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

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2answers
150 views

Name of the Number series

Is there are name for the number series which has the following pattern Starts small, rises in the middle and goes down as in 1,2,3,4,3,2,1 To give you a ...
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3answers
1k views

Latin phrase for “accepting without proof”

Is there a Latin phrase that would be used when accepting some statement without providing the proof of such a statement? For example, say you are working on an elementary number theory proof, and ...
3
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2answers
283 views

Is a 2-dimensional subspace always called a plane no matter what the dimensions of the space is?

Is a 2-dimensional subspace in a 7-dimensional space still called a plane? I know that a 6-dimensional space in 7-dimensional space is called a hyperplane because the difference in the number of ...
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1answer
94 views

Am I talking right?

I'm trying to describe expected value. My paragraph goes: From probability theory we have $E[f(x)] = \int{f(x)p(x)dx}$. That is, the expected value of $f(x)$ is equal to the sum of infinitesimals ...
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1answer
54 views

Knotted up over “unique”

"Every boy has a unique shirt." Does this mean no two boys share the same shirt, or does it mean no two shirts belong to the same boy? I suppose the former, but then what is the most succinct way ...
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1answer
128 views

functions vs parameterized families

This post is rather short and concerned with terminology. I hope it is still a valid question, I shall try to make it as clear and precise as possible! What is the difference between a one - ...
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2answers
472 views

What exactly is a manifold?

Wikipedia's "Simple English" entry describes a 2D map of the Earth as a manifold of the planet Earth. Does this mean that in mathematics a manifold is essentially a representation of something that ...
2
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2answers
276 views

What does “$f$ is a function on $S$” mean?

If somebody says "$f$ is a function on $S$", what do they mean? Does it mean that $S$ is the domain of the function, the codomain, or both?
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3answers
3k views

Difference between “space” and “mathematical structure”?

I am trying to understand the difference between a "space" and a "mathematical structure". I have found the following definition for mathematical structure: A mathematical structure is a set (or ...
2
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1answer
82 views

What is the name of the group linear functions on a finite field?

More precisely what is the name for the group $$\{ X\mapsto \alpha^2X+\beta : \alpha,\beta \in GF(q), \alpha \neq 0\}$$ I've always called it the special affine group, but I see that can mean ...
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3answers
2k views

Is a total function also a partial function?

Is there a consensus on whether a total function, i.e., a function defined for each element of the domain, is also a partial function?
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1answer
87 views

Name for a set which has an order?

As we all know, a set is a collection of elements which have no particular order and no multiplicity. So what do you call a construct which does store its elements in a specific order? What is the ...
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1answer
265 views

Are there any synonyms of “pair of pants” in topology?

I used to know a term for pair of pants, but perhaps there is none. It looks like this also.
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1answer
67 views

Higher dimensional analogue of an arc of a circle

What is the higher dimensional analogue for the arc of a circle? I'd like to work with the set of all points lying within a certain distance of a given point on an n-sphere, and I'd like to describe ...
4
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1answer
63 views

Backward records

Given a sequence $A=(a_1,\ a_2,\ \ldots)$ one can define the records of $A$ as numbers $a_n:n\in\mathbb{Z}^+$ such that $a_n>a_m$ whenever $n>m.$ So you start at 1 and write down every number ...
3
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2answers
236 views

Does “nullity” have a potentially conflicting or confusing usage?

In Linear Algebra and Its Applications, David Lay writes, "the dimension of the null space is sometimes called the nullity of A, though we will not use the term." He then goes on to specify "The Rank ...
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1answer
324 views

What is the name of the top of a hemisphere?

I need to refer to the "top" of a hemisphere - the "highest point" on a hemisphere. I am thinking it must be called the "apex" of the hemisphere, but I am not sure.
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2answers
25k views

Difference between “probability density function” and “probability distribution function”?

I am studying for my statistics exam, and have to know a lot of theory. My question is: Whats the difference between probability density function and probability distribution function?
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2answers
794 views

What does “harmonic” mean in “harmonic mean”?

Pun aside, what is harmonic about the harmonic series or the harmonic average? I assume it has a direct connection to music, but I cannot see it.
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0answers
38 views

Names of certain morphisms in Pos

Pos is the category of small posets and monotone maps. I call a morphism $f:\mathfrak{A}\rightarrow\mathfrak{B}$ of Pos monovalued iff it maps every atom of $\mathfrak{A}$ either into an atom of ...
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2answers
472 views

Why are $\sin$ and $\cos$ (and perhaps $\tan$) “more important” than their reciprocals?

(My personal "feel" is that $\sin$ and $\cos$ are first-class citizens, $\tan$ is "1.5th-class," and the rest are second-class; I'm sure there are others who feel the same.) Main question(s): From a ...
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1answer
84 views

“Base for a neighborhood system at a point” vs. “base at a point”

For a topological space X do the terms "base for a neighbourhood system at a point" and "base at a point" have the same meaning?
12
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3answers
601 views

Elementary Geometry Nomenclature: why so bad?

A long-ish wall of text, and I apologize. Some background: when I was a first-year university student, my chemistry professor was lecturing and was trying to find the word to describe a shape. A ...
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1answer
1k views

What is the difference between FWHH and FWHM?

The title says it all really. I wanted to know if there is a situation where full width half height half maximum is more appropriate than full width half height or vice versa. Thank you
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3answers
812 views

Difference between “space” and “algebraic structure”

What is the difference between a "space" and an "algebraic structure"? For example, metric spaces and vector spaces are both spaces and algebraic structures. Is a group a space? Is a manifold a space ...
6
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1answer
151 views

Is there a name for the “most square” factorization of an integer?

For the definition that follows, I'm curious to know if there's a known name (to enable a literature search relating to algorithms). Definition. Given an integer $n$, the maximally square ...
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5answers
19k views

What is the difference between normal and perpendicular?

What is the difference when a line is said to be normal to another and a line is said to be perpendicular to other?
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0answers
89 views

Bridge in a multigraph

According to Wikipedia, "a bridge in an undirected graph is an edge whose deletion increases the number of connected components. Equivalently, an edge is a bridge if and only if it is not contained in ...
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3answers
810 views

What is a Neighborhood?

Which of these definitions is more commonly used, and in which contexts? Fix a point $x\in (X, \tau)$. Then a neighborhood around a point $x$ is: a set $N\ni x$ and $N\in \tau$ a set $N$ with $x\in ...
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2answers
132 views

What does diameter mean in the sentence of Borsuk's conjecture?

What does diameter mean in the following sentence of Borsuk's conjecture? Sentence: Can every set $S \subseteq \Bbb R^d$ of bounded diameter $\operatorname{diam}(S)>0$ be partitioned into at most ...
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2answers
114 views

Notation for function that returns exponent of primes in factorisation?

Consider the function $f(n, i)$ which returns the exponent of the $p_i$ in the factorisation of $n$, where $p_i$ is the $i$-th prime. Question: is there a standard label for $f$? Context: In the ...
46
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3answers
11k views

difference between class, set , family and collection

In school I have always seen sets. But I was watching a video the other day about functors and they started talking about any set being a collection but not vice-versa and I also heard people talking ...
11
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0answers
167 views

Official name(s) for a certain type of p-group

I'm implementing a class of groups into Sage (sagemath.org), a computer algebra system, and I'm wondering if it has any official names. I found it in Gorenstein's "Finite Groups." It is there called ...
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2answers
358 views

Why does Maclaurin get his own polynomial?

Why is a Taylor polynomial centered around $0$ called a Maclaurin polynomial? It's only a special case of the Taylor polynomial, and it is calculated the exact same way as a Taylor polynomial centered ...
12
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3answers
775 views

What are rational integer coefficients?

I have a question about the following excerpt from Atiyah-Macdonald (page 30): “A ring $A$ is said to be finitely generated if it is finitely generated as a $\mathbb Z$-algebra. This means ...
2
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3answers
272 views

Intertwiner in german?

What is the best way to translate the mathematical term ''intertwiner'' (between two representations of a group) into German?
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0answers
87 views

Is there any standard nomenclature for the sets of rational, algebraic, and elementary functions?

The rational functions of $X$ can be denoted $\mathbb{C}(X)$, i.e., quotients of polynomials. Is there a standard notation for the algebraic and elementary functions? By the set of elementary ...
3
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2answers
162 views

Does this kind of matrix have a name?

Are these kind of matrices generally known in mathematics? Do they have a name? $$ \left[\begin{array}{rrr} A & B \\ B & A \\ \end{array}\right] $$ $$ \left[\begin{array}{rrr} ...
4
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1answer
107 views

Name for a type of subgraph that comes from identification of vertices?

Is there a special name for the kind of subgraphs you get by taking some sequence of the following operation: Pick two vertices and identify them so all edges going to either vertex get sent to the ...
7
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3answers
1k views

What is the importance of functions of class $C^k$?

In all calculus textbooks, after the part about successive derivatives, the $C^k$ class of functions is defined. The definition says : A function is of class $C^k$ if it is differentiable $k$ ...
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1answer
1k views

Name for a horizontal line function

What is the, or what are the, technical terms for a function that produces a horizontal line (all inputs map to the same output), like $f(x) = 5$?
2
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1answer
309 views

What does “quotient-ring” mean?

I am reading a paper about rings (http://malaschonok.narod.ru/publ/ma01.ps, page 3). In this paper the term "quotient-ring" appeared. What is a quotient-ring? (Note: The text in the original ...
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1answer
120 views

numbers, matrices, vectors are groups? addition is possible between any combination?

Mathematical structures such as Numbers, Matrices, Vectors are all groups, rings, or similar? Can you provide more examples of more thease. Do operations such as addition occur (although in ...
3
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0answers
71 views

Isotropic subspaces [duplicate]

Possible Duplicate: Etymology of the word “isotropic” Let $V$ be a vector space and we have a symmetric, non-degenerate bilinear form with signature $(n,n)$ on it. A subspace ...
2
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1answer
86 views

Is there a special name for matrices consist of repeated unit vectors?

For example this one: $$Q=\begin{pmatrix} 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 ...
2
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1answer
71 views

What means the boundary of a space

By definition topological spaces are clopen and then their boundaries are empty, but for example, is said that the boundary of the closed unit interval is it's two endpoints a so on. whath is the ...
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2answers
112 views

Quibble with terminology

Proposition 5.15 on page 63 in Atiyah-Macdonald goes as follows: Let $A \subset B$ be integral domains, $A$ integrally closed, and let $x \in B$ be integral over an ideal $ \mathfrak a$ of $A$. Then ...
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1answer
29 views

In an engineering/optimisation context, does set $E$ have any special significance?

I am reading a paper about optimsation and the description, while mostly being a very good description, makes reference to some variables being in some set $E$. For example, it states that parameter ...
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2answers
2k views

opposite of disjoint

Sets whose intersection is the empty set are called disjoint. What is the opposite of a disjoint set? For example the sets $\{1,2\}$ and $\{2,3\}$ satisfy this condition. I know that you can just say ...
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3answers
4k views

What does a “convention” mean in mathematics?

We all know that $0!=1$, the degree of the zero polynomial equals $-\infty$, the interval$[a,a)=(a,a]=(a,a)=\emptyset$ ... and so on, are conventions in mathematics. So is a convention something that ...