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

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1answer
34 views

What are “irreducible factors” in a field?

I am really not understanding what "irreducible factor" in $F[X]$ for field $F$ means. can someone explain? for example is $(x - 1)^2$ irreducible? in my current understanding I think yes. but I ...
0
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1answer
58 views

A term for a function $f$ such that $x f'(x)$ is decreasing

Consider a differentiable, monotonically increasing function $f$. If $f'(x)$ is increasing, then $f$ is convex. If $f'(x)$ is decreasing, then $f$ is concave. Is there a term that describes $f$ when ...
0
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1answer
44 views

Are matrices 2D by definition?

On the one hand, I read on Wikipedia that [A] matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. However, googling "3D matrix" ...
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1answer
34 views

What is the proper notation for vectors that uses only integers? $\Bbb Z^n$?

How do I denote vectors, similar to $\Bbb R^n$ but with integers instead of the reals? Just $\Bbb Z^n$? Would vectors of exclusively positive integers be $\Bbb Z^{{+n}}$ then? (since $\Bbb Z^+$)
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0answers
11 views

Name for a “pseudo-diagonally dominant matrix”

I'm doing a literature search, and I'm just wondering if there is a name for (Hermitian positive definite) matrices which have the sum of the off-diagonals in any given row dominated by the diagonal ...
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0answers
34 views

Is there a term for the dimension of the annihilator of an element of an algebra?

Let $\mathcal{A}$ be a finite dimensional $R$-algebra, and for $x \in \mathcal{A}$ consider $\mathrm{Ann}(x) = \{ c \in \mathcal{A} \mid cx = 0 \}$. Is there a term for the dimension of this subspace? ...
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0answers
39 views

Alternative view of matrix inversion (explanation required)

We were taught in linear algebra that in order to try to find the inverse of a matrix we can create an augmented matrix $[AI]$ where $A$ is the original matrix and $I$ is the identity matrix. Then we ...
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1answer
65 views

What does it mean for an automorphism to centralize factor group $G/M$?

Let $G$ be a group and $M$ be a normal subgroup of it. An automorphism $\phi$ centralizes the factor group $G/M$. What does it mean for an automorphism to centralize a factor group $G/M$? I ...
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3answers
46 views

Are scalars a synonym for the elements of $\mathbb R^1$?

Are scalars a synonym for the elements of $\mathbb R^1$, or is there a subtle difference?
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1answer
52 views

Terminology: is it random?

The topic of research of my master thesis is the use of probabilistic methods and models in music composition, particularly in the field of algorithmic music. As often is the case, artists tend to be ...
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0answers
35 views

Is there a math notation/ term for “$f(x_n) \to 0$ iff $g(x_n) \to 0$”?

I have two real-valued functions $f,g$ defined over the $N$-dimension Real Euclidean space: $$ f,g: \mathbb{R}^N\to\mathbb{R}. $$ They satisfy this property: $$ \forall x_n \in \mathbb{R}^N: f(x_n)\to ...
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1answer
43 views

Is there a term for a function which is not continuous on any open set?

A function is said to be nowhere continuous if it is not continuous at any point of its domain. Is there a similar term encompassing functions like $$f(x) = \begin{cases} x & \text{ if } x \in \...
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1answer
26 views

Why/What is this shape possible/classified as?

From supernatural season 9 episode 23. Circle is divided to 6 parts with a hexagram(? I guess), but then each line is divided to 5 parts with kissing circles, the fact that all the circles are ...
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0answers
7 views

interpolation terminology

I am trying to write a discussion on various interpolation methods, and I need a systematic terminology for interpolation, or the article will have an unnecessary digression to define terms, which won'...
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2answers
36 views

Does “sphere” denote the surface or the entirety of a solid ball?

In everyday English, the word "sphere" denotes a 3-dimensional object, including the points inside the surface and its center. However, I get the sense that in mathematics, the sphere is used ...
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1answer
40 views

How to read $\frac{dy}{dx} $ when the term is only given?

When the term $\frac{dy}{dx}$ (not $\frac{d}{dx}y$) is only given, how to read the term between "the derivative $y$ with respect to $x$" and "the quotient of the differential $dy$ by the differential $...
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1answer
35 views

Is there another name for a vector?

I am writing a program uses contains both vectors (direction and magnitude) and vectors (a matrix with one row/column) and my head is spinning. I could replace the latter kind of vector with ...
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0answers
18 views

Terminology for property of two branches of a tree

Consider a tree $T$. A branch $B$ of a tree $T$ is just a proper subtree of $T$ (that is a subtree $B \subset T$ and $B \neq T$). Lets consider $B_1$ and $B_2$, two branches of a tree such that $B_1$ ...
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3answers
76 views

I don't get it, does “augmented chain complex” actually mean anything?

If I understand correctly, chain complexes make sense in any category enriched in the world of pointed sets. In practice, there's also a notion of an augmented chain complex, where we have an extra ...
4
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3answers
53 views

Vectors sometimes used in math just as arrays/lists of numbers, sometimes as concept of “change”

As a freshman in a small town college. Ive been getting mixed signals to what vectors (and matrices/tensors) are. Sometimes I get the feeling they are used just as containers/arrays for multiple ...
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0answers
12 views

name/term for the property of non-analytic complex functions causing “anisotropy”

I'm looking for a mathematical term here so I can understand the consequences of nonlinearity in a system of interest to me. Here's an example system that exhibits this behavior: $$ f(z) = \begin{...
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0answers
17 views

What is the point of solving a system of linear equations using back-substitution (as opposed to reduced echelon form)

In lecture the other day, my professor offhandedly mentioned the existence of a process called back-substitution a way in which a computer program would solve a system of linear equations rather ...
0
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1answer
14 views

Monoid operation order sensitive?

It is a basic question, none the less I cannot find an answer: A monoid is associative (with an identity) (m1∙m2)∙m3=m1∙(m2∙m3). e∙m=m∙e=m If you consider a monoid over natural numbers (N,+,0) for ...
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1answer
30 views

Compact set contained in the interior of another compact set

Let $X$ be a locally compact Hausdorff space. Does the property "every compact set is contained in the interior of some compact set" has a special widely known name? Is it related to paracompactness?
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1answer
56 views

What is the Fibonacci-like sequence called where one sums the last 3 numbers

The Fibonacci-sequence is defined like. $F_{x+1} = F_{x} + F_{x-1}; F_0 = 0, F_1=1, x \in {\Bbb N}$ Is there a special name for this sequence: $F_{x+1} = F_{x} + F_{x-1} + F_{x-2}$ ? Which?
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2answers
33 views

Why are Optional Stochastic Processes Important?

I understand to some degree why adapted processes, progressive processes, and predictable processes are important. EDIT: I am referring only to the continuous time case, NOT discrete time. But why do ...
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4answers
563 views

Why do they call it base 10?

Now, I know intuitively why it's called base 10: because there's 10 numbers. But see here's the thing, if we're working with numbers 0-9 (and of course we are), we use up our numerical artillery at 9....
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2answers
53 views

What is the sample space of a dice labelled with 1,2,2,3,3,3 for the standard dice?

When we roll a dice labelled with 1,2,2,3,3,3 for the standard dice. What is the sample space of this activity? If someone argues the probability of getting 1 is $\frac{1}{3}$. Because the person ...
1
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1answer
41 views

Term for a 'coefficient' used in multiple places.

Consider the case where I have a 'coefficient' $T$ such that: $f(x) = T(1 - e^{-x/T})$ What would you call this term? It's certainly being used as a 'coefficient', but its reciprocal is also being ...
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2answers
39 views

What is Convex about Locally Convex Spaces?

This might be a silly question, but what motivates the name "locally convex" for locally convex spaces? The definition in terms of semi-norms seems to have nothing to do with convexity or with the ...
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1answer
48 views

Product of sets as complexes

What does it mean to take the product of two sets of complex numbers as complexes? Reading this paper: "The Determinant of the Sum of Two Normal Matrices with Prescribed Eigenvalues" by N. Bebiano ...
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1answer
36 views

Terminology of “Random variable”

A random variable $X$ is a measurable function $X : \Omega \rightarrow E $ where $\Omega$ and $E$ are measurable sets. So, as far as I can see from this definition, random variables are just ...
0
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1answer
38 views

Inner, outer, tensor, cross product - where do the names come from

Well, I could imagine the reason for the latter - due to the convention to write the cross product as $\alpha_1 \times \alpha_2 \times \dots \times \alpha_n$. But for the others - where do their ...
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2answers
36 views

What is the difference between Mapping and Morphism

I wonder if there's differences between Mapping and Morphism. Although the terms are used in different context i.e. mapping for set theory and morphism for category theory, from my understanding they ...
2
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1answer
53 views

What is the difference between an adapted process and a predictable process?

As the footnote on page 1 of this document mentions, even most experts in the field of stochastic processes don't seem to know rigorously what the difference is. However, since I don't have any idea ...
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2answers
308 views

Is it bad to call series a generalization of sum?

In a recent question I asked why series has a name separate from that of sum, and the general answer was that a series does not have the nice properties of sum. Does this mean it is bad to call series ...
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3answers
1k views

Why is it called a series?

Why did we make a new name for infinite sum? Was something wrong with calling it an infinite sum, or is it highlighting a difference between finite and infinite?
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0answers
39 views

Is there a name for this measure?

For any given set $X$, define a measure $u$ on $\wp(X)$ where for all $A \in\wp( X)$: $$u(A)=0\text{ if }A\text{ is countable, and }u(A)=\infty\text{ otherwise}$$
1
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1answer
32 views

Name of a family of Coxeter groups

From the following image I know that the first of group is the symmetric group of rank $n$ and the second is known as the Hyperoctahedral group. I want to know if someone knows the name of the ...
0
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1answer
51 views

What is the meaning of (resp. closed) in set theory?

I'm sure this a spectacularly basic question but I can't seem to find the definition of this anywhere. Here's some context: If $U$ and $V$ are open (resp. closed) then $U\cup V$ is open (resp. $...
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1answer
37 views

Terminology: If $A, B$ are subspaces of $V$ and $A \cap B = \{0\}$ then they are …?

If $A, B$ are subspaces of $V$ and $A \cap B = \{0\}$ then ... If $V = A \oplus B$ they are complementary, otherwise I think that Halmos describes them as disjoint but this seems at odds with the ...
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0answers
43 views

The notation of 'greater than or equal to'.

I've known that the following marks are equal. However, both marks are used in the same book. I was wondering whether there is some difference between them.
12
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1answer
113 views

Why is the Topology of a Graph called a “Topology”?

The topology of a graph (i.e. a network topology), as far as I can tell, doesn't actually have anything to do with open or closed sets, nor does it have any consistent, rigorous definition in practice....
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0answers
17 views

What is the name of function, which codomain is a given set?

Is there a special short term for any function $F$ from the family of functions $F(A)$ for the given set $A$ so that $A$ is the codomain of any function $F \in F(A)$? For example, suppose we ...
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0answers
29 views

Why we name one side as the perpendicular of an angle but does not actually define it?

If I have a right angled triange: $\qquad \qquad \qquad \qquad$ I was wondering why we name the sides like this? The base of $A$ kind of make sense. But the perpendicular of $A$ what relation does it ...
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1answer
19 views

Definition of vertex-cut for digraph?

I am trying to understand vertex cut for digraph. I could find this for graphs Vertex cut is a vertex whose removal increases the number of components in a graph. (D67, Handbook of Graph Theory by ...
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1answer
80 views

What do you call such an object?

I would like to know if there is a name for an object $X$ in a (finitely complete and cocomplete) category $\mathcal{C}$ which has the following property: $X$ is non-empty and for every sub-object ...
2
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1answer
32 views

Definition of component for a digraph?

I could find this in Wikipedia Component: A connected component of a graph is a maximal connected subgraph. The term is also used for maximal subgraphs or subsets of a graph's vertices that have ...
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0answers
11 views

K-wise identical marginal distributions

Suppose I have two joint distributions described by the two sequences of random variables,$X_1, \ldots, X_n$; $Y_1, \ldots, Y_n$. Is there a name/theory/reference for when these two distributions ...
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3answers
86 views

What is the reason for naming a function odd or even [duplicate]

We say that a function is called odd if $$f(-x)=-f(x)\\ (1)$$ and a function is called even if $$f(-x)=f(x)\\\\\\ (2)$$ But why do we call them odd and even. It feels a very peculiar choice of ...