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

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4answers
80 views

What is $\sqrt{(-1)^2}$ [duplicate]

This question is primarily terminology based. In that $\sqrt{}$ denotes the principal square root. Here are two reasoning $\sqrt{(-1)^2}=1$ since $\sqrt{(-1)^2}=\sqrt{1}$ which we know has a ...
2
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0answers
37 views

Given bifunctor $F$, what is the name of the functor with switched arguments?

Sorry for the unspecific title. Here the actual question: Given categories $\mathcal{A},\mathcal{B}$, let $S$ be the canonical functor $\mathcal{B} \times \mathcal{A} \to \mathcal{A} \times ...
3
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2answers
39 views

Terminology: The difference between $X$'s convention

I am reading the paper, Classification in Networked Data: A Toolkit and a Univariate Case Study. And I have a question about the terminology of this paper, on page 938: Also, see the following ...
4
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2answers
48 views

How would you call geometric objects that lie on a single surface, e.g. a sphere, plane, torus, etc.

I'm looking for an extension of the name coplanar to something like "cosurfacial", but I guess their must be a correct term.. Edit: In the comments, the context was asked for where I would use that ...
0
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0answers
36 views

Is this an improper method of averaging grades? If so, what is a simple mathematical way of explaining it?

I have a professor who employs a unique method of averaging grades. On each assessment, the professor assigns a raw numerical score to each student based on performance. He then converts particular ...
1
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1answer
32 views

What is the remainder of an n-th root called?

I feel like there should be a better word than remainder, but I don't know it. What do you call the thing that's left over when performing an $n$-th root? For example, $\sqrt[3]{29}$ is $3$ with 2 ...
4
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1answer
48 views

How to say math terms in English

I would like to know how to say in English the following objects: the quotient $\mathbb R / \mathbb Z$ (is it "Ar over zee"? or "Ar modulo zee"?) things like $[0,1]^n$ (is it "the n-th power of the ...
0
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0answers
12 views

Name for space of piecewise continuous functions

The space of $k$ times continuously differentiable functions (on $\mathbb R$) is called $C^k$. Is there a similar name for functions that are piecewise continuous? For example the box function ...
1
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1answer
28 views

Terminology for splittings of a set into two parts

I have a set of values $V$ that can be split by any combination $C$ of the elements $v$ that belongs to $V$. Order is not important and repetitions are not allowed. For example, $V := \{1,2,3,4\}$ ...
0
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2answers
66 views

If $f(x) = 0$ has a countable set of solutions, what is $f$?

Is there a name given to functions $f$, where the roots of $f(x) = 0$ are countable? I am assuming $f$ is a real function of a real variable, $x$.
34
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1answer
380 views

Sign Language and Deaf Mathematicians

Something I've often wondered (and I suppose this goes for all kinds of technical terminology, not just that of mathematics) is what kind of sign language exists for practising professional ...
1
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1answer
29 views

Help in this teminology in Hartshorne's algebraic geometry book

I'm studying Hartshorne's Algebraic Geometry book and on page 51: What the author means by $M_{\mathfrak p}$ and "length"? I suppose $S_{\mathfrak p}$ is the localization of the ring $S$ at ...
0
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1answer
12 views

Splitting of primes terminology doubt

What do we mean when we say that a given prime $p$ splits completely in an algebraic extension of $\mathbb Q$? Are we talking about the splitting of prime ideals into unique factors? And, in that ...
1
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1answer
47 views

Are pairwise mutually exclusive events the same as mutually exclusive events?

Larson (1982) defining the probability axioms talks about "mutually exclusive" events, while Poirier (1995) about "$A_1, A_2, \ldots$ as a sequence of pairwise mutually exclusive events events in the ...
5
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1answer
75 views

Question about terminology in number theory

The following transformation appears often in number theory: $$F(x) = \sum_{n \le x} f \left( \frac{x}{n} \right)$$ What is the name of this transformation? PS. I will accept as answer something ...
5
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1answer
131 views

What is the origin of the terms 'jet' and 'prolongation' in differential geometry?

I am just curious what is the reason for the terms 'jet' and 'prolongation' in differential geometry? Is there some mental imagery that these names are supposed to evoke? Or are they so-named because ...
4
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1answer
51 views

What should you call a property, like an invariant, but that is reversed instead of preserved?

Suppose $P$ is some property of some objects and $f$ is a function on those objects. If $Px$ implies $Pf(x)$ and $\lnot Px$ implies $\lnot Pf(x)$, then we might say that "$P$ is invariant under $f$". ...
1
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1answer
39 views

Labeled commutative diagram

Consider a commutative diagram. For example the following diagram in $\mathbf{Set}$: $$ \begin{array}{ccc} & \overset{+1}{\longrightarrow} &\\ \mathbb{Z} & & \mathbb{Z} \\ & ...
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1answer
63 views

What's the meaning of “drop” in mathematics?

What's the meaning of "drop" in following sentence: "the term can be dropped from the numerator"
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0answers
53 views

An endomorphism $f$ such that $f\circ f=1$

What is the name for an endomorphism $f$ of a category such that $f\circ f=1$? Note that I work with category $\mathbf{Set}$.
2
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1answer
83 views

Is $\mathbb{Z}/p^\mathbb{N} \mathbb{Z}$ widely studied, does it have an accepted name/notation, and where can I learn more about it?

Fix a positive integer $p$, possibly prime. For each natural number $n$, there is a ring $\mathbb{Z}/p^n \mathbb{Z}$ together with a distinguished ring homomorphism $$\pi_n:\mathbb{Z} \rightarrow ...
3
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2answers
157 views

Is there a formal definition for antiderivatives?

In the way the derivative can be defined as a limit, specifically $$f'(x):=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$ or any of the other possible variants, is there a way to define the antiderivative, as in ...
0
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1answer
19 views

Does the operand in a convolution have a particular name?

In a convolution: $$(f*g*h)(t) = \int f(x)g(y)h(z) \delta(t-x-y-z) dxdydz$$ do the operands $f,g,h$ have a specific name, besides the general "operand"?
1
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1answer
48 views

What is the scientific term form something that 'wraps around' a shape

I was wondering if there is a mathematical term for this: Imagine you had given the black shape - what does the red shape? I would call it, it wraps around the black one. Actually I am looking ...
0
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1answer
20 views

What does “decreases more slowly” mean mathematically with regard to distributions?

In a paper I'm reading, the authors state that a certain distribution "decreases more slowly than exponentially over a portion of the range". What does this mean, mathematically? Assuming $A$ is the ...
1
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1answer
39 views

Wording in English for “quantité conjuguée” in French

In French when you have an expression of the type $\sqrt{x}-\sqrt{y}$, the expression $\sqrt{x}+\sqrt{y}$ is named the "quantité conjuguée". This is useful when you want to bound $$\vert ...
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0answers
45 views

The definitions of “transformation” and “isometry”

Let $T$ be a mapping from the plane to itself. In the context of Euclidean geometry, can $T$ be called a "transformation", or is this word reserved for cases where $T$ is bijective? Is there ...
0
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0answers
21 views

Why is equivalence 'class', not equivalence 'set'? [duplicate]

Why do we call it a class, not a set? Is it not a set? Can it be a proper class?
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0answers
25 views

What are these algebraic properties called?

Suppose $O$ is some operator, suppose $f$ and $g$ are both functions, then linearity implies that: $O(\alpha f + g) = \alpha O(f) + O(g)$ What about the following property: $(O_1+O_2)(f) = O_1(f) ...
3
votes
1answer
32 views

Is there a mathematical distinction between “on” and “in”?

Is there any difference if I said a function on an interval or a function in an interval? or a vector field on a manifold versus a vector field in a manifold? The main reason is because some online ...
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0answers
14 views

Definition of (minimal) domain?

Consider the following links: http://www.glottopedia.org/index.php/Domain_%28Syntax%29 http://www2.let.uu.nl/uil-ots/lexicon/zoek.pl?lemma=Minimal+domain&lemmacode=542 What kind of mathematical ...
1
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1answer
48 views

Why the spatial/mathematician's Fourier Transform?

I was wondering why the sign-change in the exponential of the spatial/mathematician's Fourier Transform and why is it called mathematician's spatial in either case?
0
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1answer
38 views

What is $D(n,k)$? (dee-en-kay) /ˈdiːˈɛnˈkeɪ/

Is this combinations with repetitions, i.e. ${n+k-1\choose k-1}$ or is this something else entirely? I see this a lot, but with this kind of language no search engine is going to help. The edit in ...
12
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1answer
806 views

Is there a term for the ratio of a function and its derivative?

Given a function $f(x)$ and its derivative $f'(x)$, is there a term for $\frac{f(x)}{f'(x)}$ or for $\frac{f'(x)}{f(x)}$?
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0answers
25 views

Are the names such as $N_1$-space, $N_2$-space used for various countability axioms

In this question the OP mentioned "$N_i$-hierarchy for various countability axioms and also that the name $N_2$-space or $N_2$-property is used for second countable space. I did not encounter this ...
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3answers
130 views

What is the significance of stuff like the “Pigeonhole Principle”? [closed]

Pigeonhole Principle if n items are put into m containers, with n > m, then at least one container must contain more than one item src I thoroughly read What is your favorite application of the ...
15
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14answers
2k views

Name of the highest power of 2 smaller than or equal to a given number

For a number $x$, I would like to know whether there is a common name for the number $2^n$ such as $2^n \leq x < 2^{n+1}$ (e.g. If $x = 7$, then $2^n = 4$, $n = 2$). I have some computer science ...
1
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0answers
38 views

What is $\Bbb E$? Is is $\Bbb R$ with the standard Euclidean topology?

What is $\Bbb E$? I believe this is just alternative notation for $\Bbb R$ where $\Bbb R$ is assumed to have the standard Euclidean topology. Is this correct? Is seems to be used in this way in ...
2
votes
1answer
35 views

Terminology: name for integer “factor” of a rectangle?

Basic terminology question from a non-mathematician. I started trying to express this with mathematical terms, but decided any potential errors might be more frustrating than the imprecision of ...
0
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1answer
27 views

What is axiomatic method? Does it mean giving definitions beforehand and then using them in the proofs?

Also, what does axiomatic approach to probability mean? Does it mean a similar thing?
5
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1answer
70 views

Why did Euclid name his book as “Elements”. What does “element” mean in this context?

Does it relate to the nature of the book in some way?
1
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1answer
57 views

How do you pronounce Richard Courant's surname?

Since his surname looks rather French than German, I started wondering how you pronounce his name. In particular, I'd be interested in how he would have pronounced his name himself (since I already ...
2
votes
2answers
122 views

Why are Natural Numbers called Natural Numbers?

When we say $1,2,3...$ are natural numbers, why don't we include rational and irrational numbers? Isn't $\pi$ something natural? Shouldn't we say all real numbers the Natural numbers? Shouldn't ...
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0answers
21 views

Is it customary to call it “R-module ring homomorphism”?

Let $R$ be a ring. Let $M,N$ be rings together with $R$-module structures, but $M,N$ are not $R$-algebras Let $\phi:M\rightarrow N$ be a ring homomorphism which is also an $R$-module homomorphism. ...
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1answer
11 views

Understanding terminology related to implementing the sobel edge detection algorithm

I'm trying to follow a scholarly paper that discusses a modified implementation of the sobel edge detection algorithm, but I'm not following the terminology 100%. The Sobel detector consists of ...
2
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4answers
118 views

I call them squares. They called them arrays. What do they mean?

So I was in C++, and we had third graders come today to play our programs. Whilst the others just drilled them with problems, my game was subtract a square. It was fun watching them discover that ...
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0answers
24 views

What's the name of this tensor product?

Fix $V$ to be a vector space over $\mathbb{R}$. For all $k \in \mathbb{N}$, let $L_k$ be the space of all $k$-tensors on $V$, and let $S_k$ be the set of all permutations of the set $\{1,\dots, k\}$. ...
0
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3answers
69 views

Is zero “finite” - Terminology

edit: This is usually done by physicists, engineers, etc. And it refers to a numerical value, not a set. It is used for cases the numerical value of $0$ is not allowed as well. Infinity, is clearly ...
9
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3answers
832 views

Why lower case “a” for “abelian group” and upper case “C” for “Cauchy sequence”?

This has been bugging me. Why is the lower case letter "a" used to spell "abelian group" when upper case letters are used to spell the terms, "Gaussian Integral", "Cantor set" or "Cauchy ...
1
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1answer
53 views

Mathematical symbol for Symbolic Replacement

(Posted at mathematica.SE, as it might be better there) I'm searching for a mathematical symbol, that describes the symbolic replacement done for instance in Mathematica: ...