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

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Terminology for particular situations?

What might be the name for a situation where a Hermitian (complex) operator produces real values? Could it be inversion, or convolution or something of that sort? And can the reverse situation be ...
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2answers
19 views

Terminology - variant of a hypergraph

In a hypergraph, we have vertices $V$ and hyperedges $H$, where each hyperedge is a subset of $V$. Suppose that we would like the hyperedges to be (ordered) tuples, rather than subsets. Does this ...
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1answer
23 views

Does a graph of this type have a name?

Does a graph of this type have a name? When I say a "graph of this type" I mean where the scales on the axes aren't uniform all the way along.
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1answer
35 views

Is algebra over a set also algebra over a field?

During my studies I have come across two different notions of the term "algebra", namely algebra over a set and algebra over a field (the field its vector space always being Euclidean space in my ...
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4answers
277 views

What is linearity?

Once someone asked me the question "What is linearity?" in a proficiency exam. I went hot and cold all over. Although, I heard and even used the term linearity many many times, I had not really ...
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1answer
25 views

Need help to understand some terminology in discrete math

1) "Suppose that f is a function from set A to itself." 2) "(...)from the set of real numbers to itself." In these two sentences, what does "to itself" mean? Is this the same as saying that 1) is f: ...
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0answers
34 views

What's the right way to write big-O?

I always write $\mathcal{O}(n)$ (\mathcal{O}(n)). But I frequently see $O(n)$ (O(n)), probably because it's shorter and more ...
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0answers
21 views

“two sets differ” in vs by “exactly 1 element”, in both cases is symmetric implied?

When a mathematician says, "two sets differ in exactly 1 element", what precisely do they mean? Does, "two sets differ by exactly 1 element", mean something different? Given $ A = \{1,2,3\}, B = ...
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0answers
31 views

Terms for particular equivalence relation and partition?

Let $T$ be a set of sets. Let $\equiv$ be an equivalence relation on $\bigcup T$ defined by the formula $$a\equiv b \Leftrightarrow \forall X\in T:(a\in X\Leftrightarrow b\in X).$$ Let $S$ be a ...
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0answers
9 views

Term for “interval with a step size”

I'm looking for a term for "interval with a step size". Let's write such an "interval" as an interval-like tuple $I=[from, step, to]$. Then $I$ is defined as $I=\{x|x=from+n \cdot step, n \in ...
4
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1answer
40 views

How to call a shape (2D or 3D) that has no dents in it?

Is there a name for a shape that has no dents in it? The shape can exist in 2D or 3D space. It is best demonstrated with a picture: On the left is a shape that has no dents in it, and on the right ...
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1answer
40 views

What's the terminology for whether a number is positive or negative?

Is there a word for the quality of a number to be either positive or negative? Consider this question: What's the ... (sign/positivity/negativity, but a word that could describe either) of number x? ...
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2answers
51 views

Terminology for $1/(e^x+1)$?

$ \frac{1}{e^x+1} $ and $ \frac{e^x}{e^x+1} $ Just wonder if either of the above function has a term/name associated with it? Or they are just functions that look beautiful without names? Maybe they ...
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0answers
10 views

Is “nonanticipating” a measurability property of a function or something more?

I have been reading some operations research papers that throw in the term "nonanticipating" at key points in the exposition, but I can't figure out precisely what they mean. My best guess is that ...
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0answers
43 views

Why are centers, centralizers and normalizers called that way?

I know what they are, but where do the names come from?
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0answers
104 views

Have these (extremely simple) classes of algebraic structures been considered in the literature? If so, what are they called?

Questions. Have the following kinds algebraic structures been considered in the abstract algebra literature etc.? If so, what are they really called? (I have used made-up terminology for the sake ...
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1answer
18 views

Is this ODE linear?

Determine whether the given first order differential equation is linear in the following variables: $(y^2-1)dx+xdy=0$; in x and y I'm pretty confused here. I've seen $\frac{dy}{dx}$ but what do $dy$ ...
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1answer
40 views

Is this an ordinary differential equation?

If a differential equation contains only ordinary derivatives of one or more functions with respect to a single independent variable it is said to be an ordinary differential equation (ODE). If ...
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0answers
24 views

For every pair of vertexes there is at most one path

A directed graph such that for every pair $(A;B)$ of vertexes there is at most one path from $A$ to $B$, is there are name for this concept? @Ishfaaq: Your answer is wrong, see such a digraph which ...
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0answers
34 views

In linear algebra, what is the word used to state that two linear equations are the same line?

If we have to solve a system of linear equations with two linear equations. What is it called if both of these two lines are the same? I.e. the first line is $x+y=1$ and the second line is ...
0
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1answer
13 views

Signal “representation” terminology

A paper I'm reading now defines invariant signal "representations" as those functions $\Phi$ of signals $x$ in a Hilbert space such that $\Phi(g\cdot x) = \Phi(x)$ where $g\cdot x$ is the action of ...
0
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1answer
26 views

The proper term to describe a category of geometric shapes.

I'm looking for geometric terminology that would describe this kind of shape, if there is a term for it. Picture any arbitrary closed 2D shape. Picture the smallest circle that will completely contain ...
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1answer
35 views

Definition Fixed Element

I am looking for the definition of a "fixed element". The context is "Let G be a group and let a be one fixed element of $G$. Show that $H_a = \{x \in G | xa=ax \}$ is a subgroup of $G$." Thanks.
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0answers
22 views

operator vs operation vs function vs procedure vs algorithm

I have a vague understanding of what operator, operation, function, procedure, algorithm mean in general. I am heavily biased towards computer science. Do you agree with them? What are the generally ...
2
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1answer
29 views

Is there a name for spaces that always have local sections?

Given a continuous map $p:E \rightarrow B$ Suppose for every point $b \in B$ and a point $x \in p^{-1}b$ in the fibre of it, there is an open set $V$ of $B$ that contains the point $b$ such that ...
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0answers
30 views

Eigenvalues that are functions

Let us have the Laplacian on a compact manifold $M$. Suppose I have some equation of the form $$-\Delta u(x) = f(x)u(x).$$ If $f \equiv c$ were a constant, this would be an eigenvalue problem ...
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0answers
20 views

The space of alternating multilinear forms

I was just wondering if there is a standard (or even just usual) notation for the space of alternating $k$-linear forms on an $F$-vector space. I know that this space is naturally isomorphic to the ...
0
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1answer
16 views

Number of variables and dimension of a function

Why is a function $f(x)$ called a single-variable function if it has coordinates represented by $x$ and $y$? Can it be called a 1D function if its plot is 2D? Subsequently, can two-variable functions ...
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4answers
3k views

Why is an image called an “image”?

Given a function $f : A \to B$, the image, denoted by $\operatorname{Im}f$ is the set of all $f(x)$ where $x \in A$. Why do we call this set the image? When was it first used, and what motivated its ...
2
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1answer
39 views

Definition of a certain matrix

I remember I came across matrix of the form $$\begin{bmatrix} 1 & 0 & 0 & 0\\ 1 & 1 & 0 & 0\\ 0 & 1 & 1 & 0\\ 0 & 0 & 1 & 1\\ \end{bmatrix}$$ There ...
1
vote
1answer
29 views

Defining a ball

Which are appropriate phrases to define a ball? Let $B$ be the open ball of radius $r$ centered at $x$. Let $B$ be the open ball of radius $r$ around $x$. Let $B$ be the open ball of radius $r$ ...
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2answers
162 views

Why should the generalization of a 'sequence' be called a 'net'?

The title says it all, really. Reading through Reed & Simon's book on functional analysis, I have now reached the chapter on topological spaces, and the notion of a net is introduced there to ...
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2answers
100 views

Definition of “contradiction” and use of the term for “⊥”

If one looks in Internet for definition of “contradiction” (including respective words in other languages), one finds a mess. See for example this index of Wikipedia articles in various languages. The ...
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1answer
28 views

Is a linear transformation just a mathematical description of a straight line?

On Physics Stack Exchange, the question was asked: Are lorentz transformations linear? The up-votes given to an answer seemed to be in proportion to how mathematically sophisticated it was, with mine ...
8
votes
1answer
84 views

Is the definition of stabilizer given at Planet Math really the currently accepted definition among group theorists?

According to Planet Math, given a group $G$ a set $X$ a subset $S \subseteq X$ and a group action $G \times X \rightarrow X,$ then the stabilizer of $S$ is define to be: $\{g \in G \mid gS ...
1
vote
1answer
32 views

A question on the rectangular region defined for a vector in $\mathbb{R}^N$

Let $K = (k_1,k_2,k_3,...k_N)$ be a vector in $\mathbb{R}^N$, consider the region $S_K$ consisting of all vectors $L = (l_1,l_2,l_3,...l_N)$ such that, $|l_i| \le |k_i| \forall i \in \{1,2,3,...N\}$. ...
4
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0answers
84 views

Is there a name for graphs with the following property?

The property of the graph is the following: For any vertex, there is a hamiltonian path starting with this vertex, but the graph is not hamiltonian. The following graph is a small example: ...
2
votes
2answers
30 views

Is there another term for “complete closure”?

I want to describe a function $f$ which, on set $S$, satisfies these properties: $$ \forall x\in S.f\ x\in S \\ \forall y\in S.\exists x\in S.f\ x=y $$ One example is the successor function upon ...
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0answers
46 views

Has this partition a name?

The decomposition in disjoint cycles in $S_n$ was inspiring for this question. I found out (if I did nothing wrong) that more generally a bijection $f:X\rightarrow X$ induces a partition of $X$ ...
1
vote
1answer
31 views

What is the numeral system which uses the number of digits as a signifier of value called?

Our standard notation of representing numbers has an implied infinite number of zero digits on the left of all numbers. 42, 042 and 00000000042 all represent the same number. I'm thinking of the ...
2
votes
0answers
38 views

Directed multigraph with numbered edges

Let we have a directed multigraph such that or every its vertex the set of edges from this vertex is finite and ordered (in other words, numbered $1,\dots,n$). I need this construct to describe ...
1
vote
1answer
40 views

“Broken-line paths” in $\mathbb R^n - \{ 0 \}$

In Munkres's Topology, he says: Suppose $x$ and $y$ are two different points from zero of the punctured euclidean space $\mathbb{R}^n -\{0\}$. We can join them a path by the straight-line path ...
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2answers
355 views

What is the history behind the development of the term “coefficient”? [closed]

Why are coefficients called "coefficients"? For example I learned that squaring a number is called "squaring" because it actually refers to "making a square". That's how it was developed. ...
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2answers
44 views

How to say the angle modulo $2\pi$

For any number $x$, there exists a unique number $y$ such that the difference $y-x$ is a integral multiple of the number $2\pi$, and that $y\in[0,2\pi)$. Is there a single word or a single wording to ...
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0answers
36 views

Building a function $p : \mathcal{D} \rightarrow \mathbf{Ord}$ from a faithful functor $U : \mathcal{C} \rightarrow \mathcal{D}.$

For simplicity, I will ignore size issues in this question. Let $\mathcal{D}$ and $\mathcal{O}$ denote categories. By a function $\mathcal{D} \rightarrow \mathcal{O},$ let us mean a functor from the ...
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1answer
36 views

Vectors-Can anyone explain me the concept of sense in vectors?

Is it same as the direction? Then, why another term "sense"is used, instead of direction? Can anyone illustrate it?
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1answer
12 views

Terminology for a set of functions formed from a basic set of functions and all their compositions?

Let suppose I have a set $A$ and a set of functions $S$ from $A$ to itself. I can define a new set $S*$ that, intuitively, is the set of all functions formed by composing zero or more copies of ...
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0answers
47 views

Fountain code and online code

Are fountain code and online code the same? It seems to me they have the same property, which is used in lossy channel and generate unlimited encoded block. If they are the same, then what encoding ...
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1answer
18 views

Collective term for interpolation and extrapolation

Is there a collective term for both interpolation and extrapolation? If there is such a term, what is it?
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1answer
41 views

What is a “closed subspace” of a topological space?

I was reading a proof online and it linked to a book by Munkres which says Every closed subspace of a compact space is compact. I dug out the book and searched the index for this term. ...