Questions tagged [terminology]

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

Filter by
Sorted by
Tagged with
0 votes
0 answers
8 views

Does this family of curves appearing in the magnetic field of a coil have a name?

While attempting to express the magnetic field induced by a single coil of current (at any point in space, not just on the coil's axis), I tried visualising the set of the infinitesimal contributions $...
Sileo's user avatar
  • 145
0 votes
0 answers
24 views

Are right-adjoints of a forgetful functor reflectors?

From what I understand, there is no formal definition of a forgetful and an inclusion functor, but more like "moral guidelines" with "good properties" of why we would call them ...
chickenNinja123's user avatar
-1 votes
0 answers
33 views

What does it mean that "every column of A adds to zero." [closed]

What does it mean that "every column of A adds to zero"? Is it the following matrix, \begin{equation}A = \begin{bmatrix} 1 & 2 & -3 \\ -1 & 0 & 1 \\ 2 & -2 & 0 \...
ArdaSenyurek's user avatar
0 votes
1 answer
38 views

The name of dual concept of evaluation map

Given a collection of sets $\{Y_\alpha: \alpha \in A \}$ for an index set $A$. For each $\alpha \in A$, let $f_\alpha: X \to Y_\alpha$ be a function. The map $f: X \to \prod_{\alpha \in A} Y_\alpha$ ...
khanh's user avatar
  • 209
0 votes
0 answers
36 views

Terminology: definition of closed submodule

I am unable to find any clear definition of the concept of a closed submodule of a module. I'd really appreciate it if someone might elaborate on it, or point me in the right direction. As far as I ...
mathieu_matheux's user avatar
0 votes
1 answer
65 views

Name this property: product of functions = function of sum

Consider a function $f(x)$ with the property $f(a)f(b) = f(a+b)$, where $a,b$ are numbers (or matrices, or operators). Is there a name for this property? For example, $f(x)=c^x$ for a fixed $c \in \...
johann's user avatar
  • 1
0 votes
0 answers
55 views

Where can I get a formal definition of "branching points"? [closed]

I'm taking my complex analysis course, and I would like to know if somebody can please give me some advice on where can I find the definition of "branching points".
Daniel Romero's user avatar
3 votes
0 answers
31 views

Can't parse a statement in an article on coalgebras and umbral calculus

I am reading Nigel Ray's "Universal Constructions in Umbral Calculus" (1998, published in "Mathematical Essays in Honor of Gian-Carlo Rota", page 344). The article reads: We ...
Daigaku no Baku's user avatar
1 vote
0 answers
15 views

Terminology to measure the ratio of the maximum value to the minimum value of a real-valued function?

Let $f:\mathbb{R}\rightarrow \mathbb{R}$. Let $f_{\mathrm{max}}=\max_{x\in \mathbb R} f(x)$ and $f_{\mathrm{min}}=\min_{x\in \mathbb R} f(x)$. Define $r$ as the ratio of $f_{\mathrm{max}}$ to $f_{\...
Mengfan Ma's user avatar
1 vote
0 answers
130 views

What does the word "indeed" mean in math? [closed]

The word "indeed" is often used in proofs, usually to begin a sentence. What is the meaning and correct usage? I've usually seen it used in this form [Assertion of $X$ without proof]. ...
SRobertJames's user avatar
  • 4,224
0 votes
0 answers
19 views

Name for algorithm grouping carryless long division

When implementing multiplication in binary finite fields, Barrett reduction allows to perform division with two carryless multiplications and two XOR additions (and some one-time precomputation). ...
dragomang87's user avatar
1 vote
1 answer
32 views

How can we distinguish elements of $D_n$ that include reflections versus those that don't?

For $n \geq 3$, the dihedral group $D_n =\langle r, s \rangle$, where $r ^n = s^2 = e$. Within this group, we can distinguish two types of elements: Those of the form $r^i$, where $i$ is any integer ...
SRobertJames's user avatar
  • 4,224
0 votes
0 answers
122 views

Why is the Monster group called that?

This is a bit of a soft question, but why is the Monster group called that? Does it have any connection with monster models in model theory? I would be interested to learn who came up with that ...
user107952's user avatar
  • 20.2k
1 vote
1 answer
50 views

Qing Liu's definition of specialization of point - follow-up question

The definition of a generic point in Qing Liu's book "Algebraic geometry and arithmetic curves" has been discussed before in these questions: Explaining the motivation behind two different ...
user128787's user avatar
  • 1,125
10 votes
2 answers
754 views

Is there a standard name for the boundary of a cube?

A distinction is commonly made between a ball (solid) and a sphere (the boundary of a ball). This distinction is made in other dimensions as well (e.g. circle versus disc, in 2D). From what I've seen ...
realityChemist's user avatar
1 vote
0 answers
34 views

Bound on the amount of probability mass 'seen' from a sample.

I was thinking of the following puzzle out of the blue and I would like to know if it has already been studied (I would assume so due to the simplicity of the setup). Imagine you have some unknown ...
SammyH's user avatar
  • 137
1 vote
0 answers
52 views

Does this shape have a name? (A 'spherical circular triangle' ???)

This shape is formed by 3 'small' circles on the surface of a sphere, each touching the other 2. On a plane, the shape is called a 'circular triangle' (refer to Wikipedia). In this particular example ...
Parsley's user avatar
  • 11
1 vote
0 answers
42 views

How do I call a matrix $A\in \mathbb{C}^{m\times n}$ satisfying $A^*A=\mathbf{1}$?

How do I call a matrix $A\in \mathbb{C}^{m\times n}$ satisfying $A^*A=\mathbf{1}$? Maybe orthogonal? Also I'd like to confirm that the following equivalences are true: Let $A\in \mathbb{C}^{m\times n}...
noob's user avatar
  • 23
0 votes
0 answers
32 views

What is the meaning of logarithmic density in layman's terms?

The way that I understand natural density is that it is an "intuitive way of describing the size of a set", whereas cardinality is an "absolute way of describing the size of a set"....
Predrag Stojadinović's user avatar
0 votes
0 answers
41 views

What does "almost all in the sense of logarithmic density" mean in Tao's Collatz paper?

Tao's paper: "Almost all orbits of the Collatz map attain almost bounded values" (via arXiv.org) 1st related question/discussion, I did not understand: Meaning of "almost all" in ...
Predrag Stojadinović's user avatar
2 votes
0 answers
146 views

When mathematicians say "true" do they mean "true in all models"?

According to the comments to this question, Truth is ordinarily defined by reference to models. If so, even axioms and theorems are not true without reference to a model. However, when ...
MathMan's user avatar
  • 55
1 vote
0 answers
80 views

what math concept would this be called?

Assume that I am trying to use reference values to evaluate an analysis of an unknown sample in order to determine what the nature of the sample is and the attribute value is an 8-bit string of binary ...
Sam Levi's user avatar
3 votes
0 answers
91 views

What is the opposite of antiparallel?

Is parallel really the opposite of anti-parallel? While anti-parallel indicates that two vectors are directed along the same line and are pointing in opposite directions then it seems to me that ...
Steeven's user avatar
  • 731
0 votes
1 answer
56 views

Is there a name for this vector space?

I've seen in some books of Analysis the notation $\mathcal{L}(\mathcal{L}(V), V) \cong \mathcal{L}_2(V)$ and I don't find anything about this vector space. What is it? Is there a name for it? Also, if ...
Paulo Estêvão's user avatar
1 vote
0 answers
20 views

terminology needed regarding convex bodies

Let $K$ be a convex body in $\mathbb{R}^n$. I'm looking for a term for a continuous function $f: \mathbb{R}^n \to \mathbb{R}$ that is zero on $\partial K$, negative on the interior of $K$, and ...
Glenn Davis's user avatar
3 votes
0 answers
53 views

Terminology for Complex Algebraic Geometry with Complex Conjugation

Semialgebraic geometry is essentially real algebraic geometry but with the defining polynomial relations allowed to be inequalities rather than just equalities. This doesn't make sense over $\mathbb{C}...
Harry Wilson's user avatar
  • 1,084
4 votes
1 answer
103 views

Minimal elements under division in a ring

Let $p$ be an element of a commutative ring with unity. The following definition is natural: $p$ is minimal under division if its only divisors (up to equivalence) are $1$ and itself. That is, for ...
Caleb Stanford's user avatar
2 votes
1 answer
82 views

Where does the term 'dense' used in forcing/Martin's axiom come from?

There are some common meanings to 'dense' in Mathematics. In Topology, a subset $S\subseteq X$ of a topological space $(X, \tau)$ is dense if the intersection of every non-empty open set with $S$ is ...
Chad K's user avatar
  • 4,331
0 votes
1 answer
29 views

Nomenclature: Collection of sets in which each set has some element unique to it

A collection $\mathcal{X}$ of sets may have the property that each member of the collection has some element unique to it, more precisely, that for each element $A$ of $\mathcal{X}$, for some object $...
A. Burrell's user avatar
-2 votes
1 answer
84 views

Does $(p\implies q)\implies\neg( q\implies p)$? [closed]

$p\implies q$ does not necessarily indicate that $q\implies p$, which is why there exists a double-sided implication: $\iff$. $p\iff q$ is the same as saying $(p\implies q)\land(q\implies p)$. However,...
The_Animator's user avatar
-3 votes
1 answer
54 views

4 elements are named x,y,z,w now how to name 8 elements [closed]

I have a vector of four elements. The elements are named x, y, z, w: Vec4(x, y, z, w) Now I have another vector of eight ...
Megidd's user avatar
  • 221
0 votes
0 answers
64 views

How to formally define this square matrix?

I was wondering if there is formal name for a 3x3 matrix where the third column is the sum of the first two columns and the third row is the sum of the first two rows. In other words, a square matrix ...
anonymous 's user avatar
2 votes
1 answer
53 views

Term for a product of groups that is neither direct, nor semi-direct, but generalises semi-direct ones

Suppose $H$ and $K$ are subgroups of a group $G$ such that every element $g\in G$ can be uniquely written as $g = hk$ with $h\in H$ and $k\in K$. (It follows then that every element $g\in G$ can also ...
Alexey's user avatar
  • 2,106
1 vote
1 answer
102 views

What are $0$ and $1$, the elements of $\mathbb Z/2\mathbb Z$? How do they relate to $\mathbb Z$? [duplicate]

I often see field $\mathbf{Z}/\mathbf{2Z}=\{0,1\}$. Without other indication we might see elements of field $\mathbf{Z}/\mathbf{2Z}$ as a subset of $\mathbf{Z}$. Operations such as $2+1=3=1$ are also ...
mins's user avatar
  • 385
1 vote
0 answers
30 views

Name for an almost diagonal real matrix

If $A$ is a real square matrix which is diagonalisable over the complex numbers, then it is conjugate (over the reals) with a matrix $D$ which is block-diagonal, where each block on the diagonal is ...
tomasz's user avatar
  • 35.4k
6 votes
2 answers
534 views

Why does “propositional calculus” have the word “calculus” in it?

We define “calculus” like this: “Calculus is the mathematical study of continuous change.” But if that’s the case, then why is the study of (true or false) propositions and their relations called: “...
user avatar
0 votes
3 answers
124 views

What is the name of the logical equivalence $p\land\neg p\equiv\bot$?

The conjunction of any statement $p$ by its negation is a contradiction. That is: $$p\land\neg p\equiv\bot$$ Do you know if there is a name for this logical equivalence?
Aria's user avatar
  • 420
3 votes
1 answer
114 views

What category is this? (Objects are sets and distinguished subsets of power set)

Let $\mathcal{C}$ be the category whose objects are sets $X$ equipped with distinguished subsets of the associated power set $\mathcal{U}_X \subset \mathcal{P}(X)$, so that their union is all of $X$ (...
cheyne's user avatar
  • 347
2 votes
1 answer
55 views

What is the name of this family of graphs?

Let $V$ be some finite set and let $V_0\subset V$ a nonempty subset. Let $G$ be the graph with vertices $V$ such that $\{i,j\}$ for $i\neq j\in V$ is an edge if and only if $\{i,j\}\cap V_0\neq\...
Hans's user avatar
  • 3,539
2 votes
2 answers
179 views

Equal sign meaning in equations vs functions

My kids are learning about functions for the first time, and I was hoping for a little clarity concerning what the equal sign means in a variety of contexts. I have checked out, and understood parts ...
Clare Mellqvist's user avatar
1 vote
1 answer
53 views

Why is a first order linear differential equation of the given form?

My Professor said that a first order linear differential equation is of the following form : $\frac{dy}{dx}+Py=Q$, where $P$ and $Q$ are functions of $x$. I am unable to understand why is this true. I ...
Charlotte's user avatar
  • 1,664
0 votes
1 answer
42 views

How do I determine the maximum subgraph that avoids certain edges?

I have a graph where I want to select a subset of the nodes subject to a particular constraint: An edge between nodes A and B indicates that I cannot select BOTH A and B to belong to the subset. I ...
Mark Lavin's user avatar
0 votes
1 answer
90 views

What's the name of this graph-like structure

So there's a type of mathematical structure I'm interested in exploring, I figure it already has been explored, so I'm curious if someone can point me in the right direction. It's inspired by trying ...
scl's user avatar
  • 57
0 votes
0 answers
51 views

Terminology for the reverse of a group element's string representation

Consider a group $A$ generated by elements $a_0,a_1,...,a_k$. Now consider element $x\in A$ given by some product of group elements under the group operation $*$. For example, $x$ may be equal to $a_9*...
FabrizzioMuzz's user avatar
0 votes
1 answer
23 views

(Terminology) Name for a subset that has non-empty intersection with every block of a partition?

Consider the following data: a set $X$, a partition $\mathcal{P} := \{B_i\}_{i \in I}$ of $X$ whose elements $B_i \subseteq X$ are called "blocks", and another subset $Y \subseteq X$. ...
hasManyStupidQuestions's user avatar
0 votes
0 answers
72 views

Meaning of "on" in the expression "operation on a set $A$"

What is the meaning of "on" in the expression "operation on a set $A$"? Does it mean that: at least one of the operands is in $A$; all the operands are in $A$; or all the operands ...
toliveira's user avatar
  • 918
0 votes
1 answer
35 views

Asymptotic notation names

Here are two asymptotic symbols: $\asymp$ and $\sim$. I know what their mathematical definitions are, namely $f(x)\asymp g(x)$ if there exist constants $A,B$ such that $Af(x)\le g(x)\le Bf(x)$, and $...
user avatar
1 vote
1 answer
74 views

The name of $p\Longrightarrow q \equiv \neg p \lor q$ logical equivalence

As we now the negation of the conditional statement $p\Longrightarrow q$ is $p\land\neg q$. Using De Morgan Law then we get: $$p\Longrightarrow q \equiv \neg p \lor q.$$ Do you know if there is any ...
Aria's user avatar
  • 420
0 votes
1 answer
69 views

Name of Simple Logical System

There's a logical system, devised by someone whose name escapes me, that consists of two moves. You begin with one line, then draw another line, and somehow this can be built to capture all sorts of ...
inkd's user avatar
  • 47
1 vote
0 answers
43 views

Is there a general consensus regarding which term is the multiplicand, and which is the multiplier in basic arithmetic multiplication?

Is there a general consensus regarding which term is the multiplicand, and which is the multiplier in basic arithmetic multiplication? In my notes I stated that in the expression $a \times b$ the left ...
Steven Thomas Hatton's user avatar

1
2 3 4 5
170