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

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Are these correct extension of injective and surjective functions?

Recall the definition of injective and surjective functions: 1.a A function $f: X \to Y$, is injective if for all $a,b \in X$, if $a \neq b$, then $f(a) \neq f(b)$ 1.b A function $f: X \to Y$,...
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22 views

Subgraph with “dangling edges”?

I was wondering if there is a notion in graph theory where one can have a subgraph such that the endpoints of all of the edges in the subgraph are not necessarily included in the vertex set of the ...
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2answers
31 views

Is Reliability Component a vertex?

The term component has a distinct definition in graph theory from vertex while the terms components and vertices can be mostly the same in Realiability Engineering, my intuition. So how is the term ...
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39 views

Does the “Leibniz multicategory over $R$” have an accepted name?

Let $R$ denote a commutative ring. Definition. The "Leibniz multicategory" over $R$ is given as follows: Objects. $R[D]$-modules (where $D$ is a formal symbol; an 'indeterminate'). ...
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1answer
58 views

How to predict the incidents of synchronization for multiple oscillations.

EDIT: I changed the title of this question and made this edit based on a conversation with a friend. While I am dealing with mechanical cams the plain fact is that what I have is an oscillation in ...
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2answers
41 views

What does the condition of $T_{3\frac{1}{2}}$ space mean exactly?

A topological space $(X,\mathcal{T})$ is said to be $T_{3\frac{1}{2}}$ if given $x \in X$, and a closed set $C \subset X$, $x \not \in C, \exists f:X \to [0,1]$ s.t. $f(x) = 0, f(C) = 1$ This ...
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4answers
242 views

Is $3+2=5$ a equation?

Problem: Is $3+2=5$ a equation ? Solution As we know that that $3+2$ is a arithmetic expression. So $3+2 = 5$ is a arithmetic equation. But my friend said that $3+2=5$ is not a equation as it ...
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1answer
20 views

Direct proportional - basic concept

Q : A stone is dropped from the top of a high tower. The distance it falls is proportional to the square of the time of fall. The stone falls 19.6 m after 2 seconds, how far does it fall after 3 ...
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1answer
29 views

Term for sum, difference, product, quotient

Feel free to let me know if this is better suited for: https://english.stackexchange.com/ https://stackoverflow.com/ That said, I'm wondering if there's a math term for the nature of "sum", "...
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12 views

What is name of structures composed of a domain set, a function and a range set?

What is name of structures composed of a domain set, a function and a range set? Are such structures fall under a subject besides set theory or function theory?
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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 ...
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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 ...
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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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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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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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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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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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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 ...
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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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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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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 ...
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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
34 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
565 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 ...
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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
40 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 ...
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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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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 ...
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1answer
54 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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309 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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39 views

Is there a name for this measure?

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