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

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0answers
148 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 ...
1
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0answers
31 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
38 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 ...
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1answer
70 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
43 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 ...
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1answer
39 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 $r$ ...
8
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2answers
247 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 ...
1
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2answers
2k 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 ...
1
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1answer
49 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
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1answer
94 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
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1answer
38 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, $|l_i| \le |k_i| \forall i \in \{1,2,3,...N\}$. ...
5
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0answers
108 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
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2answers
40 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 ...
1
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1answer
65 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
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0answers
180 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
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1answer
48 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 ...
9
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2answers
528 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. ...
1
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2answers
54 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
48 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 ...
0
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1answer
41 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?
1
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1answer
16 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
61 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 ...
2
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1answer
41 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
86 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. ...
0
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1answer
26 views

Terminology: 'pointwise monotone functional'?

I have a set $\mathcal{F}$ of real-valued functions, $$f_i(\cdot):\mathbb{R}\to\mathbb{R} \, ,$$ and a (linear) functional $T$ defined on $\mathcal{F}$, $$T:f_i \mapsto T[f_i] \in \mathbb{R} \, ,$$ ...
0
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1answer
41 views

What is the name of this property of relation?

What is the name of property of a binary relation $R$ that states that $\lnot(a\mathrel{R} b) \iff \lnot(b \mathrel{R} a)$ for all $a, b$?
3
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2answers
85 views

Is calling a linear-equation a linear-function, misnomer or completely wrong?

From my college life, I remember many professors used to call a linear-equation a linear-function, however: A standard definition of linear function (or linear map) is: $$f(x+y)=f(x)+f(y),$$ ...
4
votes
1answer
117 views

What is the mathamatical term for this programming concept?

In python's itertools, there is a function called permutations. It returns the number of ways to arrange x number of variables into a given space. For example, ...
2
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1answer
24 views

How is it called when you apply min / max seperatly to each dimension?

I want to do the following: $$\begin{pmatrix}3\\1\\4\\1\end{pmatrix} = \min( \begin{pmatrix}4\\4\\4\\4\end{pmatrix}, \begin{pmatrix}3\\1\\4\\10000\end{pmatrix}, ...
1
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0answers
22 views

A standard terminology for different definitions of complete sublattice

Let $(X,\le)$ be a complete lattice and $A\subseteq X$. I'm trying to find a standard terminology for special types of sublattice. What is $A$ called if $(A,\le_A)$ is a complete lattice. ...
0
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1answer
76 views

generators vs basis of an algebra

Are all bases of an algebra generating sets, but all generating sets are not bases? A basis can only use addition and scalar multiplication to generate an algebra, which means it is a generating ...
0
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0answers
37 views

What's the name of $\sum_{k = 0}^{n} (-1)^k {n \choose k} (n-k)^w$?

I worked out the following expression as the number of all possible "words" consisting of exactly $w$ letters from an alphabet $L$ of size $\left|L\right| = n \leq w$, and containing each of these $n$ ...
1
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1answer
36 views

Terminology for idempotents that commute with every other idempotent

Given a semigroup $S$, is there terminology for those $x \in S$ such that the following hold? $x$ is idempotent Given any idempotent $y \in S$, we have $xy=yx$. Comments. Let $E$ denote the set ...
5
votes
2answers
125 views

Usage of the term “Free”

What is the difference between free groups and free modules/vector/algebras spaces, or in other words what does free mean in algebra? I have seen two uses of the term free: something of ...
0
votes
1answer
232 views

Does “arbitrarily small” mean very close to zero or very negative?

In mathematical writing, does “arbitrarily small” mean very close to zero (like $0.000001$) or very negative (like $-1000000$)? Are there better phrases to distinguish these two cases?
4
votes
1answer
91 views

Is there a name for the property of a function f such that $f(x,y)=f(y,x)$?

As in the title: is there a name for the property of a function such that $f(x,y)=f(y,x)$. I don't know how to be clearer than that. I tried to look for symmetric property on Google, but without any ...
4
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1answer
142 views

Why are normal subgroups called “Normal”?

Why are normal subgroups called "Normal"? Who is credited with naming them, and why are they named such?
21
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6answers
3k views

Is there a name for the function $\max(x, 0)$?

Is there a name for the function $ \max(x, 0) $? For comparison, the function $ \max(x, -x) $ is known as the absolute value (or modulus) of x, and has its own notation $ |x| $
2
votes
0answers
63 views

What do you call a matrix where the rows sum to zero and the columns sum to zero?

What do you call a matrix where the rows sum to zero and the columns sum to zero? Or is there no standard name for this type of matrix?
0
votes
0answers
42 views

Is a set of some $m \times n$ matrices a relation?

A relation between sets $A_i, i = 1, \dots, n$ is defined as a subset of $\prod_i A_i$. Given $m, n \in \mathbb N$, is a set of (some or all) $m \times n$ matrices over $\mathbb R$ considered a ...
0
votes
1answer
72 views

Is there a name for continuous functions $\Omega \rightarrow \mathbb{R}$ that can be continuously extended to $\overline{\Omega}$?

Given topological spaces $X$ and $Y$ together with a subset $\Omega \subseteq X$, is there a name for those continuous functions $f : \Omega \rightarrow Y$ such that $f$ can be extended to a ...
0
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1answer
48 views

Is there a name for sum over one set divided by the cardinality of another set?

What is the summation of one set real numbers divided by the cardinality of another set called? $$A \subset\mathbb R$$ $$\frac{\sum A}{|B|}$$ I will try and be specific to my problem because I lack ...
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1answer
33 views

Is there a technical term for a 'complementing' number that sums to 1?

I'm looking for a technical name (if one exists) for a number that 'completes' or 'complements' another. The motivation for this is to develop a proper understanding of mathematical language, for ...
0
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1answer
69 views

Is there a name for this variant on “continuous function”?

Let $X$ and $Y$ denote topological spaces. Then a function $f : X \rightarrow Y$ is said to be continuous iff for all $U \in \mathcal{P}(Y)$, it holds that if $U$ is open in $Y$, then $f^{-1}(U)$ is ...
2
votes
1answer
90 views

What does it mean for a function to be uniquely determined by another function?

In munkres topology, I went through an exercise which asks me to show that a function is uniquely determined by another function. I wonder, What does this mean? I googled it but No answer! Here is ...
5
votes
3answers
133 views

Is $x^x$ a polynomial, an exponential or both?

If $c$ is a constant, and $x$ is a variable, we'd say that $f(x) = x^c$ is a polynomial function of order $c$. Conversely, the function $f(x) = c^x$ would be called an exponential function. Is there ...
1
vote
0answers
85 views

What is even meant by the “cardinality of a model?”

Please help me understand even the most basic ideas in model theory: When in model theory we speak of the cardinality of a model, what exactly is meant by that? I assume that when we say that the ...
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2answers
524 views

Names of 3 input logic gates

I've tried to look this up online, I may have used the wrong terminology. This question is about the names of logic gates with three boolean inputs, and one boolean output. This is a truth table for ...