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

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0
votes
4answers
41 views

Is there any notation for general $n$-th root $r$ such that $r^n=x$?

As we know that the notation for the $n$-th principal root is $\sqrt[n]{x}$ or $x^{1/n}$. But the principal root is not always the only possible root, e.g. for even $n$ and positive $x$ the principal ...
0
votes
1answer
10 views

What is it called when you have two systems of measurement and each scale has two different numbers that can represent the same thing?

I'd like to know what it is called in Math when you have two numbering systems and they represent the same thing, but with different numbers. Let me give you an example, when you have civilian and ...
0
votes
0answers
16 views

Mathematical formal expression of find “subfunction” in function

Imagine if I have a function $s(t)$ and $r(t)$. $s(t)$ may contain $r(t)$ one or more times as $s(t)$ is a quasi-period function. What is the correct expression if I want to say the $s(t)$ contains ...
53
votes
6answers
3k views

Why is a geometric progression called so?

Just curious about why geometric progression is called so. Is it related to geometry?
3
votes
1answer
102 views
+50

What is known about these arithmetical functions?

Let $n=\prod_p p^{c_p}$ and $$ \alpha(n)=\prod_p p^{c_p \bmod 2}. $$ The function $\alpha$ is multiplicative since $\alpha(n)\alpha(m)=\alpha(nm)$ for co-prime $n$ and $m$. If you replace $\bmod 2$ ...
1
vote
0answers
31 views

What is the opposite of a derangement?

A derangement is a bijection $f : A \rightarrow A$ such that $f(x) \ne x$ for all $x \in A$. Is there a name for a bijection $f : A \rightarrow A$ that is not a derangement? That is, is there a name ...
3
votes
1answer
57 views

Isomorphic or equal?

Let $\sim_n$ be the usual equivalence relation of congruence modulo $n$ in $\mathbb{Z}$, i.e., for $a,b\in\mathbb{Z}$, $a\sim_nb\Leftrightarrow a-b=k\cdot n$ for some $k\in\mathbb{Z}$. For $n=0$ the ...
0
votes
1answer
30 views

How do you call a vector of length $n$, with all values equal to $\frac{1}{n}$?

Is there a specific name for a vector of dimension $n$, with all values equal to $\frac{1}{n}$? So, a vector that looks like this: $\vec{v} = \underbrace{(\frac{1}{n}, \frac{1}{n}, ..., \frac{1}{n}, ...
0
votes
1answer
36 views

How to mathematically state y - 1 unless y - 1 < 0 then y is 0

I have a formula and I don't know how to write it in mathematical form (I'm a programmer.) The formula needs the variable y to be y - 1 unless y <= 0, in which case y should just be 0. ...
34
votes
1answer
353 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 ...
2
votes
0answers
22 views

Name of the segment connecting a point's coordinate axis projections?

Given any point $(x,y)$ in the real plane consider the corresponding line segment connecting $(x,0)$ with $(0,y)$. See diagram. Is there a name for this special segment? (I believe that in ...
4
votes
1answer
148 views

Semi-partition or pre-partition

For a given space $X$ the partition is usually defined as a collection of sets $E_i$ such that $E_i\cap E_j = \emptyset$ for $j\neq i$ and $X = \bigcup\limits_i E_i$. Does anybody met the name for a ...
10
votes
7answers
12k views

What is the difference between only if and iff?

I have read this question. I am now stuck with the difference between "if and only if" and "only if". Please help me out. Thanks
19
votes
7answers
6k views

Operator vs function

Could someone please explain the MATHEMATICAL difference between an operator and a function? I am not talking about these in terms of coding but rather the mathematical difference. Is operator also a ...
-1
votes
1answer
38 views

What's the name of this type of a set?

So I have a set $\{i_1,i_3,i_5\}$. What do we call the following set? Is there a standard name for it? $\emptyset, \{i_1\}, \{i_1,i_3\}, \{i_1,i_3,i_5\}$. Note that we do not have $\{i_3,i_5\}$ in it ...
1
vote
1answer
16 views

Terminology: Expected Value, Expectation, Expectation Value

According to [Wikipedia::Expected Value] expected value and expectation are correct terms for the first moment of a random variable. What about expectation value? I have heard and read this term ...
3
votes
1answer
17 views

What is the difference between functions and operations?

Wikipedia says that an operation $\omega$ is a function of the form $\omega: V \to Y$, where $V \subset X_1 \times\cdots\times X_k$. But as far as I know, every function's domain is a set, so ...
1
vote
2answers
73 views

Is 'clamp' a formally recognized mathematical function?

I was surprised to find the clamp function absent from Mathworld and Wikipedia. Is this mainly a concept particular to computer programming? Is it known by another ...
9
votes
1answer
95 views

What are the formal terms for the intersection points of the geometric representation of the extended trigonometric functions?

Mike Pierce's answer to this question, regarding trigonometric functions beyond the common (co)sine, (co)secant, and (co)tangent, points to a figure on the Wikipedia page on trigonometric functions ...
0
votes
0answers
14 views

mathematical name for the relationship between capacity utilization and overcapacity

I'm writing a report on industrial overcapacity, which is capacity not utilized by current production. If capacity utilization is the percent of total capacity utilized, what is the mathematical name ...
13
votes
2answers
390 views

Why we use the word 'compact' for compact spaces?

Considering the definition of compactness in either Analysis or Topology books, or its equivalent definitions (i.e. [It] is compact $\Longleftrightarrow\dots$), I couldn't understand why ...
4
votes
0answers
35 views

Graph vertex set with a certain property

Let $G$ be a graph and let $V$ be a set of vertices with the following property: If a vertex $v$ is connected to every $u\in V$, then $v$ has to be in $V$. Does such $V$ have a (standard) name? Note ...
9
votes
4answers
9k views

Difference between formula and algorithm

What is the difference between the terms formula and algorithm in mathematics? I haven't seen the definition of formula anywhere. I know that algorithm means that Turing machine halts for every input. ...
-2
votes
1answer
36 views
20
votes
5answers
1k views

Is there anything special about this matrix?

I've just encountered a matrix which seems to display nothing special to me: $$B=\begin{pmatrix}1&4&2\\0 &-3 &-2\\ 0 &4 &3 \end{pmatrix}$$ But further observation reveals ...
4
votes
1answer
51 views

Right modules Vs Left modules.

I have been reading Frobenius Algebras, Volume 1 By Andrzej Skowroński, Kunio Yamagata. On page 18 I came across the following paragraph, and I founded interesting, I will quote it and then ask my ...
1
vote
4answers
75 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 ...
1
vote
1answer
209 views

Name of the intersections of a ball with the octants?

The eight regions of space defined by the eight possible combinations of signs for $(+/- , +/-, +/-)$ for $x$, $y$, $z$ are called octants. Given a ball of radius 1 centered in the origin $(0, 0, ...
3
votes
2answers
32 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 ...
2
votes
0answers
34 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 ...
4
votes
2answers
47 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 ...
1
vote
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, $V := \{1,2,3,4\}$ ...
6
votes
1answer
318 views

Difference between elementary submodel and elementary substructure

This is a really "elementary" question, forgive the pun. What is the difference between an elementary submodel and an elementary substructure (in first-order Logic)? Sincere thanks for help.
1
vote
1answer
31 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 ...
0
votes
0answers
31 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 ...
4
votes
1answer
45 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
votes
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 ...
0
votes
2answers
65 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, $x$.
2
votes
3answers
221 views

“Slow” and “fast” rates of convergence

I have recently read about convergence and divergence. However, I am having trouble understanding how something can converge/diverge "slowly" or "fast". If you sum up two series (that converge to the ...
0
votes
1answer
84 views

What does it mean to say that determinant is multilinear?

Can someone clearly explain to me what is meant by the determinant being multilinear, and what (multi-)linear functions are? I can't find a clear answer to this question.
1
vote
1answer
29 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 ...
1
vote
1answer
28 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
votes
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 ...
5
votes
1answer
72 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 ...
1
vote
1answer
68 views

In a dagger category, what do we call an arrow $f$ such that $f \circ f^\dagger \circ f = f$?

In a dagger category, what do we call an arrow $f$ satisfying $f \circ f^\dagger \circ f = f$? In $\mathrm{Rel}$ (and, more generally, an allegory) this is straightforwardly equivalent to $f \circ ...
1
vote
1answer
57 views

In a dagger category, is there a name for morphisms $f : X \rightarrow Y$ with $\mathrm{id}_X = f^\dagger \circ f$?

In a dagger category, is there a name for morphisms $f : X \rightarrow Y$ with $\mathrm{id}_X = f^\dagger \circ f$? Clearly, every such arrow is a split monomorphism; further, if such an $f$ is ...
23
votes
3answers
2k views

Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?

I know that $1$ is not a prime number because $1\cdot\mathbb Z=\mathbb Z$ is, by convention, not a prime ideal in the ring $\mathbb Z$. However, since $\mathbb Z$ is a domain, $0\cdot\mathbb Z=0$ is ...
1
vote
1answer
37 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} \\ & ...
5
votes
1answer
118 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 ...
8
votes
6answers
858 views

What's the difference between tuples and sequences?

Both are ordered collections that can have repeated elements. Is there a difference? Are there other terms that are used for similar concepts, and how are these terms different?