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

learn more… | top users | synonyms (2)

0
votes
1answer
258 views

In 3D: column major, row major, … major?

If we use column and row major to describe dimension-majority for x and y respectively, what word is commonly used (if any) to describe such majority for the z dimension?
3
votes
2answers
516 views

Semiring between measure theory and abstract algebra

What is the relation between semirings in measure theory and semirings in abstract algebra? Why are they called the same? You can see : http://en.wikipedia.org/wiki/Semiring
4
votes
1answer
2k views

What is a blow-up?

Can anyone explain to me what a blow-up is? If would be great if someone could provide a definition and some examples. Any free introductory texts are welcome too. Thanks!
4
votes
1answer
220 views

Eigenvalues for Sturm Liouville problems and more general ODE/PDE Problems

I'm struggling to find a geometric, or at least some intuitive understanding of eigenvalues and eigenfunctions in Sturm-Liouville problems (which I've been looking at in a PDE course). For instance, ...
0
votes
0answers
117 views

Is there a term for the union of disjoint intervals?

I know a set like $(a, b)$ with $a < b$ is an interval on the reals (in particular, this one happens to be an open interval on the usual topology on $\mathbb{R}$, but I'm not specifically ...
7
votes
1answer
536 views

Why do Quaternions and octonions exist?

Ok so I have known about imaginary numbers for quite some time now. I also understand why we want them to exist (to have a solution for $x^2=-1$). I also remember reading that the complex numbers are ...
4
votes
1answer
173 views

Problem with “tree” definitions

In my studies of choice principles, I've encountered the concept of a tree several times. Frustratingly, no two of the sources I've been working with define it in quite the same way! Notation: Given ...
4
votes
2answers
79 views

Is the cycle graph $C_n$ defined only for $n \ge 3$?

I'm having a hard time seeing what $C_n$ would be for $n = 1$, or $n = 2$. Can someone clear up my confusion?
0
votes
4answers
213 views

What sets satisfy $V = V^V$?

I'm not sure if said set exist or whether it is unique, but what name could I use to find more about it and what kind of interesting properties does it have? Clarification edit: I meant a set $V$ ...
1
vote
1answer
304 views

What is the purpose of the characteristic exponent?

I just came across the term "characteristic exponent" of a field $\Bbbk$. Apparently, it is equal to $1$ if $\DeclareMathOperator{\c}{char}\c(\Bbbk)=0$ and it is equal to $p=\c(\Bbbk)$ otherwise. ...
8
votes
2answers
8k views

Difference between Slope and Gradient

It has been a few years since studying contour maps. Often I hear slope and gradient interchangeably in describing steepness. Does anyone know any good definitions and analogies of slope and ...
15
votes
5answers
4k views

In Group theory proofs what is meant by “well defined”

What is exactly meant or required for a mapping to be well defined. I was reading the first Homomorphism theorem (link) and the first thing the proof does is define a map and find it if its well ...
1
vote
2answers
130 views

Which separation axiom?

Let $X$ be a topological space. Assume that for all $x_1,x_2 \in X$ there exist open neighbourhoods $U_i$ of $x_i$ such that $U_1 \cap U_2 = \emptyset$. Such a space, as we all know, is called ...
3
votes
3answers
185 views

What is a non-degenerate module?

I know what a non-degenerate bi-linear form is, but what does it mean for say a left $R$-module $M$ to be non-degenerate? (Here $R$ is a ring without unit$) I came across a module being called ...
3
votes
0answers
276 views

Formal name for polygon with hole

Is there a formal name for an irregular polygon that has 1 or more holes or cutouts in it? I've heard it refered to as a "swiss cheese polygon" or a "Donut polygon". Is this even strictly a polygon?
0
votes
1answer
499 views

LP: nonbasic solution made into basic solution, help me with this terminology

Related chat here, reading the Bertsimas book now on pages 50-51. By the way, I am gathering Linear-Programming -related studying material here, welcome to read a book and have coffee :) I cannot ...
3
votes
2answers
96 views

Cube with the product uniform measure

Let $([0,1],\mathscr B([0,1]),\lambda)$ be the probability space where $\lambda$ is th Lebesgue measure and $\mathscr B([0,1])$ is the Borel $\sigma$-algebra of the unit interval $[0,1]$. Let us ...
3
votes
3answers
289 views

Why are “irrational numbers” not named “nonrational numbers”?

Possible that I'm misunderstanding the concept of irrational numbers, but seems like the term nonrational would be much more clear. Why is "irrational" more clear than "nonrational"? UPDATE: Just to ...
2
votes
2answers
176 views

What is the name of $V_\alpha$?

In the Von Neumann cumulative hierarchy, $V:=\bigcup_\alpha(V_\alpha)$ is called the universe. Is there a name for the individual levels $V_\alpha$? Just as one can say "The closure of $A$ is defined ...
7
votes
1answer
157 views

When do modifiers denote sub or super? Pseudo-, quasi-, ultra-, strong-, well-, pre-, c0- …

One only needs to search MMA.SE, math journals, wikipedia, or god-forbid, n-cat lab, for keywords listed in the title, which can be extended with: uniform-, regular-, complete-, local-, partial-, non- ...
4
votes
2answers
111 views

If $\sim$ is an equivalence relation on $X$, and there is a strict total order on $X/\sim$, what kind of ordering does $X$ have?

I would like to know if there's a special name for this kind of ordering. When I say there is a strict total order on $X/\sim$, what I mean is that two distinct elements in the same equivalence ...
1
vote
1answer
94 views

What preposition to use when fitting data?

Please could some real experts give an opinion on this question on English.SE: What preposition to use when fitting data? Do we fit data with, by, or as a linear function? Forgive me as I do ...
1
vote
1answer
302 views

About the term “continuous monotone map”

In this wiki a monotone map is defined, but in this paper in theorem 1.1 the definition of a monotone function is recalled. The first is concerned with points of the image, but the second is about ...
0
votes
2answers
116 views

How is it called a minimal morphism of category Rel?

How is it called a Rel-morphism $(f;A;B)$ such that: a. $f=\varnothing$; b. $f\ne\varnothing$? Is there any special term for this?
0
votes
4answers
202 views

is there unique name of inequality $ \leq $ and $ \geq $

I'm tutoring a 8th grader. Once that kid asked me if there is a unique name for $ \leq $ and $ \geq $. Question goes like this: "Since it holds both equality $ = $ and inequality $<, >$ ...
2
votes
1answer
78 views

Looking for the Name of this property: $\mathsf{P}\left(X \leqslant x\right) = \mathsf{P}\left(h(X) \leqslant h(x)\right)$

$h(\cdot)$ denotes a strict monotonic increasing transformation such as $\log$. Another inequality I do not quite get is that $$\mathsf{P}\left(h(X) \le h(x)\right) \ge \mathsf{P}\left(X \le ...
2
votes
0answers
86 views

Term for intersection of lattice and convex region?

Is there a special term or convenient phrase for the restriction of a convex region to points of a lattice? This is motivated by wanting to talk about the feasible points of a discrete problem. I'd ...
3
votes
2answers
202 views

Question about topology definition

I am reading a topology definition: Let $X$ be a set and let $\tau$ be a family of subsets of $X$. Then $\tau$ is called a topology on $X$ if: Both the empty set and $X$ are elements of ...
1
vote
1answer
134 views

Foam-like graphs

What's the "official" name of a connected planar graph consisting entirely of polygons (cycles), glued together at edges, e.g. - among other things - without "end vertices" (of degree 1) and without ...
2
votes
1answer
126 views

Elementary rectangles in product measurable spaces

I am working with showing certain equivalence between two probability spaces, one of them being a countable product space of finite spaces, i.e. $$ (\Omega,\mathscr F) = \prod_{k=0}^\infty ...
3
votes
1answer
67 views

Uniform planar graphs?

What's the name of a planar graph in which every (inner) face has the same number $k$ of vertices? Something like $k$-uniform planar graph? And is there a name for planar graphs in which every face ...
10
votes
3answers
4k views

What does “calculus” mean in the most general sense? [duplicate]

Possible Duplicate: What do Algebra and Calculus mean? I understand that there is calculus, as in math 101 integration and differentiation. Then there is lambda calculus, and there is ...
1
vote
1answer
257 views

Is there name for arithmetic mean divided by RMS average?

Is there a mathematical term for the ratio of arithmetic mean to the root mean square average? (FWIW, in the context where I'm concerned about this the component values will always be >= 0.)
5
votes
2answers
653 views

“Commutative” functions

Say a function is commutative if it remains unchanged under any permutation of its arguments. E.g. $f(0,1)=f(1,0)$. (Alternatively we could describe these as functions over multi-sets, or say that ...
0
votes
2answers
111 views

Total function and termination

If we have a total function, is it by default terminating function? How can we prove the termination for this total function?
2
votes
0answers
97 views

Is there a term used to describe both an equation and inequality?

Is there a term used to describe both an equation and inequality? The closest thing I can think of is "relation".
4
votes
0answers
69 views

What is the term used for space of analytic functions?

I deal with analytic functions in the unit disc represented as the series $\sum_{n=0}^\infty u_n z^n$, where the coefficients $u_n$ satisfy the condition $\sum_{n=0}^\infty n^\alpha|u_n| < \infty$ ...
0
votes
3answers
1k views

What does mantissa mean here?

I was going through this SO post on Math.random() vs Random.nextInt(int) and encountered the following line : Random.nextDouble() uses Random.next() twice to generate a double that has ...
1
vote
1answer
109 views

What is the meaning of the term “inductively P map”?

In this page is the definition of an inductively open map. But in this pdf is the definition of a inductively P map, where P is a property of maps. But there is a difference in the definitions. In ...
1
vote
1answer
471 views

Do the terms “quiver” and “meta graph” refer to the same concept?

Do the terms "quiver" and "metagraph" refer to the same concept? Or is there a distinction I am missing. My sources are Quiver - http://ncatlab.org/nlab/show/quiver Metagraph - ...
19
votes
3answers
545 views

How do you pronounce the inverse of the $\in$ relation? How do you say $G\ni x$?

If I am talking about sets $G$ and $H$ and I want to say in words that $G\subset H$, I, like everyone else, will say that $G$ is contained in $H$, or that $H$ contains $G$. But if I am talking about ...
2
votes
0answers
45 views

The definition of simultaneous conjugacy class

I would like to know the definition of "simultaneous conjugacy class". I have found this concept in "Compact connected Lie transformation groups of spheres with low cohomogeneity".
0
votes
1answer
730 views

Elements of order $n$ in a cyclic group of order $N$

The number of elements of order $n$ in a finite cyclic group of order $N$ is $0$ unless $n|N$, in which case it is $N/n$. Is "the number of elements of order $n$" referring to the number of ...
6
votes
1answer
81 views

Standard terminology for the relation between $A$ and $B$ if $B= Q^t A P$?

Let $A,B$ be two rectangular $m\times n$ matrices related by $$B= Q^t A P$$ with $P$ an $n\times n$ and $Q$ an $m\times m $ matrix. Is there a standard terminolgy for this relation? If instead of ...
3
votes
1answer
112 views

use of the word “object”

I have a nit-picky question about how the word "object" (as in "mathematical object") is generally used/understood. I'll ask by way of a simple, specific example. Consider 1) the set of permutations ...
6
votes
1answer
711 views

“So That” vs. “Such That”

In definitions and exercises, I notice that "so that" and "such that" are seemingly used interchangeably. Are they in fact interchangeable, or is one more appropriate for a specific context? Note: ...
3
votes
2answers
224 views

Why is 'Antisymmetry' named so?

So when we talk about order relations for the familiar number systems, we are always introduced to the antisymmetry property which is $x \le y, x \ge y \implies x=y$. When I think of the word ...
0
votes
2answers
83 views

What is a conformal mapping with $\infty$ in its image?

Suppose we have a bijection $f$ between two open sets in $\mathbb{C}\cup\{\infty\}$, for example $U=\{|z|<1\}$ and $\Omega$, with $\infty\in\Omega$. Let $f(0)=\infty$. What do we mean by saying ...
2
votes
2answers
395 views

Terminology for operation where vertex is deleted and its parents/children are connected

I'm currently documenting an algorithm which involves deleting a node in a directed dependency graph while maintaining the implied dependencies between its parents and children. Take for example the ...
4
votes
1answer
275 views

“Without restriction of generality” same as WLOG?

Does the term "without restriction of generality" mean the same as "without loss of generality"? EDIT: I encountered the phrase in this paper (PDF).