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

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1answer
19 views

Notation and name for this function?

Let $k \geq 1$; let $V,W$ be vector spaces; and let $T: V \to W$ be linear. Then how do we call and denote the function $(v_{1},\cdots, v_{k}) \mapsto (T(v_{1}), \cdots, T(v_{k})): V^{k} \to W^{k}$?
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2answers
16 views

if n is a positive integer let Z be the subset of integer in {1,…,n} which are relatively prime to n

if n is a positive integer let Z be the subset of integer in {1,...,n} which are relatively prime to n my effort to solve this question I''m confused and need help to solve this question please ...
2
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0answers
13 views

What is the purpose of continuous and differentiable dependence

In learning Gronwall's inequality you also get to learn about continuous an differentiable dependence. I know the theorems but I have no idea about their application. What is the big idea of ...
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2answers
21 views

a bijection is an injective (one-to-one) , surjective (onto) map between sets. if S = (0, 1) and T =R, find a map from S to T which is

a bijection is an injective (one-to-one) , surjective (onto) map between sets. if S = (0, 1) and T =R, find a map from S to T which is my effort 1) (a) f(x) = x is a one to one function but it ...
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2answers
16 views

What does a left-continuous version of a function mean?

I'm reading Extreme Value Theory: An Introduction by Laurens de Haan and Ana Ferreira. I've had some trouble following the way they throw around concepts, but this is something I'm really having hard ...
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0answers
39 views

What do we call the function $R \rightarrow \mathrm{End}_{\mathbf{Set}}(X)$ associated with an $R$-module $X$?

First, a convention: given a mathematical structure $X$, write $\mathrm{End}_{\mathbf{Set}}(X)$ for the set of all functions $$X \rightarrow X.$$ Now let $R$ denote a ring. Question. Given an ...
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0answers
24 views

If $A: M \to M$ then $M$ is $A$-invariant subspace and $A $ is an endomorphism?

Just straightening out the terminologies here... Given If $A: M \to M$ then $M$, $M$ some subspace of a vector space, is the following statement equivalent: $M$ is a $A$-invariant subspace $A $is ...
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7answers
1k views

Right English wording for “counterexamples to a theorem”

This question is about the right English wording. I give here what I call "counterexamples to Banach fixed-point theorem". What I do, is that I look to what happen if some hypothesis of the theorem ...
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0answers
28 views

What is (if there is) the generic term for equalities and inequalities

I'm writing a text about a particular linear programming (LP)I optimization problem, that is described using a mixture of inequalities (, ...
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3answers
89 views

Is this called an identity?

Identity is an equation which is true regardless of what values are substituted for any variables (if there are any variables at all). The question is: $$\frac{x^2-a^2}{x-a}=x+a$$ Is this an ...
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0answers
18 views

*Solved* Terminology in DE, difference between Particular and Actual solution

Yesterday I started studying and preparing for a course in Differential Equations and today I came across something that confuses me; I watched a lecture on IVP and they used both Actual solution and ...
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1answer
21 views

Terminology - “Sample space” vs “sample set”?

Given that a "sample space" is defined as the set of possible outcomes of a given random experiment, is there a fundamental reason to use the term "sample space" instead of "sample set" in probability ...
1
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1answer
31 views

How do we call a pair of sets $A,B$ such that there is some injection $f: A \to B$?

Let $A,B$ be sets and let $f: A \to B$. If $f$ is a surjection, then we may simply write $f(A) = B$ or say in a more laborious way that $f$ maps $A$ onto $B$, to mean the same thing. However, if $f$ ...
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2answers
221 views

How do we call a pair of sets between which there is a bijection that need not have additional property?

Let $A,B$ be sets and let $f: A \to B$. Then we say that $A,B$ are isomorphic under $f$ if $f$ is a linear function that maps $A$ onto $B$ in a one-to-one manner; that $A,B$ are homeomorphic under $f$ ...
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0answers
6 views

tree symmetric across middle edge, all the way down

I came upon a tree which is symmetric across a middle edge in the sense that it is bicentral and removing the middle edge leaves two identical halves, and then the half in turn has the same "symmetric ...
5
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1answer
40 views

Does it matter if you use big $L$ or little $l$ when talking about $L$-norms?

I was reading a post on Quora regarding the application of "$l_1$", "$l_2$" norms for convex linear programming when I became very confused at which $L$-norm the posters are actually referring to. I ...
2
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3answers
141 views

Is there a name for this type of expression?

Forgive me if this seems like a silly question. I know that the following expression is an example of a polynomial: $a_{4}x^{4}+a_{3}x^{3}+a_{2}x^{2}+a_{1}x+a_{0}$ but I am wondering if there is a ...
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2answers
25 views

How to symbolize impossible discrete logarithm?

the task is 2^k mod 14 = 12 The output is a cycle of 4, 8 and 2 making this impossible. What is the correct symbol to claim task an impossibility/invalid? 2^k mod 14 ≠12 is the best ...
0
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1answer
36 views

Is there a name for operators of the type $A: M \to M$

In some theorem in functional analysis I have noticed that it is important to assume that an operator $A: M \to M$ where $M$ is some set plus conditions, as opposed to $A: M \to N, M \neq N$ Is ...
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1answer
21 views

Can someone please help me understand what a “player set” is in extensive form game

my text defines player set as: In N-player game $g$, each non-terminating node is partitioned into $N+1$ sets $g^0, ... g^N$. These are player sets. However it makes no attempt to identify ...
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0answers
21 views

“Second kind” orthogonal polynomials and functions

Recently I've been doing reading in the subject of orthogonal polynomials on the real line (OPRL). Such OPs arise in solving the three-term recurrence relation $$x ...
2
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0answers
64 views
+50

What do we call collections of subsets of a monoid that satisfy these axioms?

Consider a monoid $M$ and a semiring $S$. Then there's an $S$-algebra freely generated by the monoid $M$, which can be described explicitly as the set of all finitely supported functions $S \leftarrow ...
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0answers
21 views

“Asymptotic” $\mathbb{R}$-algebras

Definition. By an asymptotic $\mathbb{R}$-algebra, I mean an $\mathbb{R}$-algebra $F$ of functions $\mathbb{R} \rightarrow \mathbb{R}$ satisfying: $$\mathop{\forall}_{f:F}\left[\left(\lim_{x ...
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0answers
28 views

hyper, super and meta. Meaning vs emphasis?

Various mathematical terms use the following prefixes, which are presumably also morphemes: hyper super meta These have different dictionary definitions, as I ...
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0answers
44 views
+50

What do we call the result of wedging together the columns of a matrix?

We can wedge together the columns of a square matrix to compute its determinant. More generally, the exterior product of the columns of a $b \times a$ matrix tells us the determinant of each $a \times ...
1
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1answer
46 views

What do you call a space whose only compact sets are finite? [duplicate]

What do you call a topological space where a subset is compact iff it's finite? Is there a technical name? For example, take the discrete topology, or the countable complement topology.
0
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1answer
43 views

Difference between a proposition and an assertion

It may be a silly doubt, but let me ask this. What is the difference between a proposition and an assertion? I know there's a very thin line between the two terminologies, but I'm unable to get ...
0
votes
2answers
57 views

A map that's 1-1 but not onto

I've got some confusion about the definition of a 1-1 map. When I searched for "1-1 correspondence" on Wikipedia, I got redirected to the "bijection" page. So I think the two words mean just the ...
1
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2answers
58 views

Why is it called a “multiset”?

According to Wolfram MathWorld, "A set is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored ..." and A multiset is "A ...
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0answers
18 views

Is there a name for a 2-dimensional dumbbell like shape?

Is there a mathematical name for a 2-dimensional shape in the general form of a dumbbell? That is two circular nodes connected by a center beam such as shown in this image from this answer. It could ...
0
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1answer
36 views

Control Theory: Why is $A+BK$ called a closed loop system?

Given a control system $\dot x = Ax + Bu$ and $y = Cx$. Suppose we use state feedback to create $u = +Kx$ where $K$ is the gain matrix. Subbing into above equation, we have $\dot x = Ax + Bu = Ax + ...
1
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2answers
43 views

vertical asymptote - is it possible to have one like this?

If my function is defined for $x > 2$ and the question asks for vertical asymptotes, do I need to write $x = 2$ as an answer? Or no?
-1
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0answers
12 views

I think cross sort is a statistical term

What does cross sort mean? Is it sorting the values in columns as well as values in rows.
8
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6answers
175 views

What does $200\%$ faster mean? (How can something be more than $100\%$ faster?)

I'm a simple man living my every day life and have not much understanding of math or science. Today I read an article where someone claimed they can charge a battery $200\%$ faster. This got me ...
1
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1answer
32 views

Has anyone ever suggested a name or notation for this operation on multisets?

A basic multiset identity says: $$A+B = (A \cap B) + (A \cup B)$$ Allowing ourselves to use negative multiplicities and rearranging: $$A-(A \cap B) = (A \cup B)-B$$ But since $A \supseteq (A \cap ...
0
votes
1answer
113 views

Is there a term in graph theory called 'GRAIL'?

I've been a talk with a PhD student about some graph issue and told me about GRAIL graph and have drawn it for me as you see in the picture, however, I try to generalize so-called "Grail graph" to ...
0
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1answer
19 views

Is there a name for a general upper triangular hollow matrix?

A hollow matrix is one with zero diagonal elements (according to this web page) Q1: Is there a name for an upper (or lower) triangular hollow matrix? Q2: Alternatively how might such an object be ...
1
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0answers
18 views

The subset of a set of vectors such the this subset has the points at most extreme values for all dimentions

Condiser $X\subset \mathbb{R}^n$ We can define some the set of per axis outermost points, on a per axis: $$Out(X) = \{ x \mid x \in X \: \wedge \: (\exists i\in[1,n], x_i=\underset{y\in ...
6
votes
1answer
99 views

What's the term for “the supremum of constants $\alpha$ such that a function is $\alpha$-Hölder continuous”?

The $\alpha$-Hölder norm of a function $f(x)\colon I \to X$ where $I=[0,T]$ and $X$ is some Banach space with norm $\|\cdot\|$ is: $$\|f(t)\|_{\alpha}\colon=\sup_{s \neq t \in ...
5
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0answers
123 views

Where does the term “mouse” (in set theory) come from?

Does the term mouse stand for "Model Of Universe with Sequences of Extenders" or perhaps mice stands for "Model Including Cardinal Extensions"? A quick review: Gödel's L-universe is a core model ...
2
votes
2answers
121 views

What is the difference between a subgroup and semigroup?

In my text it says $\{e^{i\theta}:\theta\in\mathbb{R}\}$ is a subgroup but it did not clarify the subgroup of which group. Furthermore I remember this entire set as being a semigroup, is there a ...
24
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6answers
3k views

The logarithm is non-linear! Or isn't it?

The logarithm is non-linear Almost unexceptionally, I hear people say that the logarithm was a non-linear function. If asked to prove this, they often do simething like this: $$\ln(x + y) \neq ...
2
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2answers
66 views

L'Hôpital or L'Hospital? [duplicate]

This may be a stupid question but I just want clarification about the use of the name of this rule. Well, most of the time what I see is L'Hospital's Rule, like in Baby Rudin and many other places. ...
0
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6answers
57 views

What is the difference between operators, functions, sequences and vectors?

To me there is a hierarchy where vectors $\subset$ sequences $\subset$ functions $\subset$ operators All vectors are sequences, but not all sequences are vectors because sequences are infinite ...
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0answers
23 views

Is there a name for this function with properties…

Let $V$ be a vector space over an algebraic structure $\mathbb{A}$, and suppose we have a binary operation $\star:V^2\to V$. Consider a function $f:V\to \mathbb{A}$ with the property that $$f(x\star ...
5
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0answers
92 views

Notation/terminology for “independent” subspaces/subalgebras

Let $V$ denote a vector space (or any other kind of algebraic structure). Question. Letting $I$ denote a fixed set and $X$ denote an $I$-indexed family of subspaces (subalgebras) of $V$, is there ...
2
votes
1answer
69 views

What is $H^\infty$ norm and why is it used in control theory?

Can anyone knowledgable elaborate on what exactly is a $H^\infty$ norm and why it is used in control theory instead of some other norms? Thanks!
0
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2answers
39 views

Is there a word for the value of a complex number multiplied by its conjugate?

For a complex number $w$, or $a+bi$, is there a specific term for the value $w\overline{w}$, or $a^2+b^2$?
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3answers
71 views

What is the difference between the closure of a set and a closed set?

Is "closure" and "closed" interchangeable? Can a set be a closure of a set without being closed?
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1answer
44 views

Can a Constant Unknown Have a Coefficient?

I have found a lot of different definitions of coefficient, many of which limit coefficient to a constant multiplier of a variable. My confusion, though, is then teaching that every unknown has an ...