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
0answers
27 views

What is the “taxonomy” or “hierarchy” (partial orderimg) of algebraic objects used to attempt to capture geometric intuition?

What follows is a list of terms all of whose relationships to one another I have never fully succeeded in establishing, despite having spent much of 6-8 years trying to so. Feel no need to give ...
20
votes
7answers
2k views

Is there such a thing as a matrix of functions?

Do we ever put functions as entries of a matrix? If so, are these matrices used in linear algebra or do they have some other special use?
1
vote
2answers
39 views

What is the mathematical term describing a pipe or a tube?

I am interested in this unanswered question Pipe-fitting conditions in 3D and so I was trying to find information about it. If the 3D curve $f(x(t), y(t), z(t)) = 0$ is a line I think that the pipe ...
-4
votes
0answers
27 views

Piecewise Contextuous Functions - A possible new branch of functions?

Let us define f(x) as the following: $$f(x) = \begin{cases} g(x) & \text{if something other than f(x) is being added to f(x)} \\ h(x) & \text{if multiplication is being applied to f(x)} \\ j(...
4
votes
1answer
102 views

Approximately not equal

What terms do you consider appropriate for the relations denoted by symbols like these: $$\Large 1.≈\qquad 2.≉\qquad 3.⪅\qquad 4.⪉$$ The first one should be easy: “almost equal to” and “...
3
votes
1answer
70 views

Is there a name for matrices that are symmetric along the cross diagonal? [duplicate]

Something like $$ A= \begin{bmatrix} a & b & c\\ b & d & e\\ c & e & f \end{bmatrix} $$ would be a symmetric matrix because the values are reflected along the ...
83
votes
13answers
9k views

Why do we use the word “scalar” and not “number” in Linear Algebra?

During a year and half of studying Linear Algebra in academy, I have never questioned why we use the word "scalar" and not "number". When I started the course our professor said we would use "scalar" ...
2
votes
0answers
51 views

How does one read a formula with subscripts and superscripts?

An expression like $\Gamma_{ij}^k$ seems to be pronounced "gamma sub i, j upper k". Is this a generally accepted usage? Question. Is there a quotable source for such usage? Note that $k$ is not a ...
3
votes
0answers
41 views

How are varieties related polynomials?

My teacher says that varieties and ideals are related to each other while I tend to mix polynomials and varieties in my terminology. Could some explain how varieties are related to polynomials? And ...
2
votes
2answers
775 views

What is an isosurface?

I am trying to understand the marching cubes algorithm. I would like very much an easier definition of an isosurface than what is available online. Could anyone please explain it? Thanks.
0
votes
2answers
122 views

When are quantities outside of the real numbers considered equal, and when do they exist?

I know of the complex number $i$ and it's existence as the result of invalid square rooting (the square root of negative one does not exist inside the real numbers), but other than complex numbers, ...
5
votes
1answer
42 views

Is it incorrect to call the probability mass function by the name “discrete probability density function”?

Commonly, the probability density function (pdf) is used when dealing with continuous random variables, while the probability mass function (pmf) is used for discrete random variables. This also ...
0
votes
0answers
9 views

Terminology for operation on matrices to check psd

This is just a question of terminology. For defining positive definiteness or negative definiteness of a square $n\times n$ matrix $A$ (say if all entries of $A$ are real numbers) one asks whether $...
0
votes
0answers
16 views

Demonstration of Cycle-cut duality on elementary graphs?

I want to see examples on the Duality theorem between cycles and cuts on the page 26 of Graph Theory Electronic Edition 2005 by Reinhard Diestel. How to demonstrate the duality theorem between ...
2
votes
2answers
65 views

Why is matrix multiplication called 'multiplication' if it is non-commutative?

This question begins with the assumption that matrix multiplication was termed 'multiplication' as a form of comparison/parallel to multiplication of integers and real numbers. Why was matrix ...
0
votes
1answer
31 views

Portuguese term for “path metric”

Do anybody knows what is the usual translation to Portuguese for "path metric"? (Given a metric space $(M,d)$, $d$ is called a "path metric" if, given any pair $(x,y)\in M\times M$, there exists a ...
1
vote
2answers
61 views

Explain Example on Maximal Element with sets

I am trying to understand maximal element and I cannot understand this example from Wikipedia As an example, in the collection $$S = \{\{d, o\}, \{d, o, g\}, \{g, o, a, d\}, \{o, a, f\}\}$$ ...
1
vote
1answer
21 views

Name for submodule killed by a right ideal

Let $\mathfrak a$ be a right ideal in a ring $R$. The set $N=\{m\in M: \mathfrak am=\mathfrak 0\}$ is a submodule of the left $R-$module $M$: If $m,n\in N$, $a\in \mathfrak a$, then $a(m-n) = am-an =...
3
votes
2answers
52 views

What is the name of the following bad “average”?

Is there a standard name for the "average" of the fractions $a/b$ and $c/d$ as $$ \frac{a+c}{b+d} \, \large ? $$ I understand that such an average is not unique in the sense that although $(2a)/(2b) = ...
3
votes
0answers
59 views

Monads in monoids

This question is almost a duplicate of this one, but not quite. There the person asked about examples and intuition, I am asking about terminology and applications, and I am addressing my question ...
1
vote
3answers
80 views

Is “Connected Component” unique for each graph?

Definition A connected component of an undirected graph $G$ is a subgraph where any two vertices are connected by paths. A connected component is a maximal connected subgraph in $G$. Consider a ...
2
votes
2answers
81 views

Why the word “projective” for $PGL_n(\mathbb{F})$?

I wrote the title for this question exactly as I had it exactly in my mind. Let me denote by $G=GL_n(\mathbb{F})$ for simplicity; I was working throughout the previous years many times with the ...
7
votes
1answer
83 views

What does the word “norm” stands for in linear algebra?

I know that "norm" is the formal name for length, but where did this name came from? or from what language is came from? Thank you in advance.
1
vote
0answers
16 views

Are there established names and/or symbols for these orderings?

Consider the following orderings on $\mathbb{Z}^2$. Say $(a, b) \leq_1 (c, d)$ if $a \leq c$ or if $a = c$ and $b \geq d$. So for instance $$(1,3) <_1 (1,2) <_1 (1,1) <_1 (2, 3) <_1 (2,...
2
votes
0answers
16 views

Is there a name for this acyclic quiver?

Sorry for the trivial question, but I don't know much about the subject and don't seem to be able to come up with much by Googling. Is there an established name for quivers of the form $$\require{...
21
votes
6answers
2k views

Is a proof also “evidence”?

Can I use the terms proof and evidence synonymously or is there a difference? You usually see mathematicians writing about "proof" while other sciences instead discuss "evidence" - is there a ...
0
votes
1answer
22 views

Characteristics and Mantessa

I've just heard about these terms. Could someone elaborate on what's their use is? And plus could you explain it using a few examples?
5
votes
3answers
2k views

What does the “closed over”/“closed under” terminology mean exactly and where did it come from?

I've been trying to teach my partner some set theory, and I got thrown for a loop while trying to give her a precise definition of some basic terminology. So we've heard of a set being described as "...
2
votes
1answer
57 views

What are all the different classes of functions upon real numbers and what do they mean, exactly? [closed]

I have been hearing terms like "piecewise C1", "continuous", "linear", "piecewise constant", "trigonometric", "logarithmic", "exponential", "elementary", etc. functions for many years. I know what ...
1
vote
1answer
30 views

Can someone please offer a simple definition of “derived net”?

I was looking up a term called "derived net", however the Google search seems to conflate "net" with .NET programming language. (And filter with electronic filters, and "derived net from a filter" ...
0
votes
2answers
45 views

Hatcher basic terminology/phrasing

I'm trying to self-study some algebraic topology, reading Hatcher. His questions seem much less straightforwardly worded than Munkres - with Munkres it was always clear that you weren't expected to ...
70
votes
6answers
8k views
1
vote
2answers
553 views

Math terminology: What are rules regarding hyphens? (Nonzero vs. non-zero)

This question is geared toward clarifying terminology in writing math. Which terms are correct and why? A set $E$ is non-empty. A set $E$ is nonempty. The number $x$ is non-negative. The ...
1
vote
0answers
23 views

Arc-bases and Point-bases: when are they different for finite digraphs?

Definitions Given a digraph $D=(X,U)$, a point-basis of a digraph $D$ is a minimal vertex set from which a dipath exist to every vertex in $D$. An arc-basis is a minimal arc-reaching set. A subset ...
4
votes
1answer
43 views

Hamiltonian Mechanics and the Symplectic Category

Are canonical transformations (in the sense of Hamiltonian mechanics) morphisms for a certain category? They seem to fit the archetypal description of morphisms being "structure-preserving maps". ...
5
votes
1answer
833 views

What is the inverse of the $\mbox{vec}$ operator?

There is a well known vectorization operator $\mbox{vec}$ in matrix analysis. I've vectorized my matrix equations, did some transformation of vectorized equations and now I want to get back to the ...
1
vote
0answers
23 views

What is the opposite of “sparsity” in a matrix?

If a sparse matrix has only 1% non-zero entries, I find it weird to speak of "1% sparsity". In particular, "increasing sparsity" goes along with a smaller percentage of non-zero entries, so this is ...
0
votes
0answers
24 views

Why is the typewriter sequence named as such?

I refer to the typewriter sequence (see https://terrytao.wordpress.com/2010/10/02/245a-notes-4-modes-of-convergence/) defined by: $$f_n := {\mathbb 1}_{\left[\dfrac{n-2^k}{2^k},\dfrac{n-2^k+1}{2^k}\...
1
vote
0answers
21 views

How is called 1D and 2D analogy to saddle point

Consider n-dimensional function with multiple local minima (e.g. http://ac6la.com/aeopt5.png). There exist some basins of attraction for which particle fall to one or the other minimum. Boundary ...
2
votes
1answer
50 views

What does it mean to “identify” two mathematical objects?

There is an informal notion of "identifying" two mathematical objects that I have run into several times, and I'm am wondering how to formally express this idea. A case of this I ran into long ago ...
9
votes
2answers
2k 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 ...
1
vote
1answer
40 views

What is the difference between accumulation point and $\omega$ accumulation point?

The title says it all. Accumulation point has a widely known definition: a point in $X$ is accumulation point if every open set containing $x$ contains infinitely many points of $X$ Sometimes I ...
2
votes
1answer
55 views

What's the numerator and the denominator of a fraction called?

Just a quick question, is it right to call the numerator and the denominator of a fraction by "terms"? I don't think that "terms" is the right word here, but i don't know any alternatives. Can any ...
1
vote
2answers
37 views

Is there an adjective to describe systems of equations which is neither underdetermined nor overdetermined?

What might I call a system of equations in which the number of equations equals the number of free variables? In other words, if a system of equations is neither underdetermined nor overdetermined, ...
0
votes
0answers
8 views

What is the term for a general set of objects whose higher dimensional analogs have hyper- in front of them?

Strange terminology question: we tend to name things in low dimensional space and then generalize after a certain point. For instance, we have point, line, plane, and then hyperplane (there is no 4 ...
1
vote
1answer
27 views

What is a polynomial with infinite number of terms?

My instructor commented that a structure function $\phi(G)$ of a graph is a polynomial if a finite number of terms. So what is the thing with infinite number of terms? Why not polynomial?
0
votes
0answers
6 views

Set intersection with margin: terminology

I implemented an algorithm that calculates the intersection of two sets with a certain margin and returns the matched tuples: Let A, B be sets. $C = \{ (a \in A, b \in B) | lowerbound <= a - b &...
1
vote
1answer
18 views

Properties of Infinite set on co-finite topology and Countable set on co-countable topology

I am trying to verify some of the properties of infinite set on co-finite topology and countable set on co-countable topology but it is proven to be very tricky because I cannot visualize the spaces. ...
2
votes
0answers
56 views

Are there any “default” properties which hold for almost all topological spaces in analysis?

What is the simplest/most general commonly used (type of) topological space in analysis? For instance, every example I can think of in analysis is first-countable. I don't think it can be metric ...