# Tagged Questions

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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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'...