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

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1answer
87 views

What is the name for a ring without nilpotent elements?

Let $n,m$ be positive integers. What is the name for a ring $A$ that satisfies the two conditions : $1)$ The ring $A$ is isomorphic to ${\Bbb R}^{n}\times{\Bbb C}^{m}$. $2)$ For every nonzero ...
2
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2answers
116 views

What do you call a function with the property $f(-x)=-f(x)$?

What is this property called? The domain and codomain of the function can be for example $\mathbb Z^n$, $\mathbb Q^n$ or $\mathbb R^n$ ($n>0$), potentially excluding the $0$ point. Examples: ...
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1answer
35 views

Term to describe the two ways of labeling the vertices of a tetrahedron.

I can label the vertices of a tetrahedron in two different ways as are depicted in the following picture. How to differentiate the two? Is there a term or a mathematical statement? I suspect that it ...
11
votes
1answer
200 views

What's the name of this quantity?

For each permutation $\sigma$ of $ \left\{ 1, 2, \dots, n \right\}$ define $$\operatorname{dist}(\sigma)=\sum_{i=1}^{n}\left| \sigma (i)-i \right|$$ For each $n\in\mathbb{N}$, I'm interested in ...
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1answer
48 views

Adding together curves or shapes to approximate something more complex

I'm looking for proper terminology / references for the following sort of problem: Say we have some one-dimensional curve like $y = 10$ defined over the real valued domain $[0,1]$, and we ask, how ...
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1answer
27 views

What's the name of these transformations.

I was self-studying Spivak's Calculus on Manifolds and on page 89, two transformations $f_*$ and $f^{*}$ are defined as the following. Given a differentiable function ...
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1answer
30 views

Surface spanning a closed curve?

This a question about math terminology - What is the meaning of "a surface $S$ spanning a closed curve $\Gamma$"? I am not looking for a technical definition, just a visual understanding is enough. ...
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2answers
37 views

What is a set of overlapping sets?

If I have a set $X$ and a set $Y$ and $\forall y \in Y : y \subseteq X \land \exists y_1, y_2 \in Y : y_1 \ne y_2 \land y_1 \cap y_2 \ne \{\}$, what is the relationship between $X$ and $Y$ called?
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0answers
26 views

Terminology for functions with $F(a,a,\dots,a) = a$

Is there a commonly used way to call functions $F : \mathbb{R}^n \rightarrow \mathbb{R}$ such that if $x \in \mathbb{R}^n$ and $x_i = a$ for all $i\in \{1,\dots, n\}$, $F(x) = a$ ?
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0answers
99 views

“clopen” terminology: acceptable?

I like the term "clopen" (a set which is both open and closed in a topological space), though an instructor of mine hated it when I used it recently. (Approximately, "never, ever use that again.") Is ...
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4answers
51 views

Name of a set of the form {x,y}

I know that a doubleton is a set with exactly two elements, but what is the name of a set with either exactly 1 element or exactly 2 elements? In other words, what is the name of a set of the form ...
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1answer
38 views

Are there specific terms for trigonometric functions raised to a power?

Related to my other question, asking for a Book on higher-power trigonometric equation simplification techniques, I am interested to learn if there are specific terms for trigonometric functions that ...
2
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1answer
60 views

Is there a special name for ring homomorphisms $f : R \rightarrow S$ with $f^*(C(R)) \subseteq C(S)$?

Edit. For some reason, I called the functor $F$ described below a full functor as opposed to a faithful functor. The problem has now been corrected. For any ring $R$, let $C(R)$ denote the center of ...
2
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1answer
43 views

terminology needed

This is just a terminology question. Let $Y$ be a topological space. Is there a word to describe those topological spaces $X$ that contain $Y$ as a dense subspace? If not, what would you call such ...
2
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1answer
41 views

Is there a name for magmas in which $y*(a*b) = (y*a)*(y*b)$?

Let $X$ and $Y$ denote magmas, suppose $f$ is a homomorphism $X \rightarrow Y$, and let $y \in Y$ satisfy the following condition. $$\forall a,b \in Y : y*(a*b) = (y*a)*(y*b)$$ Then $y * f$ is a ...
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2answers
83 views

Does this graph have a special name? (8-connected neighborhood)

Does this graph have a special name? The vertices are arranged on a square square grid with a side length of $n$ and each inner vertices has an edge to its 8 neighbors. And what about a similar ...
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1answer
19 views

Terminology for a type of indecomposable module

Let $R$ be a ring. Is there a name for an $R$-module that is indecomposable, and each of its quotients is also indecomposable?
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4answers
231 views

how do you read: “$\lim (n-1)/(n-2) = 1$”

The limit of the fraction $(n-1)/(n-2)$ with $n$ approaching $+\infty$ is $1$. But how do you read that, concisely? (say during chalking the formula on a blackboard). Is it acceptable to say "lim", ...
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1answer
82 views

From $\mathsf{O}$ to $\mathsf{I}$ via $\infty$

The following is not true mathematics, but a little imaginary story about mathematical symbols. I wonder if there is - in parts - a true (etymological) story behind it. Once there was a symbol ...
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3answers
89 views

Is there a notation for $((n!)!)!$?

I wonder if there is a notation for repeating factorials such as $((3!)!)!$. Without the parentheses, $(3!)!$ could be confused with the double factorial $3!!$. Is there is no such notation known, ...
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1answer
89 views

What is matrix inequality such as $A>0$ or $A\succ 0$?

I am trying to gather here different meanings of the same symbol, inequality symbol or the succ symbol. I find many other use them so many different ways. Sometimes, $A>0$ means $\bar x^T A \bar x ...
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0answers
55 views

Taking the (pseudo)inverse of a monoid operation.

Let $M$ be a monoid with binary operation $f : M \times M \to M$. I'm interested in functions $g : M \to M\times M$ that obey the property: $$ f(g(m)) = m $$ I want to understand what all of the ...
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3answers
53 views

Parameter, variable, and argument

I asked a question on English.stackexchange.com but they told me that my question was not about English, and it was rather about math. So, I decided to ask it here :( They closed my thread, so please ...
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2answers
61 views

$f(x_1,x_2)=\frac{x_1^2}{x_2}$ quasiconvex and/or quasiconcave or nothing on $\mathcal R\times \mathcal R$?

Related to the 3.16e question in Boyd's book. It asks what is $f$ in $\mathcal R\times R_{++}$. I am not interested in it but related thing when the domain is larger. So $f(x_1,x_2)=\frac{x_1^2}{x_2}$ ...
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1answer
42 views

What do we call a lattice that does not have a sublattice the shape of the diamond $M_3$?

Let $L$ denote a lattice. If no sublattice of $L$ is shaped like the pentagon $N_5$, we call $L$ modular. Supposing furthermore that no sublattice of $L$ is shaped like the diamond $M_3$, we call $L$ ...
6
votes
2answers
110 views

Terminology: How should we call $\mathbb{Z}[\sqrt{5}]$?

I'm wondering, what shall we call the ring $\mathbb{Z}[\sqrt{5}]$? I know that $\mathbb{Z} \left[ \frac{1+\sqrt{5}}{2} \right]$ is called a quadratic integer ring. But do we have something similar for ...
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1answer
2k views

What is the difference between an identity, an equation and a conditional equation?

What is the difference between an identity, an equation and a conditional equation? Thank you?
6
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2answers
92 views

Is there a latus other than the one in the rectum?

The name "Latus Rectum" sounds so very specific. Infact when I once asked why it is called as such, an explanation stated that the concave side of a parabola is called a rectum and that latus was ...
0
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1answer
71 views

How's a semialgebra actually a “semi”-algebra?

According to the definitions that I'm familiar with, a semialgebra of a set $X$ defined as a collection $S \subset\mathcal{P}(X)$ , such that: $\emptyset,X\in ...
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1answer
45 views

What do you call a convex polyhedron whose symmetry group is transitive on the facets?

I'd like to know a name/source for the following concept: Let $P$ be a convex polyhedron in $\mathbb{R}^3$. Let $G$ be its symmetry group, and let $F$ be the collection of (top-dimensional) faces of ...
2
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1answer
29 views

What do we call functions that return axioms / axiom schemata?

Consider the function $\mathrm{Assoc}$ defined by: $$\mathrm{Assoc}(X,*) = (\forall x,y,z \in X)((x*y)*z=x*(y*z))$$ This is a function that accepts symbols $X$ and $*$ and returns the axiom (a ...
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1answer
25 views

Formal name for a closed connected graph

I have to name an abstraction representing a mechanical truss diagram. It consists of a set of polygons that must overlap, viz. share an edge or a corner. In other words it must not only be a ...
0
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1answer
24 views

Complex function terminology question

Suppose that I have a function $f:\mathbb{C}\rightarrow\mathbb{C}$. Representing the complex number in polar notation $z=re^{i\theta}$, I integrate the phase $\theta$ out as follows: ...
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2answers
102 views

Are the differential and derivative of a single-variable function exactly the same thing?

I just started taking a calculus class but I got in late and it had already started like weeks ago, so I'm completely lost. I believe the teacher uses this same formula in order to get the ...
2
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4answers
68 views

Geometry terminology: concrete vs. continuous polygons?

I am trying to find the proper terminologies for 2 kinds of shapes: The first type of shape I'm calling "concrete polygons". They have a finite number of straight sides (connecting at vertices) and ...
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2answers
104 views

Name for Euclid, Book III, Proposition 21?

Euclid's Proposition 21 in Book III is something I learned in 11th grade. Is there a standard name for it? http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII21.html
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1answer
103 views

Given a subcollection of a powerset, do these “separation” relations have names?

Let $X$ denote a set and $\mathcal{F}$ denote a subcollection of $\mathcal{P}(X).$ Do the following relations on $\mathcal{P}(X)$ have a name? For $A,B \subseteq X$, call $A$ partially separated from ...
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3answers
58 views

Elementary proof.

What actually elementary proof means ? If there is an elementary proof for a conjecture , then is it a theorem ? I saw papers on some conjectures proving stating as elementary proof. Then it means ...
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0answers
49 views

Quasicompact? Why the distinction?

What is the reason that some topologists use quasicompact? Why is the distinction made? quasi means "not really", so why use this terminology?
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1answer
44 views

How to correctly write this ring theoretic thing?

Im unsure how to write this thing below in a formal way : For an integer $n>2$ Let $F_n(x) = a_0 + a_1 x + a_2 x^2 + ... + a_{n-1} x^{n-1}.$ Also we have $x^n = 1$ and $1 + x + x^2 + ... + ...
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0answers
50 views

Ergodic and space-time differences

I read a resolution of St. Petersburg paradox, which says that the game is not ergodic. Yet, if you play n games in row, you average income will be the same as if you play n parallel games, This ...
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1answer
19 views

What does it mean for a reccurence relation to be homogeneous?

I've seen definitions (such as the one here) that state Homogeneous: All the terms have the same exponent. but others (such as this one) claim that if the equation $a_n=\alpha_1 a_{n-1}+\alpha_2 ...
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2answers
92 views

Notation and terminology for functions, interpreting $f(y)$

It seems to me there are two different interpretations of a symbol $f(y)$. I will explain what I mean: Suppose I have a function $f(x) = x$. (I took the identity map to have a simple example). Also ...
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2answers
65 views

What is it called when you replace sine with cosine in a Fourier series?

Suppose you have a Fourier sine series: $$f(t) = \sum_{n=0}^{\infty} a_n \sin(n \omega t)$$ and you replace sine with cosine: $$g(t) = \sum_{n=0}^{\infty} a_n \cos(n \omega t)$$ or conversely, ...
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6answers
4k views

What is the difference between an indefinite integral and an antiderivative?

I thought these were different words for the same thing, but it seems I am wrong. Help.
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1answer
100 views

Jargon: almost everywhere (or almost surely) on a subset

Let $(X,\mathcal{F},\mu)$ be a measure space. I want to know the correct jargon to say that a property holds everywhere except possibly a measure zero subset of a given set $E\in\mathcal{F}$, that is, ...
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3answers
136 views

What is the correct English name of these lines?

Hello. I'm looking for the English name of these two lines in a two dimensional plane: they go through the origin they make angles of 45° and 135° with the $x$-axis, dividing the plane in two parts ...
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0answers
22 views

What can I use as the generic term for “a function that is composed with another”?

Suppose I am talking about the composition $g \circ f$ (or more generally $f_n \circ \cdots \circ f_1$). Is there a generic term for the functions $f$ and $g$ (the functions $f_i$)? "Compositand"?
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1answer
128 views

Is this a misuse of the word “evaluate”?

I have found the following use of the word "evaluate" in several math books: "To evaluate the continued fraction, start at the bottom and work your way up:" $\huge \underbrace{2 + ...
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1answer
48 views

Is there a name for magmas with $[x+y]+[x'+y'] \equiv [x+x']+[y+y']$?

Is there a name for magmas (written additively) satsisfying the following identity? The square brackets have no particular signifance, but will hopefully promote readability in what follows. ...