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

learn more… | top users | synonyms (2)

0
votes
0answers
12 views

Is there a notation for saying that a function is defined on some subset of a set?

Let $X,Y$ be sets and let $f$ assign to every $x \in X$ some unique $y \in Y$. Then we may write $f: X \to Y$. This notation has the advantage that $f(X)$ need not be $Y$ but must be "within" $Y$. But ...
2
votes
1answer
16 views

How strong is the operator norm topology?

Let $(V,\tau_V), (W,\tau_W)$ be normable topological vector spaces. Let $||\cdot||_V, ||\cdot||_W$ be norms on $V,W$ inducing $\tau_V, \tau_W$ respectively. Let $||\cdot||_{op}$ be the operator norm ...
3
votes
2answers
45 views

Why is it called linearly independent?

For a system of linear equations in $\Bbb R^n$ to be linearly independent, there must be a unique solution to the system (at least I'm pretty sure that's true). There are definitely other definitions, ...
0
votes
1answer
36 views

Does the term “Proportional” have different meanings?

I have recently been confused by the term "Proportional". This started when I came across 2 different websites that seem to contradict one another when it comes to $y = x^2$. The first implies that ...
2
votes
1answer
20 views

Notation for the set of the subgroups of a group?

Given a group $G$, is there a "standard notation" to denote the set of the subgroups of $G$?
0
votes
0answers
41 views

If d/dx is an operation in functions, why do we need f(x)? [on hold]

This might be a little pedantic, but I need to sort out my terminology. Point 1:When mathematicians think of a function, they think of a mapping: $f:x \mapsto f(x)$. $f$ is a function that maps a ...
3
votes
1answer
17 views

Type of relation (between relations)

Is there a word for the type of relation $R$ and $S$ are with respect to each other, if $xRy \iff ySx$? Reciprocal relations?
3
votes
1answer
35 views

What would a 300% decrease in something actually mean?

I was looking at a site search product and one of the testimonials was 300% drop in "no results" searches What would this manifest as ? All I can come up with ...
2
votes
0answers
34 views

How do we address a function whose values are again functions?

One may call a function whose values are functions simply a function-valued function. But is there a canonical name for such an object? A $k$-form on some open $A \subset \mathbb{R}^{n}$ is an ...
0
votes
2answers
34 views

Terminology for complex numbers

Let $c=x+iy$ be a complex number (with $x\ne0, y\ne0$). Then $x-iy$ is the conjugate of this number. Is there any term (or use) for the number $-x+iy$?
1
vote
1answer
15 views

What does it mean when someone say “as long as a value (say x) is linear in another value (say n)”?

I was reading about bucket sort and then I came to the following statement: "As long as the input has the property that the sum of the squares of the bucket sizes is linear in total number of ...
3
votes
0answers
56 views

Very special geometric shape (No name yet?)

I suppose this geometric shape is something very 'special'. I cannot clarify in short about being 'special', but I think this shape stands together with such special shapes like square and hexagon. ...
10
votes
4answers
1k views

Why is it necessary for a ring to have multiplicative identity?

I have read earlier that in a ring $(R,+,.)$ the following needs to hold: $(R,+)$ is an abelian group multiplication is associative and closed left and right distribution laws hold. However, I ...
1
vote
1answer
24 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 $(v_{1},\cdots, v_{k}) \mapsto (T(v_{1}), \cdots, T(v_{k})): V^{k} \to W^{k}$?
0
votes
2answers
18 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
votes
0answers
14 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 ...
0
votes
2answers
24 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 ...
0
votes
2answers
17 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 ...
1
vote
0answers
54 views

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

First, a convention: given an abelian group $X$, write $\mathrm{End}_{\mathbf{Ab}}(X)$ for the set of all group homomorphisms $$X \rightarrow X.$$ Now let $R$ denote a ring. Question. Given an ...
0
votes
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 ...
7
votes
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 ...
0
votes
0answers
31 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 (, ...
0
votes
3answers
90 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 ...
0
votes
0answers
19 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 ...
0
votes
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
vote
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 $f$ ...
4
votes
2answers
223 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 $f$ ...
0
votes
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
votes
1answer
42 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
votes
3answers
142 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 ...
0
votes
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
votes
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 ...
1
vote
1answer
23 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 ...
1
vote
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 ...
3
votes
0answers
74 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 ...
0
votes
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 ...
0
votes
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 ...
3
votes
0answers
51 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
vote
1answer
47 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
votes
1answer
44 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
vote
2answers
60 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 ...
1
vote
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
votes
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
vote
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
votes
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
votes
6answers
178 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
vote
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
votes
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 ...