jordan arc

This question was part of a mock test which I am trying to solve. Let $X : [-1,1] \to \mathbb{C}$ defined by $X(t)= t+ i|t|$ , $t\in [-1,1]$ then A) $X$ is jordan curve B) $X$ is jordan arc I ...
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Are “non-zero eigenspaces of a matrix” the same as “eigenspaces corresponding to non-zero eigenvalues”?

Sorry for the long title. In essence, I'm wondering if non-zero eigenspaces are the same as eigenspaces corresponding to non-zero eigenvalues. That is, are non-zero eigenspaces = $E$$\lambda$ for $\...
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What's the English term for this algebra operation?

I didn't study maths in English so apologies for this trivial question. How do you say in English when you have a formula 3n + 3 and you want someone to convert it ...
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Is there an analogue of the word “parity” for infinite/finite?

We say that two integers have the same parity if they are both even or both odd. Is there a word like this but for infinite/finite instead of odd/even? That is, if a quantity $X$ is finite if and only ...
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Dominant eigenvalue definition — is this paper wrong?

I have been reading this paper by Neubert et al. (2004) on calculating reactivities of dynamical models. On page 31, equation 11, they define the two matrices: \begin{equation} \begin{pmatrix} -1 &...
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Does distinct sets mean disjoint sets?

If A and B are two distinct sets, does that mean A and B are disjoint? Or if A is the subset of B, can A and B be two distinct sets? I am confused here that whether distint and disjoint sets mean the ...
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In graph theory, is there a term for the value of the difference between indegree and outdegree?

I'm working on a Graph Theory research project, and one of the key components is talking about the indegrees and the outdegrees of a few particular vertices. I need to define a term for the value of ...
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What is the name of the functions $V\to V$ which map every 1-dimensional subspace of $V$ to an 1-dimensional subspace of $V$?

Motivation: the permutations of the projective space $P(V)$ can be regarded as the equivalence classes of such functions (two such functions, $f$ and $g$ are regarded to be equivalent if for every 1-...
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Why is there no real coefficients in $g(x) = x - i$, yet there is in $f(x) = x^2 + 1$

Currently, I am going through Precalculus: With Limits (Cengage Textbook), and the topic in class is conjugate pairs. The book defines a conjugate pair as this: "Let be a polynomial function ...
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In the notation $T\colon\mathbb{R}^{n} \to \mathbb{R}^m$, does $\mathbb{R}^m$ refer to the codomain or the image of $T$?

Question: It is my understanding that the term codomain refers to a set, of which the image is a subset (although, not ...
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Need help understanding notation in mathematical optimization equation?

I have been reading the research paper ["Distributed Joint Power, Association and Flight Control for Massive-MIMO self-Organizing Flying Drones"][1](Paper is from IEEE so it might be stuck behind a ...
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Is there a single term for the *pair* (domain, codomain) of function $f$, or generally the (source, target) of morphism $f$?

This is just about finding concise terminology. So if $f:A \to B$, is there a single generic name for the pair (A,B)? What about for the pair (domain, image)?
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Is softmax “omni-periodic”?

A function is said to be "periodic" if there's a finite $T$ such that $f(t) = f(t \pm T), \forall$. Usually there's either one such $T$, or none at all. How about infinitely many $T$, that ...
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Motivation for the integral notation $\int _{I \in \mathbb{I}} D(I)$ for a categorical limit?

What is the motivation for the integral notation $\int _{I \in \mathbb{I}} D(I)$ for a categorical limit, which is otherwise known as $\underset {\mathbb{I} \leftarrow} {lim} \ D$?
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Name for nearly linear (line-shaped) subgraph of a graph

Given a graph, it's straightforward to define a "linear" or line-shaped subgraph: a connected subgraph with two ends which are nodes of degree one, and intermediate nodes of degree two. And ...
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Non-trivial connected semi-simple compact Lie group

This is a question about some terminology I'm not familiar with and was hoping to clarify. I've seen it written that every "non-trivial connected semi-simple compact Lie group" contains a ...
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What is this notion in statistics?

Question and request I'm sure the following idea is known, and must be basic, in statistics. I suspect it's related to the confidence interval (CI). However, CI is a statistical notion notorious of ...
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Linear subspace tangent to a manifold

What does it mean for a vector space/linear subspace to be tangent to a manifold (e.g. in $\mathbb{R}^n$ or $\mathbb{C}^n$)? Does it mean that it is contained in the tangent plane to some point? If ...
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What is a subinterval?

I got a specific question, and I think I'm forgetting some of my terminology, specifically what a subinterval is. Here is the question 3 engineers work on a cluster which has a daily limit of 2 ...
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How to properly read this proposition?

I'm reading this book (OK, Efe A. Real analysis with economic applications. Princeton University Press, 2007.) and in page 143 the author claim this proposition: I don't know how to properly read the ...
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Dartboard paradox and understanding independence

By definition, events $A$ and $B$ are independent if $$P(A \cap B) = P(A)\:P(B).$$ Therefore if an event $A$ happens almost never $\left(P(A)=0\right)$ or almost surely $\left(P(A)=1\right)$, then ...
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What is the general solution?

More specifically, does the general solution work for all cases? I am currently learning ordinary different equations but am curious about its meaning in general. Thanks!

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