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

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division algebras in Weil's Basic Number Theory

I have a question regarding the terminology in Weil's Basic Number Theory. In Corollary 5 of I-§4 (p. 14) there is a statement regarding division algebras over local fields. It starts like this: Let ...
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1answer
17 views

What is “Real coordinate space”?

What is the Real Coordinate Space in the discussion of vectors? How does it relate to Cartesian Coordinate System and Euclidean Space? P.S. Please, use naive terms.
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1answer
45 views

Name for a continuous surjection such that $\operatorname{cl}(f^{-1}(A)) = f^{-1}(A') \implies \operatorname{cl}(A) = A'$

Consider a continuous surjective map $f \colon (X, \tau) \to (X', \tau')$ satisfying $$\operatorname{cl}(f^{-1}(A)) = f^{-1}(A') \implies \operatorname{cl}(A) = A'$$ for all $A, A' \in \wp(X')$ I ...
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2answers
44 views

What is the general definition of a discriminant? (Not just the definition for polynomials)

For example, in regards to the second derivative test for a function of two variables, $D=f_{xx}f_{yy}-(f_{xy})^2$ is refered to as the "second derivative test discriminant." I know that D is the ...
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0answers
14 views

Is there a name for “scales” that are bounded? (e.g. “severity scales”)

I'm coding a piece of software that has to deal with many quantities and mappings of these quantities to a this is "10 out of 100 bad" scale. For example: a server response time of 200ms is 50/100 ...
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2answers
83 views

Why are some branches of mathematics called 'theory' and others not? [on hold]

We say: graph theory , group theory, number theory , set theory, what is definition of theory? We also say abstract algebra, real analysis, but why we do not say abstract algebra theory or real ...
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3answers
23 views

What does it mean for an object to be “under” an operation?

In the book Roads to Infinity: The Mathematics of Truth and Proof, the author stated: For each n, one has the n-string braid group $B_n$, consisting of all the n-string braids under the braid ...
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81 views

Why is the sheaf $\mathcal{O}_X(n)$ called the “twisting sheaf” (where $X=\operatorname{Proj}(S)$ for a graded ring $S$)?

Basically my question is why the sheaf $\mathcal{O}_X(n)$ is called the twisting sheaf, here $X=\operatorname{Proj}(S)$ and $S$ any graded ring.
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3answers
85 views

Explaining the meaning of equality

I've been tasked with explaining to a group of people what the notion of equality means in mathematics, I've come up with a working explanation, but would appreciate some input, suggestions etc. ...
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0answers
32 views

What are the numbers in an inequality called?

Summand is to addition what multiplicand is to multiplication, but what is the terminology for the quantities of an inequality, such as 1<4? My best guess is simply "quantity" for both parts of ...
3
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0answers
27 views

Technical name for an almost-monotonic function

I'm wondering if there’s a technical name or short phrase that describes a function that’s monotonic, subject to some uniformly bounded amount of backtracking. $\exists \epsilon \forall x , y : y \gt ...
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2answers
23 views

Name for plane perpendicular to a vector

In writing some vector processing requirements, I want to use the correct terminology. For a 3D vector defined between the origin and a point, is there a term or name for a plane that is perpendicular ...
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0answers
98 views

Is there a special name for functors from a category C to a subcategory of C?

Is there a special name for functors from a category $C$ to a subcategory $S$ of $C$ where $S \ne C$? I'm using $\ne$ pretty informally above. I'd be happy with anything that reasonably captures the ...
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0answers
39 views

Why do we call a linear mapping “linear mapping”? [migrated]

What are the historical reasons that created the term "linear mapping"?
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6 views

Like “time-inhomogeneous,” but for space

I'm talking about a random walk that is homogeneous in time but not in space--is there a term for this? I've searched for "space-inhomogeneous" but nothing came up. Thank you!
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1answer
40 views

Looking for a terminology in ring theory (“ideal” which is not necessarily closed under addition )

I am wondering if there is a name for the subsets $S$ of a commutative ring $R$ such that for every $r\in R$ and every $s\in S$ we have $rs\in S$. Thus $S$ is ...
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1answer
30 views

Existence of Partials Imply the Existence of Gradient Vector?

Let $f$ be a scalar function of three variables. Then the gradient vector is defined by: I read here that the existence of partial derivatives at some point $(x_0, y_0, z_0)$ does not imply the ...
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5answers
60 views

Is there any notation for general $n$-th root $r$ such that $r^n=x$?

As we know that the notation for the $n$-th principal root is $\sqrt[n]{x}$ or $x^{1/n}$. But the principal root is not always the only possible root, e.g. for even $n$ and positive $x$ the principal ...
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0answers
22 views

Mathematical formal expression of find “subfunction” in function [on hold]

Imagine if I have a function $s(t)$ and $r(t)$. $s(t)$ may contain $r(t)$ one or more times as $s(t)$ is a quasi-period function. What is the correct expression if I want to say the $s(t)$ contains ...
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1answer
20 views

What is it called when you have two systems of measurement and each scale has two different numbers that can represent the same thing?

I'd like to know what it is called in Math when you have two numbering systems and they represent the same thing, but with different numbers. Let me give you an example, when you have civilian and ...
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1answer
76 views

Contracted version of “isomorphic”

Had a look around and I can't find a word which acts as a contraction for "isomorphic" in the same way that "monic/epic" is a contraction of "monomorphic/epimorphic". For some reason this strikes me ...
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0answers
33 views

What is the opposite of a derangement?

A derangement is a bijection $f : A \rightarrow A$ such that $f(x) \ne x$ for all $x \in A$. Is there a name for a bijection $f : A \rightarrow A$ that is not a derangement? That is, is there a name ...
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1answer
57 views

Isomorphic or equal?

Let $\sim_n$ be the usual equivalence relation of congruence modulo $n$ in $\mathbb{Z}$, i.e., for $a,b\in\mathbb{Z}$, $a\sim_nb\Leftrightarrow a-b=k\cdot n$ for some $k\in\mathbb{Z}$. For $n=0$ the ...
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1answer
30 views

How do you call a vector of length $n$, with all values equal to $\frac{1}{n}$?

Is there a specific name for a vector of dimension $n$, with all values equal to $\frac{1}{n}$? So, a vector that looks like this: $\vec{v} = \underbrace{(\frac{1}{n}, \frac{1}{n}, ..., \frac{1}{n}, ...
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1answer
36 views

How to mathematically state y - 1 unless y - 1 < 0 then y is 0

I have a formula and I don't know how to write it in mathematical form (I'm a programmer.) The formula needs the variable y to be y - 1 unless y <= 0, in which case y should just be 0. ...
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0answers
22 views

Name of the segment connecting a point's coordinate axis projections?

Given any point $(x,y)$ in the real plane consider the corresponding line segment connecting $(x,0)$ with $(0,y)$. See diagram. Is there a name for this special segment? (I believe that in ...
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1answer
40 views

What's the name of this type of a set?

So I have a set $\{i_1,i_3,i_5\}$. What do we call the following set? Is there a standard name for it? $\emptyset, \{i_1\}, \{i_1,i_3\}, \{i_1,i_3,i_5\}$. Note that we do not have $\{i_3,i_5\}$ in it ...
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1answer
16 views

Terminology: Expected Value, Expectation, Expectation Value

According to [Wikipedia::Expected Value] expected value and expectation are correct terms for the first moment of a random variable. What about expectation value? I have heard and read this term ...
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1answer
17 views

What is the difference between functions and operations?

Wikipedia says that an operation $\omega$ is a function of the form $\omega: V \to Y$, where $V \subset X_1 \times\cdots\times X_k$. But as far as I know, every function's domain is a set, so ...
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1answer
154 views
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What is known about these arithmetical functions?

Let $n=\prod_p p^{c_p}$, $N\in \mathbb N$ and $$ \alpha_N(n)=\prod_p p^{c_p \bmod N}. $$ The function $\alpha_N$ is multiplicative since $\alpha_N(n)\alpha_N(m)=\alpha_N(nm)$ for co-prime $n$ and $m$ ...
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2answers
73 views

Is 'clamp' a formally recognized mathematical function?

I was surprised to find the clamp function absent from Mathworld and Wikipedia. Is this mainly a concept particular to computer programming? Is it known by another ...
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0answers
14 views

mathematical name for the relationship between capacity utilization and overcapacity

I'm writing a report on industrial overcapacity, which is capacity not utilized by current production. If capacity utilization is the percent of total capacity utilized, what is the mathematical name ...
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1answer
95 views

What are the formal terms for the intersection points of the geometric representation of the extended trigonometric functions?

Mike Pierce's answer to this question, regarding trigonometric functions beyond the common (co)sine, (co)secant, and (co)tangent, points to a figure on the Wikipedia page on trigonometric functions ...
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0answers
37 views

Graph vertex set with a certain property

Let $G$ be a graph and let $V$ be a set of vertices with the following property: If a vertex $v$ is connected to every $u\in V$, then $v$ has to be in $V$. Does such $V$ have a (standard) name? Note ...
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2answers
394 views

Why we use the word 'compact' for compact spaces?

Considering the definition of compactness in either Analysis or Topology books, or its equivalent definitions (i.e. [It] is compact $\Longleftrightarrow\dots$), I couldn't understand why ...
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1answer
36 views

What do the letters a, b and c stand for in linear programming?

From the definition of linear programming: ...
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1answer
51 views

Right modules Vs Left modules.

I have been reading Frobenius Algebras, Volume 1 By Andrzej Skowroński, Kunio Yamagata. On page 18 I came across the following paragraph, and I founded interesting, I will quote it and then ask my ...
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4answers
75 views

What is $\sqrt{(-1)^2}$ [duplicate]

This question is primarily terminology based. In that $\sqrt{}$ denotes the principal square root. Here are two reasoning $\sqrt{(-1)^2}=1$ since $\sqrt{(-1)^2}=\sqrt{1}$ which we know has a ...
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0answers
35 views

Given bifunctor $F$, what is the name of the functor with switched arguments?

Sorry for the unspecific title. Here the actual question: Given categories $\mathcal{A},\mathcal{B}$, let $S$ be the canonical functor $\mathcal{B} \times \mathcal{A} \to \mathcal{A} \times ...
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2answers
35 views

Terminology: The difference between $X$'s convention

I am reading the paper, Classification in Networked Data: A Toolkit and a Univariate Case Study. And I have a question about the terminology of this paper, on page 938: Also, see the following ...
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2answers
47 views

How would you call geometric objects that lie on a single surface, e.g. a sphere, plane, torus, etc.

I'm looking for an extension of the name coplanar to something like "cosurfacial", but I guess their must be a correct term.. Edit: In the comments, the context was asked for where I would use that ...
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0answers
31 views

Is this an improper method of averaging grades? If so, what is a simple mathematical way of explaining it?

I have a professor who employs a unique method of averaging grades. On each assessment, the professor assigns a raw numerical score to each student based on performance. He then converts particular ...
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1answer
32 views

What is the remainder of an n-th root called?

I feel like there should be a better word than remainder, but I don't know it. What do you call the thing that's left over when performing an $n$-th root? For example, $\sqrt[3]{29}$ is $3$ with 2 ...
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1answer
45 views

How to say math terms in English

I would like to know how to say in English the following objects: the quotient $\mathbb R / \mathbb Z$ (is it "Ar over zee"? or "Ar modulo zee"?) things like $[0,1]^n$ (is it "the n-th power of the ...
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0answers
12 views

Name for space of piecewise continuous functions

The space of $k$ times continuously differentiable functions (on $\mathbb R$) is called $C^k$. Is there a similar name for functions that are piecewise continuous? For example the box function ...
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1answer
28 views

Terminology for splittings of a set into two parts

I have a set of values $V$ that can be split by any combination $C$ of the elements $v$ that belongs to $V$. Order is not important and repetitions are not allowed. For example, $V := \{1,2,3,4\}$ ...
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2answers
65 views

If $f(x) = 0$ has a countable set of solutions, what is $f$?

Is there a name given to functions $f$, where the roots of $f(x) = 0$ are countable? I am assuming $f$ is a real function of a real variable, $x$.
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1answer
360 views

Sign Language and Deaf Mathematicians

Something I've often wondered (and I suppose this goes for all kinds of technical terminology, not just that of mathematics) is what kind of sign language exists for practising professional ...
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1answer
28 views

Help in this teminology in Hartshorne's algebraic geometry book

I'm studying Hartshorne's Algebraic Geometry book and on page 51: What the author means by $M_{\mathfrak p}$ and "length"? I suppose $S_{\mathfrak p}$ is the localization of the ring $S$ at ...
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1answer
12 views

Splitting of primes terminology doubt

What do we mean when we say that a given prime $p$ splits completely in an algebraic extension of $\mathbb Q$? Are we talking about the splitting of prime ideals into unique factors? And, in that ...