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

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29 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 ...
3
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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 ...
0
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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. ...
2
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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
37 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 ...
3
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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 ...
3
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1answer
96 views
+50

What is known about these arithmetical functions?

Let $n=\prod_p p^{c_p}$ and $$ \alpha(n)=\prod_p p^{c_p \bmod 2}. $$ The function $\alpha$ is multiplicative since $\alpha(n)\alpha(m)=\alpha(nm)$ for co-prime $n$ and $m$. If you replace $\bmod 2$ ...
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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
94 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 ...
4
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0answers
34 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
388 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: ...
4
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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 ...
2
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0answers
34 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 ...
3
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2answers
32 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 ...
4
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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
31 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 ...
4
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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 ...
1
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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
352 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 ...
1
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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 ...
0
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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 ...
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1answer
29 views

Are pairwise mutually exclusive events the same as mutually exclusive events?

Larson (1982) defining the probability axioms talks about "mutually exclusive" events, while Poirier (1995) about "$A_1, A_2, \ldots$ as a sequence of pairwise mutually exclusive events events in the ...
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1answer
72 views

Question about terminology in number theory

The following transformation appears often in number theory: $$F(x) = \sum_{n \le x} f \left( \frac{x}{n} \right)$$ What is the name of this transformation? PS. I will accept as answer something ...
5
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1answer
118 views

What is the origin of the terms 'jet' and 'prolongation' in differential geometry?

I am just curious what is the reason for the terms 'jet' and 'prolongation' in differential geometry? Is there some mental imagery that these names are supposed to evoke? Or are they so-named because ...
2
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0answers
30 views

What should you call a property, like an invariant, but that is reversed instead of preserved?

Suppose $P$ is some property of some objects and $f$ is a function on those objects. If $Px$ implies $Pf(x)$ and $\lnot Px$ implies $\lnot Pf(x)$, then we might say that "$P$ is invariant under $f$". ...
1
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1answer
37 views

Labeled commutative diagram

Consider a commutative diagram. For example the following diagram in $\mathbf{Set}$: $$ \begin{array}{ccc} & \overset{+1}{\longrightarrow} &\\ \mathbb{Z} & & \mathbb{Z} \\ & ...
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1answer
61 views

What's the meaning of “drop” in mathematics?

What's the meaning of "drop" in following sentence: "the term can be dropped from the numerator"
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0answers
53 views

An endomorphism $f$ such that $f\circ f=1$

What is the name for an endomorphism $f$ of a category such that $f\circ f=1$? Note that I work with category $\mathbf{Set}$.
2
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1answer
78 views

Is $\mathbb{Z}/p^\mathbb{N} \mathbb{Z}$ widely studied, does it have an accepted name/notation, and where can I learn more about it?

Fix a positive integer $p$, possibly prime. For each natural number $n$, there is a ring $\mathbb{Z}/p^n \mathbb{Z}$ together with a distinguished ring homomorphism $$\pi_n:\mathbb{Z} \rightarrow ...
3
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2answers
155 views

Is there a formal definition for antiderivatives?

In the way the derivative can be defined as a limit, specifically $$f'(x):=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$ or any of the other possible variants, is there a way to define the antiderivative, as in ...
0
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1answer
19 views

Does the operand in a convolution have a particular name?

In a convolution: $$(f*g*h)(t) = \int f(x)g(y)h(z) \delta(t-x-y-z) dxdydz$$ do the operands $f,g,h$ have a specific name, besides the general "operand"?
1
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1answer
46 views

What is the scientific term form something that 'wraps around' a shape

I was wondering if there is a mathematical term for this: Imagine you had given the black shape - what does the red shape? I would call it, it wraps around the black one. Actually I am looking ...
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1answer
20 views

What does “decreases more slowly” mean mathematically with regard to distributions?

In a paper I'm reading, the authors state that a certain distribution "decreases more slowly than exponentially over a portion of the range". What does this mean, mathematically? Assuming $A$ is the ...
1
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1answer
39 views

Wording in English for “quantité conjuguée” in French

In French when you have an expression of the type $\sqrt{x}-\sqrt{y}$, the expression $\sqrt{x}+\sqrt{y}$ is named the "quantité conjuguée". This is useful when you want to bound $$\vert ...
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0answers
42 views

The definitions of “transformation” and “isometry”

Let $T$ be a mapping from the plane to itself. In the context of Euclidean geometry, can $T$ be called a "transformation", or is this word reserved for cases where $T$ is bijective? Is there ...
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0answers
21 views

Why is equivalence 'class', not equivalence 'set'? [duplicate]

Why do we call it a class, not a set? Is it not a set? Can it be a proper class?
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0answers
24 views

What are these algebraic properties called?

Suppose $O$ is some operator, suppose $f$ and $g$ are both functions, then linearity implies that: $O(\alpha f + g) = \alpha O(f) + O(g)$ What about the following property: $(O_1+O_2)(f) = O_1(f) ...
3
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1answer
32 views

Is there a mathematical distinction between “on” and “in”?

Is there any difference if I said a function on an interval or a function in an interval? or a vector field on a manifold versus a vector field in a manifold? The main reason is because some online ...
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0answers
14 views

Definition of (minimal) domain?

Consider the following links: http://www.glottopedia.org/index.php/Domain_%28Syntax%29 http://www2.let.uu.nl/uil-ots/lexicon/zoek.pl?lemma=Minimal+domain&lemmacode=542 What kind of mathematical ...
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1answer
46 views

Why the spatial/mathematician's Fourier Transform?

I was wondering why the sign-change in the exponential of the spatial/mathematician's Fourier Transform and why is it called mathematician's spatial in either case?
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1answer
38 views

What is $D(n,k)$? (dee-en-kay) /ˈdiːˈɛnˈkeɪ/

Is this combinations with repetitions, i.e. ${n+k-1\choose k-1}$ or is this something else entirely? I see this a lot, but with this kind of language no search engine is going to help. The edit in ...
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1answer
794 views

Is there a term for the ratio of a function and its derivative?

Given a function $f(x)$ and its derivative $f'(x)$, is there a term for $\frac{f(x)}{f'(x)}$ or for $\frac{f'(x)}{f(x)}$?