# 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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### 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"](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 ...
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 ...