Tagged Questions

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

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10 views

Does this notion of the “directed area” of a closed curve in $\mathbb R^3$ have a standard name?

Given an oriented surface $\Omega$ in $\mathbb R^3$, consider the quantity $\mathbf A=\int_\Omega\hat n\,\mathrm dA$. We may call this the "directed area" of the surface because, when $\Omega$ is ...
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0answers
20 views

nice name for the image of multivariable function

Consider a differentiable function $f:D\subset\mathbb R^m\mapsto \mathbb R^n$ with $m\le n$. I know if $m=1$ then $f(D)$ is called by "path", if $m=2$ then $f(D)$ is called by "surface" and if $m=3$ ...
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0answers
42 views

Why is the natural logarithm 'natural'? [duplicate]

Simple question: Why is it that the natural logarithm is called 'natural'?
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1answer
50 views

Multiple integral differential notation

When writing a multiple integral, I have noticed there is sometimes used a shorthand for writing the differential in the integral. For example in $\mathbb{R}^3$ instead of writing $\mathrm{d}x\ ...
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0answers
29 views

The meaning of “In general” in mathematics

What is the meaning of "in general" in mathematical texts? Does it mean usually or it means always or sometimes usually and sometimes always according to the text?
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1answer
16 views

How do you say that variable is randomly chosen with a random distribution for range [3, 42]?

This question is only about how to formulate something in English for a bachelor's thesis in computer science. I have a variable $x$ which is randomly initialized. It is chosen from a (continuous) ...
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1answer
18 views

Monotonicity of a sequence of length 1 or 0

A sequence or list $a_i$ is said to be strictly monotonically increasing if for each pair of adjacent elements the successor is greater than its predecessor, or: $a_i < a_{i+1}$. But what if there ...
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0answers
6 views

What is the name of the function $s_p$?

Let $p$ be a prime. Define $s_p(n)\triangleq \max\{m\in\mathbb{N}:p^m|n\}$, for all $n\in \mathbb{Z}^+$. Is there a name for this arithmetic function $s_p$?
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1answer
34 views

How do expressions like “more than” and “is more than” have different meanings?

I've looked up in my present math book that expressions like (1) "less than" and "is less than" and (2) "more than" and "is more than" have different meanings. I saw that "less than" indicates ...
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1answer
16 views

How is a coordinate system called where values increase to the bottom instead to the top?

In some computer graphics libraries the coordinate system is almost like the "usual" cartesian coordinate system. The only difference is that the $y$ values increas to the bottom, not to the top. ...
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1answer
24 views

What is the different between chirality and chiral symmetry?

I read this article in Wiki about Chiral symmetry and I get confused in the terms "chiral symmetry" and "chirality". Are they the same? Does "chiral symmetry" literally mean the symmetry of the hands? ...
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2answers
97 views

Etymology of “flabby” or “flasque” sheaf

I just started working with flasque, or flabby sheaves, that is sheaves whose restriction maps are surjective for any two open set of the space. I wonder about the etymology of the term. In French, ...
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0answers
23 views

Term for a bad quantity ranging between 1 and infinity

Mathematical terms are often selected based on the emotion they generate. For example, if we define a quantity we consider "good", we would term it something like "efficiency", and define that its ...
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0answers
13 views

What type of expression is this: (X/Y)*X

It has 2 Variables, and I believe Polynomials exclude dividing by a variable... so then what would I call this type of function? Is there even a term?
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0answers
19 views

What are such pairs of monotone mappings?

Let $P, P'$ be some partial orders and $f$ and $g$ two monotone mappings of type $P \to P'$. Consider the property $g(f(x)) \leq f(x)$, for all $x \in P$. My questions: Have you encountered such ...
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8answers
1k views

Are there mathematical contexts where “finite” implicitly means “nonzero?”

I recently gave my students in a discrete math class the following problem, a restatement of the heap paradox: Let's say that zero rocks is not a lot of rocks (surely, 0 is not a lot of rocks) and ...
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1answer
17 views

Connection between adjoint of a matrix and adjoint of an operator

Let $T:\mathbb{R}^2 \rightarrow \mathbb{R}^2$ with $$T(x,y) = \left[ \begin{array}{ccc} 1x+2y \\ 3x+4y \end{array} \right] $$ The matrix representation of $T$ is $$ A= \left[ \begin{array}{ccc} 1 ...
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0answers
20 views

optimization terminology

For the function plotted below, x = 14.5/15 and x = 15.5/15 are two local maximizers. So gradient-based optimization methods could find the global minimum if the initial guess of x is in the range ...
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2answers
33 views

The name for the quotient property.

We call a surjective $f:X\rightarrow Y$ a quotient mapping if it satisfies, for every $U\subset Y$ (continuity, continuous) $U$ is open $\Rightarrow$ $f^{-1}(U)$ is open and (???) ...
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1answer
73 views

“Isomorphy” in mathematical texts

I want to use the term "isomorphy" in a mathematical text, like: There is isomorphy of objects A, B, C, D, E and F. which is equivalent to There exist isomorphisms between the objects A, B, ...
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1answer
33 views

Terminology of “G over H”

I am trying to find the definition of G/H (which is read as "G over H", "G modulo H", or "G mod H"). I believe that, in this case, G is a group and H is a subgroup of G.
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3answers
54 views

Name for introducing negation with quantifiers

The rewriting of $\varphi\to \psi$ into the logically equivalent $\neg \psi\to\neg \varphi$ is called contraposition. Is there a similar word for rewriting $\forall x.\varphi$ into $\neg\exists ...
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0answers
24 views

Operator for scaling a function?

Let $\mathbb{F}$ denote the set of functions of the form $f: \mathbb{R} \to \mathbb{R}$. I am interested to know whether there exists a well-known linear map $T_\alpha: \mathbb{F} \to \mathbb{F}$ ...
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0answers
29 views

Partially ordered sets

I have a question on Posets. Suppose we have $P = \{3, 6, 9, 18, 7, 14\} $ ordered by divisibility. We want to partition $P$ to subsets so that each two elements in each subset are related directly ...
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0answers
23 views

On the Name of the Amplituhedron

Shouldn't the 'amplituhedron' really be called an 'amplitutope' since it's really a polytope and not strictly a polyhedron?
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0answers
14 views

A Geometry Terminology Question

Edges and diagonals are to polygons as faces and X are to polyhedrons? What is the answer to X? I've been touching up on geometry and I'm having trouble finding an answer to this, and inconsistency ...
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0answers
60 views

Can we consider a hypergeometric function as a closed-form?

Let's say a calculus problem like an integral or a series has a solution that inevitably involving a hypergeometric function. It turns out that hypergeometric function cannot be expressed in term of ...
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6answers
572 views

Problem in the second-derivative symbol.

The second derivative of this symbol according to the rules that we have learned the correct mathematical, I wish to know why this symbol is not used.
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1answer
27 views

Term for functions with infinite derivatives [closed]

Functions that include a negative indice such as x-1 or similar have an unlimited number of derivatives, so f'(x), f''(x), and fn(x) exist. Is there a technical term for functions like these? I've ...
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0answers
11 views

Are there terminologies distinguishing modules over ring and rng?

Let $R$ be rng. Let $M$ be a left $R$-module. Let's say, after some verification, one realized that $R$ has a unity and it doesn't satisfy $1_R \cdot x$ for all $x\in M$. Hence, one cannot call $M$ ...
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0answers
9 views

Is there a name for products $\Delta(v)\!\cdot\!M$ and $M\!\cdot\!\Delta(w)$?

For any vector $u$, define $\Delta(u)$ as the diagonal matrix whose diagonal elements correspond to the entries in $u$. Now, let $M$ be an $m \times n$ matrix, and $v$ and $w$ be $m$- and ...
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1answer
35 views

What properties does a rank one matrix have?

My question is what properties does a rank one matrix have? I saw a lot of papers mentioning that the matrix is rank one and so on. I know rank one of a matrix means that there are no independent ...
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1answer
27 views

Bigger and Smaller for numbers - Works in both directions?

I wanted to know how to use the right term when explaining the difference between numbers. For example, I have two lenses: Lens 1 = 10x zoom Lens 2 = 5x zoom I know I can say that the 1 has 2x ...
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2answers
15 views

Origin of the words arithmetic and geometric progression

Why are arithmetic progression and geometric progression called arithmetic and geometric respectively?
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0answers
15 views

Financial math vocab; “convertible”, “roll over”?

I am having trouble understanding what is going on regarding the following problem. Smith receives income from his investments in yen. He finds a bank that will issue a term deposit that allows ...
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0answers
19 views

Nomenclature for posets s.t. for all $x<y$, there exists $z$ with $x<z<y$.

I can't remember the nomenclature (if it exists) for a poset with the property in the title, that is, a poset $(P,\leq)$ with the following property: If $x<y$ in $P$, then there exists $z\in P$ ...
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1answer
35 views

What do “canonical” and “natural” mean exactly?

"Canonical" and "natural" are two words frequently seen in mathematical literature. For example, we often find "there is no canonical/natural way to", "it's canonical/natural to". So I'd like to know ...
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1answer
40 views

One Half of a Primorial

Is there a name for a half primorial? How should a half primorial be notated? The first three primorials are 2,6, and 30. The first three half primorials are 1,3, and 15. I have found that the half ...
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0answers
27 views

Usage of the term Q.E.F.

While researching the term Q.E.D last night, the phrase Q.E.F was mentioned, which was apparently "used by Euclid to indicate the end of the justification of a construction". Does Q.E.F indicate the ...
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2answers
85 views

Spivak “min” notation confusion

Spivak uses a notation: min$(1, \frac{\epsilon}{2|a| + 1})$ What does he mean by this notation? especially by "min"??
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0answers
11 views

Term of partially ordered set with “levels”

Suppose that we have a partially ordered set $(X,\leq)$ such that the following condition holds: There exists a disjoint partition $X = \bigcup_{ i \in \mathbb N_0 } X_i$ such that for $i < j$ we ...
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0answers
18 views

The name of $fusc$ (Calkin-Wilf sequence)

I was just wondering where $fusc$ got its name (where $fusc(2n) = fusc(n), fusc(2n + 1) = fusc(n) + fusc(n + 1)$, seeds: $fusc(0) = 0, fusc(1) = 1$). The function is of some importance in the ...
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0answers
67 views

Name of a certain set

I want to know if there is any already-standard way to refer to the sets described as follows. For a set $X$, let $-X = \{-x: x \in X \}$; call it the negative of $X$. Take the set of all primes in ...
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1answer
16 views

The Value of One Function Determines the Value of Another

The value of $\pi(s)$ determines the value of $m(n)$. How do we describe such a relationship between two functions in standard terminology? How do we express this mathematically?
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44 views

Products of All Primes Up To The $n$th Prime

The first prime is 2. The second prime is 3. 3·2=6. The product of the first three primes is 30. The product of all the primes up to the fourth prime is 210. My question is this: Is this sequence ...
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0answers
37 views

Is there accepted terminology for algebraic structures whose every subalgebra is free?

Is there accepted terminology for algebraic structures whose every subalgebra is free? Examples: Any free group Any vector space More generally, any free module over a PID. In fact, this ...
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0answers
32 views

Does the phrase '$S$ is independent' have an accepted meaning in universal algebra?

Let: $T$ denote an algebraic theory $F$ denote the free functor $X$ denote a $T$-algebra. $\mathrm{cl}_X : \mathcal{P}(X) \rightarrow \mathcal{P}(X)$ denote the function such that for all $S ...
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1answer
17 views

Which operations create a minor of a graph?

I came across two definitions which operations are allowed to construct a minor from a given graph. One definition allows edge contractions and edge deletions, the other additionally vertex ...
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0answers
29 views

Definition For Bound

Let $a$ be any natural number and $b$ be the next prime greater than $a$. Let $m$ be the maximum distance from $a$ to $b$ such that $a+m$ is equal to or greater than $b$. Can I call $m$ the bound? ...
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2answers
43 views

Sequence vs Series

What is the difference between a sequence and a series and how should they be used i.e. give examples of the usage of these terminologies in separate senarios.