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

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11
votes
1answer
252 views

If $u=\frac{1+\sqrt5}{2}$, then $u^3=2+\sqrt5$, but $u^2=\frac{3+\sqrt5}{2}$. What is the group that measures the power that makes units look nice?

For $A=\mathbb{Z}[x]/(f)$ with quotient field $K$ and ring of integers $B$, does $U(B)/U(A)$ have a name? For instance $u = \tfrac{1+\sqrt{5}}{2}$ is a unit in $\mathbb{Q}[\sqrt{5}]$, but neither ...
5
votes
1answer
594 views

what does the “L” in “L-function” stand for?

I haven't been able to find a reference that tells what word (if a word) the L is short for.
1
vote
1answer
406 views

What is the correct term for an increasing or decreasing function which “flattens out”?

I'd like to say logarithmically decreasing but it does not have to decrease to zero. An example of an increasing function which flattens out at around 4.5%.
0
votes
2answers
355 views

Terminology: generic word for increase and decrease

This is a really basic question. Consider a statement: A painted line is increased by length $x$ Can $x$ be a negative number just by the wording of the question? What would be a better way of ...
1
vote
0answers
74 views

Terminological question: generalization of rank to matrices over modules

I'm interested in what to call the length of the sequence of ones in the Smith normal form of a matrix. Equivalently (or so it seems to me), this is the rank of the largest submodule of M, on which A ...
5
votes
1answer
145 views

What is the name for the topology where every point forms an open set

I remember there is some name for a special topology on a set, such that every subset is open i.e. every point forms an open set, but I cannot recall it. Please tell me its name or say I ...
9
votes
1answer
442 views

Why are spectral sequences called “spectral”?

Why are spectral sequences called "spectral"? Is that use of "spectral" related to other uses in math, such as spectra in homotopy theory, the spectrum of a ring in algebraic geometry or the spectrum ...
4
votes
1answer
242 views

Origin of mathematical use of “orbit”

If $G$ is a group acting on a set $S$, then the "orbit" of a point $x$ in $S$ is defined as the set of all elements of the form $gx$ where $g \in G$. My question: why was the word "orbit" chosen for ...
20
votes
2answers
889 views

A place to learn about math etymology?

I was recently wondering where the word `kernel' comes from in mathematics. I am sure the internet must know. I did manage to find http://www.pballew.net/etyindex.html#k which contains the origin ...
2
votes
1answer
664 views

In linear optimization, what does “AP” stand for?

I am learning algorithms, and there is a chapter which uses linear optimization methods to solve a matching problem. This is the problem definition: I find the abbreviations AP for the constraints ...
1
vote
3answers
868 views

Explanation of term “closed under” in the definition of a sigma algebra?

A sigma algebra is closed under countable intersections. This is a property of a sigma algebra, but I don't understand what this means in plain English. Can someone explain this to me in terms ...
2
votes
1answer
268 views

How do I describe the growth of something that scales by a factorial?

I just wrote a blog post and wasn't sure how to word a particular sentence. Say I have the following function: \begin{equation} f(x) = x^2 \end{equation} Then I can say that the value of f(x) grows ...
17
votes
4answers
18k views

Is positive the same as non-negative?

I would assume the answer to my question is yes, but I want to make sure because my book uses both terminologies. Please also indicate where zero falls into the mix. UPDATE: Here is an excerpt from ...
12
votes
2answers
305 views

Preimaging units to units

I'm interested in (unity-preserving) homomorphisms $f: S \to T$ between (commutative, with-unity) rings $S$ and $T$ so that if $f(x)$ is a unit, then $x$ was a unit to start with. For example, an ...
1
vote
2answers
215 views

Does the term localized function exists?

I am looking for a term that describes function that is "localized". What I mean is a function that is non zero in a bounded range and zero else where, such as the a rectangle pulse function. But ...
2
votes
2answers
116 views

Graph invariant that encodes number of subgraphs with $i$ vertices and $j$ edges

Suppose we have invariant of graph $G$ that tells us number of subgraphs with $i$ vertices and $j$ edges for every setting of $i$ and $j$. Is there a name for it? I searched for "subgraph ...
5
votes
2answers
1k views

What is the property where f(g(x)) = g(f(x))?

What is the property where f(g(x)) = g(f(x))?
5
votes
2answers
326 views

name of a shape

Let P be a point, not the center, in the interior of a (round) disk D⊂ℝ² and let A and B be points on ∂D such that the line segments AP and BP have equal length. Choose an arc AB. What's the shape ...
2
votes
0answers
178 views

What is it called when a subalgebra contains its centralizer?

In the question Math.SE #16716, Natalia asked about representing rings of matrices as centralizers of a matrix. This is an intriguing question, but had some clear problems as rings of matrices need ...
4
votes
1answer
111 views

How to define a profinite morphism

What is the definition of a profinite morphism in http://www.math.upenn.edu/~pop/Teaching/2010_Math624/2010_Math624PS08.pdf problem 5? This is not actually a homework of mine but I was unable to find ...
3
votes
3answers
130 views

Term for Voronoi diagrams with non-point sites

I am looking for a term used to describe an analog to Voronoi diagrams where instead of a single point defining a cell, a continuous set of points is used. For example, starting with five triangles ...
3
votes
0answers
284 views

How do they know an integral has no closed form solution? [duplicate]

Possible Duplicate: How can you prove that a function has no closed form integral? When they say that, e.g., Li(x) has no closed form (for some agreed upon definition of "closed form"), do ...
4
votes
2answers
388 views

Square for $x^2$, Cube for $x^3$, Quartic for $x^4$, and what's for $x^1$?

What's the general form for $x^y$? What's the specialized form for $x^1$ and $x^0$?
6
votes
1answer
298 views

What is the origin of the term “Differentiable”?

I was wondering today about why the word differentiable is used for describing functions that have a derivative or are differentiable. Perhaps because originally one considered finite differences? ...
2
votes
2answers
98 views

Are there standard terms for more fine/coarse grained (but otherwise consistent) ways of ordering values?

Consider an sequence of unique values. Each value is composed of a surname and a first name in that order of significance. Based on that, I can define a complete ordering of values in the sequence. ...
9
votes
3answers
695 views

What “general” in “general topology” refers to

What does general in general topology really refer to? We use the term all the time without thinking about its origin.
2
votes
3answers
360 views

Does saying “to negate a sign of a const term” has a meaning

If I have term -5 and I want to change its sign to opposite can I say that I'm negating its sign?
1
vote
2answers
284 views

What do we mean by an algebra is complete with respect to a filtration

What does it mean to say that an algebra is complete with respect to a filtration? Thanks!
3
votes
3answers
164 views

Name of an operation on graphs

Let $G$ and $H$ be two possibly directed, non necessarily simple, vertex-labelled graphs with respective adjacency matrices $A_G$ and $A_H$ and $V(G)=V(H)$. 1) What is the name of the graph $M$ with ...
7
votes
2answers
1k views

Distinction between 'adjoint' and 'formal adjoint'

in functional analysis, you encounter the terms 'adjoint' and 'formal adjoint'. What does 'formal' in that case mean? It Sounds like a hint that 'formal adjoints' lack a certain property to make them ...
2
votes
2answers
265 views

Broken glass geometry

If topology is called rubber-sheet geometry, would it be accurate to describe the "cut and shuffle" topic of "piecewise isometries" as broken glass geometry ? Isometry sounds more geometrical than ...
3
votes
1answer
395 views

What is the name of the matrix used to weight an inner product?

In Linear Algebra, when computing an inner product $<x,y> = y^*Wx$, what is the name of the matrix W? If it doesn't have a name, where can I find a practical explanation of how to construct ...
4
votes
2answers
806 views

Terminology - Nth rule

I'm trying to help my son study 8th grade math (in Texas). He's having trouble with the "Nth rule". Is anyone familiar with this terminology? I think that it may be related to the Nth term in a ...
2
votes
4answers
291 views

A root? Or two roots?

It is known that, in the universe of complex numbers, the only root of the equation $x^2 - 2x + 1 = 0$ is $1$. Could we say that the equation has two equal real roots? Or should we say that the ...
10
votes
5answers
14k views

Is the void set (∅) a proper subset of every set ?

I am a bit confused about the concept of proper subsets,precisely whether to include one or both of the void set and the set itself. An extract from my module goes like this : Obviously,every set is ...
1
vote
2answers
148 views

What is the name for a function of a matrix that changes the matrix size?

I have a set of functions that map square matrices with $n$ rows and columns to square matrices with $k < n$ rows and columns. Is there a name for this property? I know that 'projection' would be ...
4
votes
1answer
601 views

Definition of direct image?

I read a little remark in a topology text that the direct image of an open set under a continuous mapping is not necessarily open. What is the definition of direct image in this case? I tried ...
5
votes
2answers
773 views

what size is a “unit torus”?

Wikipedia articles on "unit sphere" and "unit circle" say the radius is 1. Articles on the "unit square" and "unit cube" say the length of the side is 1. Would you expect a unit torus to have major ...
2
votes
1answer
552 views

“circumference” of a sphere

What is the name for I can only describe as the circumference of a sphere. I mean like the equator on a planet. What is the line called which goes around the entire sphere, it can be anywhere (so not ...
5
votes
2answers
183 views

Function of two variables as a function of a function

Consider a function $f : \mathcal X \times \mathcal Y \mapsto \mathbb R$. I want to define $g_x(y) = f(x,y) : \mathcal Y \mapsto \mathbb R$. I want to say that $g_x$ is a ___ of function $f$. ...
2
votes
2answers
177 views

polynomial of $x$?

I want to refer to functions of the form $f(x) = \sum_{i=1}^n a_i x^{\alpha_i}$ where $\alpha_i < 1$. This is not a polynomial, because $\alpha_i$ could be just real arbitrary numbers (though ...
26
votes
4answers
41k views

Difference between axioms, theorems, postulates, corollaries, and hypotheses

I've heard all these terms thrown about in proofs and in geometry, but what are the differences and relationships between them? Examples would be awesome! :)
1
vote
1answer
92 views

Does the term Row-Complete have any synonyms?

I'm wondering if there is other terminology that describes row-completeness, outside the context of a latin square, or if row-complete is actually a general term.
4
votes
1answer
2k views

What are valent vertices?

Page 13 of Tropical Algebraic Geometry by Itenberg, Mikhalkin, and Shustin mentions 1-valent vertices, but I haven't been able to find a source that actually defines this term or managed to guess the ...
3
votes
1answer
308 views

Is there a name for this kind of number?

A perfect number is a number that is the sum of its proper divisors: 28 = 1 + 2 + 4 + 7 + 14 Is there a name for numbers whose only proper divisors are 1, 2, and ...
8
votes
4answers
871 views

How can I read this mathematical sentence aloud in English?

A map $s : \mathbb{N} \to X$ is a computable sequence in $(X,\nu_X)$ when there exists a computable map $f : \mathbb{N} \to \mathbb{N}$ such that $s(n) = \nu_X(f(n))$ for all $n \in ...
2
votes
1answer
111 views

The name for a subobject(subgroup) which is annihilated by action

I know this question is easy, but for the life of me, I cannot remember what we call this thing. Googling for this has offered no help. Consider an object $A$ and a second object $B$(let them be ...
1
vote
1answer
370 views

What is the difference between constants of proportionality and constants of integration?

I've been doing some maths work using the rate of flow of liquids. I've used various models for the flow and various methods to integrate these models. The one thing that is confusing me is the ...
2
votes
0answers
84 views

is there a name for this construction? (taking a pairing and obtaining a perfect one)

I believe that if we are given two modules $M,N$ over a ring $R$, and a pairing between them $M \otimes_R N \to R$, we can construct a perfect pairing $M'\otimes_R N' \to R$ by taking kernels. Is ...
10
votes
6answers
1k views

How is the codomain for a function defined?

Or, in other words, why aren't all functions surjective? Isn't any subset of the codomain which isn't part of the image rather arbitrary?