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

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1answer
26 views

Non-measurable sets and sigma-algebra definition

I´m starting to study about measure theory, but I have problems regarding the definition of measure space. In my class we saw that there exists sets that are not measurable(Vitali sets in $\mathbb ...
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0answers
10 views

How do you call the curve described by this equation: $A e^{-\frac{{(x-\mu)}^2}{2\sigma^2}} + C$ ? And how do you call the parameter $C$?

How do you call a curve described by this equation: $$A e^{-\frac{{(x-\mu)}^2}{2\sigma^2}} + C.$$ It looks like a gaussian, but it's not exactly a gaussian. And how do you call the parameter $C$? ...
2
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4answers
60 views

Is there in literature a descriptive abbreviation phrase for “for infinitely many $n$”?

Let $P(n)$ be a property for all $n \geq 1$. For the phrase "there is some $N \geq 1$ such that $P(n)$ holds for all $n \geq N$" there are some suggestive, convenient abbreviations such as "$P(n)$ ...
0
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1answer
32 views

Correctly quoting a Hamilton Circuit

This might come across as a slightly petty question. Apologies for this, I am only asking as I have an exam on Graph Theory soon and want to make sure I do things correctly. The definition of a ...
0
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1answer
23 views

What is the correct term for the “major axis” of an oblong?

Suppose you have an oblong, with a line extending across its length. The line begins and ends at the midpoints of the shorter sides. What is the correct term for this line? Major axis seems to be ...
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1answer
20 views

Integrand of a definite integral

If we have an integral $\int_A f(x)dx$, or what I am more specifically interested in, $\int_A fd\mu$ where $\mu$ is a measure, is the integrand $f$ or is it $f$ on the domain $A$, where A is some set ...
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0answers
45 views

Is there a name for this closure (boundary, interior) operator on sets of sets

Sorry, I couldn't find anything and without proper names it's even harder. It sounds like something reasonably simple to consider and name though. Given a set of sets $\bf S$, we define some kind of ...
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1answer
46 views

Is it typically assumed that functions are bijective?

That is, if I'm reading a textbook, or perhaps even lecture notes, and there are theorems or definitions regarding functions, is it typically assumed that functions are bijective or if nothing is ...
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0answers
36 views

Does a plane curve with polar equation $r=\lambda_1\cos^2\theta+\lambda_2\sin^2\theta$ have a name?

Does a plane curve with polar equation $$r=\lambda_1\cos^2\theta+\lambda_2\sin^2\theta$$ where both $\lambda_i>0$ have a name? It's very similar to hippopede, also known as lemniscate of Booth, ...
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1answer
27 views

Definition: honest distance function

What does honest distance function mean? In the context of metric spaces.
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3answers
55 views

Is there a name for $2^n$ in combinatorics?

$2^n$, with $n$ corresponding to the number of elements, is an almost unavoidable calculation involved in counting. At the root of its usefulness there lies - I presume - the identity: ...
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0answers
75 views

What is the name of this binary operation on vectors?

What is the name of this operation $\bigoplus$? Where does $2$ come from? $$\vec u \oplus \vec v = \begin{pmatrix}x\\y\end{pmatrix}\oplus \begin{pmatrix}s\\t\end{pmatrix} = ...
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1answer
26 views

“Proportional to” - but nonlinear.

If $A$ is proportional to $B$, then it means that $A$ varies with $B$ linearly (we're just not specifying the linear constant). Is there a similar notion for the case that $A$ increases as $B$ ...
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2answers
30 views

Can $\text{ arg}$ be thought of as operator?

Forgive me if the question is to vague. The argument, denoted by $\text{arg}$, is a commonly used notation. I am specifically interested in the following use of $\text{arg}$: \begin{align} a=\text{ ...
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2answers
239 views

What does “dual” mean exactly in mathematics?

I'm not a math expert but I know a little bit of calculus and theorems. I've heard things like "this result is "dual"", or this "...
0
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2answers
92 views

How is it possible that if I have $2$ choices and $1$ of them is taken away, I have $0$ choices? [closed]

I'm a simple man living his life and enjoying mathematics. Today while thinking about choices I realized this paradox: If I have $2$ choices and $1$ of them is taken away, I have $0$ choices. How is ...
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2answers
40 views

What does it mean when we say a sequence is ordered?

From wikipedia, we have the definition of a sequence to be "a sequence is an ordered collection of objects in which repetitions are allowed." But I don't understand the meaning of "ordered". For ...
5
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1answer
45 views

Is there a name for a monoid with a distinguished absorbing element?

Let $M = (M,·,1,0)$ be a monoid $(M,·,1)$ together with an distinguished absorbing element $0 ∈ M$, that is such that $∀x ∈ M\colon 0·x = 0 = x·0$. Does such a structure $M$ have a nice name? ...
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2answers
32 views

A question concerning mathematical nomenclature - formal and informal, rigorous and non-rigorous

I've never been quite sure of the exact meanings of the terms formal, informal, rigorous and non-rigorous in mathematics. For example, I've read a set of notes in which the author speaks of a ...
0
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3answers
31 views

Subtle difference between convex and strictly convex, why?

A function is convex if $f(\theta x + (1-\theta) y) \leq \theta f(x) + (1-\theta) f(y)$, $\theta \in [0,1]$ A function is strictly convex if $f(\theta x + (1-\theta) y) < \theta f(x) + ...
3
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3answers
77 views

Difference between “property” and “structure”

I sometimes hear that "$A$ is a property of $V$, not a structure." But I am not sure how to distinguish "property" from "structure" in general. Could you explain the difference with some easy ...
3
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2answers
46 views

What's the name of this basic formula

Is there a name for this formula $$ x^n -y^n = (x-y) \cdot \sum_{k=0}^{n-1} x^{n-1-k} \cdot y^k$$
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2answers
47 views

In German, what does “Skalarraum” mean?

Is it just that $\mathbb K$ is the Skalarraum of $\mathbb K^{m \times n}$, or does it have other applications also? From a Google search it would seem so, but I'd like to make sure, as none of the ...
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2answers
35 views

Point addition not Allowed

In what Structure point addition is not allowed and that makes points different from vectors.I mean in any Field or even Group i can add without problem but i have seen people saying point addition ...
0
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1answer
16 views

Terminology when referring to bias

I am confused about the way in which I should use the word "bias". Suppose that $r$ is the true value of a variable and $\hat{r}$ is an estimate for $r$. Let $a$ be an arbitrary real number. If ...
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0answers
43 views

In mathematics what does it mean “to occur naturally”?

In mathematics, I often meet the expression " 'x' occurs naturally", or " 'x' occurs naturally in 'Y' ". For example: "You should know why eigenvectors and eigenvalues occur naturally in linear ...
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2answers
30 views

Confusion between vector space, field and sets

From my understanding, a vector space is a set that is closed under addition and multiplication, so let $A$ denote a set, a vector space $V = (A, +, \times)$ But whenever you read the definition of ...
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1answer
28 views

Let $v,w$ be vectors of some vectorial space $V$. If $v=w$, are they said to be equivalent?

Of course two geometrical vectors are called equivalent if they have the same magnitude, direction and orientation. But what about a generic vectorial space? Does the relation $v=w$ keep this name? I ...
3
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2answers
36 views

What is the etymology of the term “reflexive” in the context of binary relations?

A binary relation $R$ over a set $A$ is called reflexive if the following is true: $$\forall a \in A. aRa$$ Why are relations called these "reflexive?"
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1answer
50 views

what has $\mathbb R$ as a proper subset of it's solution sets that has nothing to do with $\mathbb C$? [closed]

what has $\mathbb R$ as a proper subset of it's solution sets that has nothing to do with $\mathbb C$? for example 1,-1 are the solutions to $x^2=1$, one can consider integers $\mathbb Z$ to be ...
0
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1answer
38 views

Do “$R_*$-modules” have an accepted name?

(All my rings are commutative and unital.) By a module, I mean an ordered pair $(R,M),$ where $R$ is a ring and $M$ is an $R$-module. There is a functor $$\mathbf{ur} :\mathbf{Ring} \leftarrow ...
1
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1answer
84 views

Is there a word for an “infinite algorithm”?

According to Knuth's notes (see Slide 3), an algorithm, by definition, satisfies the following five properties: Finiteness: Terminates after a finite number of steps. Definiteness: Each step is ...
1
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1answer
21 views

What is the name of $E_n[x]$ ?!

I am writing a paper, I want to introduce the $E_n[x]$ Is it correct to write: $E_n[x] $ represents exponential integral of order of n I know $E_i[x]$ or $E_1[x]$ is called exponential integral. ...
2
votes
1answer
73 views

The mathematics underlying Rubik's games

I am interested in knowing (a little more) about the mathematics underlying some of Erno Rubik's games. I guess we all know his famous cube. I heard at some point that a solution was possible because ...
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0answers
25 views

Terminology for function that has only one peak

I am forgetting what the terminology to describe a function that has no local maxima but only a global maximum is. So the function, $f(x)$ monotonically increases till $x = x'$ and then monotonically ...
1
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1answer
76 views

Examples of tangent cone

In http://users.ece.utexas.edu/~cmcaram/EE381V_2012F/Lecture_2_Scribe_Notes.final.pdf The definition of a tangent cone is defined as the closure of the feasible directions. Definition 9. (Tangent ...
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1answer
75 views

Right module vs left module

I would like to have your help on this. Consider the following diagram summarizing the opposition left module-right module: Left module vs Right module (s an t represent scalars) Left module: $$s(x ...
1
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1answer
27 views

Is there a concise, specific name for a transform that consists of rotate, scale and translate?

I'm working on software that involves transforming between different mapping coordinate systems. In one part of the maths/logic, I have to derive, then apply a transform between two cartesian ...
0
votes
1answer
47 views

What is the name of the (k-1)-faces of a k-cell?

Is there an own name of the (k-1)-cells that are attached to a given k-cell (or in other words: of the (k-1)-cells that intersects a given closed k-cell, or yet another words: of the (k-1) cells that ...
0
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1answer
18 views

Difference between set of $n$ points and just $n$ distinct points?

What is the difference between saying "given set of $n$ points" and just "given $n$ distinct points"?
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0answers
60 views

“-in” term in equation

I found the following equation in an article and I don't understand what the "in" term means. It's not a variable nor a parameter. The article can be found in ...
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1answer
44 views

The class of $0-1$ matrices with row sums at least $2$, where distinct columns have dot product $1$

There is an $m\times n$ matrix of ones and zeros where the dot product of any two different columns is one and any row have at least two ones in it. My question is: Is this a popular matrix? Does it ...
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0answers
20 views

A doubt regarding the Yale sparse matrix

While reading the wiki entry for Sparse Matrix (Section Yale Sparse Matrix) https://en.wikipedia.org/wiki/Sparse_matrix#Yale I came across the following difficulty: Let us consider the first ...
3
votes
1answer
48 views

Is there a name for the “with-respect-to variable” of a partial derivative?

In a fraction $\dfrac{a}{b}$, a is called the numerator or dividend and b is called the denominator or divisor. These names are helpful when discussing an equation. In a derivative or partial ...
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1answer
45 views

What is an n-cell?

In my Topology lecture notes, 'n-cell' seems to be mentioned a lot, but it never says what exactly it means. Does it mean $n$-dimensional space?
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1answer
41 views

Notation of rules of a calculus in “Mathematical Logic” by Ebbinghaus [duplicate]

I have a basic question on the notation used in "Mathematical Logic": Ebbinghaus writes rules of a calculus as $$\frac{\zeta_1,...,\zeta_n}{\zeta}$$ and by that he means that if the strings ...
2
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2answers
39 views

Why is “similarity” more specific than “equivalence”?

At least regarding matrices, we have $A$ is similar to $B$ if $\exists S: B=S^{-1}AS$ $A$ is equivalent to $B$ if $\exists P,Q: B=Q^{-1}AP$ I am confused about the usage of the terms "similar" and ...
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4answers
106 views

Can I use greek letters such as alpha to denote a set? [duplicate]

Can we have a set which is called by a small greek letter, e.g. a set $\alpha$?
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1answer
28 views

Terminology for a function, that “is” a morphism in some concrete category

Suppose I've got a category $\mathcal{A}$ equipped with an obvious faithful functor $\underline{} : \mathcal{A} \to \mathsf{Set}$; $A,B\in \mathcal{A}$ and a function $\tilde{f} : \underline{A} \to ...
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0answers
29 views

Is there a single word for a function $f$ such that $f(S \cup T) \le f(S) + f(T) - f(S\cap T)$?

Say we have a function $f: \mathcal{P}(X) \rightarrow Y$ and $f(S \cup T) \le f(S) + f(T) - f(S\cap T)$. The function that takes in sets and returns their cardinality of course has this property (if ...