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.

1
vote
0answers
53 views

Is there a name for manifolds that can be covered by a single chart?

this is more of a definitional question, but I'm wondering if there's a name or term for a manifold that can be covered by a single chart. More precisely, I'm speaking of manifolds for which there ...
0
votes
1answer
19 views

What is a non-concave and non-convex polygon called?

I am writing a software function to plot the outer points of an n-sided polygon and I'm having trouble ensuring I use the correct terminology. The function I've written simply renders the calculated ...
0
votes
0answers
13 views

Help with “partial differential equation” definition

From wikipedia: "PDE is a differential equation that contains beforehand unknown multivariable functions and their partial derivatives". My dubt is: suppose you have the following variable $u =u(x_1,...
4
votes
2answers
53 views

Is there a term for 'complementary factor'?

Please forgive this incredibly lame question, but if I have factor $n$ of $x,$ and I find its complementary factor $y= \frac xn$, does that complementary factor $y$ have a specific name? I haven't ...
0
votes
0answers
24 views

Definition of “almost everywhere”

Let $(X,ℳ,μ)$ be a measure space and $μ^*$ the external measure induced by $μ$. Which one of the following definition of "almost everywhere" (a.e.) is preferable, from both the points of view of ...
1
vote
1answer
44 views

What is the difference between “divides” and “divides exactly”? [duplicate]

Maybe this is the sort of question I could find the answer myself if I just knew the right search terms. I've gotten a whole bunch of search results and quite a bit of sidetracks. In my handwritten ...
3
votes
1answer
291 views

What algebraic structure does the set of endomorphisms of a ring have?

Let $R$ be a ring, and let $End(R)$ be the set of ring endomorphisms of $R$, i.e. the set of all ring homomorphisms form $R$ to $R$. Then we can define three binary operations on $End(R)$: $+$, ...
1
vote
1answer
56 views

A new category $C^*$ from a given category $C$

For a given category $C$ define the category $C^*$ as follows: the objects of $C^*$ are those of $C$; for given objects $u,v$, the $C^*$-morphisms $u\to v$ are all finite sequences $(a_1,\dots,a_n)$ ...
1
vote
0answers
14 views

Appropriate terminology for classifying some assumptions

I would like your help in order to choose the appropriate terminology for classifying the assumptions below. Consider a random vector $X\equiv (X_1,X_2,X_3)$. Let $\Delta X\equiv (X_1-X_3, X_2-X_3, ...
2
votes
1answer
23 views

On terminology; what is meaning of the “decrement” of a permuation? (or what is the alternative word or phrase used for this definition)

I am currently studying some lecture notes in Russian and I frequently look up the theorems and topics in English for better understanding (I'm not a native Russian so I merely just use the Russian ...
2
votes
1answer
51 views

Terminology for half the difference

Is there a term for half of the difference between two numbers $$x=\dfrac{a-b}{2}$$ Analogous to say the mean?
12
votes
4answers
2k views

What's the difference between “relation”, “mapping”, and “function”?

I think that a mapping and function are the same; there's only a difference between a mapping and relation. But I'm confused. What's the difference between a relation and a mapping and a function?
-2
votes
1answer
43 views

What means classify a Riemann Manifold? [closed]

I must resolve an exercise in which I have some condition on a Riemann manifold and the question is to classify all Riemannian manifold that satisfies that conditions.. I don’t understand what means ‘...
0
votes
0answers
9 views

Terminology request for a linear combination of residues of coprime integers

Let $m$ and $l$ be coprime natural numbers. Question: What is the name of the set $$ A_{m,l} = \left\lbrace n \mid n = lx - my, x\in \{0,\ldots,m-1\}, y\in \{0,\ldots, l-1\} \right\rbrace? $$ As ...
0
votes
0answers
29 views

What is $H_G^{(n)}:=\{h\in G: \operatorname{ord}(h)\mid n\}$ called for any fixed abelian group $G$ and $n\in\Bbb N$?

I'm reading "Contemporary Abstract Algebra," by Gallian. This is based on exercises 3.45 and 4.15 ibid. What is $H_G^{(n)}:=\{h\in G: \operatorname{ord}(h)\mid n\}$ called for any fixed abelian ...
0
votes
0answers
40 views

Is there a name for a collection of sets with the following property?

Is there a conventional name (term) for a collection $\mathbb{S}$ of sets with the following property: for any natural $k$ and $A_1,...,A_k\in \mathbb{S}$ there are $m,n\geq 0$ and pairwise disjoint $...
1
vote
0answers
25 views

Difference between Stable, unstable sets , manifolds and subspaces?

I am confused about the difference between the stable sets, unstable sets ; stable and unstable manifolds; and stable and unstable subspaces of a fixed point $p$ of a map $f : M \rightarrow M$ where $...
0
votes
0answers
17 views

Calculating the stability of frame rate given a frequency histogram of contiguous missed refresh periods

First off, I'm looking at the output of video to a screen, and I've captured the timing for when each frame is drawn to the screen. What I'm trying to capture is the stability of this frame rate for ...
2
votes
0answers
54 views

Notation for using a relation as a function from an element to set?

Let $R \subseteq X \times Y$ Is there a commonly used term/notation for the functions $f:X\rightarrow \mathcal{P}(Y)$ and $g:Y\rightarrow \mathcal{P}(X)$ defined as follows?: $$f(x) = \{ y \mid (x, ...
3
votes
0answers
50 views

Why are categories and monads called that way?

The words "category" and "monad" existed already in philosophy. The usage of the terms in category theory seems to be slightly influenced by the philosophical meaning, but actually the concepts are by ...
1
vote
2answers
35 views

Is the row space of a matrix A a subspace A? If so, what are the objects of A?

I have problems with an assertion that I read in a definition of the row space. I hope somebody can help me :) This part is clear: Let A be a mxn-matrix, with rows $ r_{1},...,r_{m} \in K^{n} $ ...
2
votes
1answer
69 views

Why is “antiderivative” also known as “primitive”?

If I had to guess, I would say that calling the antiderivative as primitive is of French origin. Is one term more popular than the other?
6
votes
0answers
46 views

A graph-coloring problem where only some of the edges should be bichromatic

In a standard graph-coloring problem, it is required that all edges will be bichromatic (i.e., all edges should be connected to two vertices with different colors). What is a term, and some basic ...
1
vote
3answers
83 views

How is “one to one” a synonym of “injective”? (Terminology question)

Am I the only one to find these alternative names stupid? one-to-one = injective one-to-one correspondance = bijective onto = surjective Why don't they simply do: one to one = bijective into = ...
5
votes
1answer
122 views

How to use the terms “fixed”, “arbitrary”, “fixed but arbitrary”, “given”, “for all” … in proofs

When I initially moved from Applied Mathematics background to Pure Mathematics (Graduate school), things were very tough in terms of proofs but they have gotten much better now. At those times, I ...
3
votes
1answer
52 views

“Famille sommable” in English

In French, given a normed vector space $(E, \Vert \cdot \Vert)$, we say that a set of vectors $\mathcal C = \{c_i \ ; \ i \in I\}$ is a "famille sommable" when $$(\forall \epsilon > 0) \, (\exists ...
0
votes
0answers
25 views

Is there a name for the extent of an object in a 4th and higher spatial dimensions? (width, height, depth, …) [duplicate]

If width is the extent in the first dimension, height in the second and depth in the third, is there a name for the extent of an object in the fourth spatial dimension? And what about a five, sixth ...
1
vote
0answers
59 views

Functions whose input is the same as the output?

Given the Dedekind eta function $\eta(\tau)$ and complex number $\tau$. I came across these family of functions, $${f_2(\tau)= \frac{i}{\sqrt{2}}\frac{\,_2F_1\left(\tfrac14,\tfrac34,1,\,1-\alpha_2\...
1
vote
1answer
60 views

Why is the sum of all external angles in a convex polygon $360^\circ$ and not $720^\circ$?

Why is the sum of all external angles in a convex polygon $360^\circ$? From my understanding, for each vertex in a convex polygon, there exist exactly $2$ exterior angles corresponding to it, which ...
0
votes
0answers
25 views

What does N stand for in Thomas Bayes' publication “An Essay towards solving a Problem in the Doctrine of Chances”

For example, in Prop 1, the beginning of the second paragraph. Suppose there be three such events, and which ever of them happens I am to receive N, and that the probability of the 1st, 2d, and 3d ...
0
votes
1answer
71 views

What is the name for this: “x^^y” (as in 2^^2=2^2 and 3^^3=3^3^3 and so on)

How do you call / is there any specific name for the following: x^^y e.g.: 2^^2 = 2^2 3^^3 = 3^3^3 4^^4 = 4^4^4^4 ...
5
votes
2answers
178 views

Probability distribution vs. probability mass function (PMF): what is the difference between the terms?

Consider a discrete case. PMF is the probability each value of random variable gets. So, for example, X ~ Poisson(2). I plot these probabilities (below), so I can say that I show the PMF of X. But on ...
1
vote
3answers
44 views

Linearity - terminology

i know that to be qualified as linear, a function must satisfy: 1) $f(u+v)=f(u)+f(v)$ 2)$f(\lambda u)=\lambda f(u)$ and a matrix multiplication $Ax=b$ is considered linear operation because b is a ...
1
vote
0answers
21 views

The name “section” for the operation of selecting representatives of an equivalence class

This is a question about terminology and sources. While looking for a name for the operation of "picking a representative from an equivalence class", I came upon the Wikipedia article on equivalence ...
4
votes
1answer
43 views

In what kind of rings a divisor of a product is a product of divisors?

In a unique factorisation domain, if $a|bc$, then $a$ can be written as $a = a_1a_2$ so that $a_1|b$ and $a_2|c$. Is this property of a commutative ring strictly weaker than the property of being a ...
2
votes
2answers
54 views

How to read $(h \circ g)\circ f = h \circ (g \circ f)$?

Let $f, g, h$ be functions. I learned that $g \circ f$ is read by "the composition of $f$ and $g$". Then, how to read $(h \circ g)\circ f = h \circ (g \circ f)$? the composition of $f$ and 'the ...
3
votes
1answer
31 views

Any standard name for this graph?

Is there any standard name for the three-vertices tournament which is not a directed triangle (equivalently, for the non-triangle orientation of $K_3$)? Thank you!
2
votes
1answer
52 views

Is $x - 4.5$ algebraic expression

From Wikipedia's definition of algebraic expression In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, ...
3
votes
1answer
52 views

I don't understand the meaning of “trace” in this context

I'm not a native English speaker and I found in an old book I'm using for research the word "trace" as it follows: It appears several times in the book, but when I look for its meaning on the ...
2
votes
3answers
97 views

Is $x+y -\pi$ an algebraic expression or not?

I came across this Wikipedia definition of an algebraic expression: "In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic ...
4
votes
4answers
391 views

Is it mathematically wrong to say “infinite number”? [closed]

I often hear the phrase "an infinite number of..." in mathematics. Is this phrase mathematically ungrammatical, since infinity is not a "number"? I'm sure some people will say that whether this ...
2
votes
2answers
53 views

Meaning of “Derive cosine of $\theta$ from $a·b$” ? (Not an native english speaker)

I'm currently trying to implement some vehicle physics in a game, and this obviously requires a lot of maths. However, I'm not an english native speaker, so I have trouble understanding some terms and ...
0
votes
1answer
33 views

What is the “common neighborhood” of a single vertex in a graph?

In the paper "On finding bicliques in bipartite graphs: a novel algorithm and its application to the integration of diverse biological data types" the authors propose an improvement to an algorithm, ...
0
votes
0answers
43 views

What do you call the number you add to a decimal to get 1?

If you have a number that is between 0 and 1, what would you call the number that you add to it to get 1? Is there a specific term for it? I was under the impression it had a name like inverse or ...
1
vote
0answers
9 views

Terminology for sets of minimum points

In optimization there are definitions of concept like a local minimizer, strict local minimizer, isolated local minimizer, isolated critical point and so on. In my experience these always refer to a ...
0
votes
0answers
113 views

What is the symbol for undefined?

Just how there is a symbol for no real solutions (the empty set) and there is DNE for does not exist, what symbol or abbreviation would you use for undefined?
7
votes
4answers
246 views

What is “exterior” about an exterior product?

This is a question about terminology. What is "inner" about an inner product, or "outer" about an outer product?
1
vote
0answers
51 views

What is the “dependency” in linear dependency?

I've got a good grasp on the definition and meaning of linear dependence and independence. If you have a set of vectors, and one of those vectors can be replicated via a linear combination of the ...
1
vote
2answers
64 views

Need for rigorous meaning in English for definitions from my reference book

I need verification for some expression in definitions which I can't completely get. Although English isn't my natal language, I still find a confusion with these words, with which just a little bit ...
3
votes
0answers
54 views

About the prime divisor of a quadratic function

Encountered in Modell's book Diophantine Equations. In the second chapter, page 3, it says: 'every prime divisor of $p$ of $x^2-a$ for integer $x$ is either a divisor of $a$, or can be represented ...