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

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0answers
9 views

Specific name of a scale from -10 to 10?

I am trying to refer to a scale from -10 to 10 with 0 being the center. Does this type of scale have a specific name?
11
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0answers
107 views

How to name these “ideals”?

Background. Let $\mathcal{C}$ be a symmetric monoidal category with unit $\mathbf{1}$. A subobject of $\mathbf{1}$ is just a monomorphism $I \to \mathbf{1}$. We may also call this an ideal of ...
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1answer
28 views

what is the name of the sum of all numbers inside a number, including the number itself?

ex.: 1+2+3+4+5+6+7+8+9+10=55 this it what I mean by "numbers inside "10", including "10" ...I was in bed, thinking of a quick way to calculate that, but with a way bigger number ( ex.: ...
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0answers
12 views

Equivalence class of functions that imply the same ordinal relations

Often we define functions only to succinctly describe an ordinal relation. For example, economists define a utility function such as: $$u(x,y)=xy$$ to imply that the point (2,5) is better than the ...
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0answers
113 views

Equivalence relation over groups $a\asymp_sb :\rightarrow\exists n\in\Bbb Z:as^n=b$: terminology and decision problem

Let's define this relation over the elements of an infinite group $(G,\cdot,e)$ $$a\asymp_sb :\rightarrow\exists n\in\Bbb Z(as^n=b)$$ where $a^n$ is defined as follow 1)$a^0=e$ 2)$a^{n+1}=aa^n$ ...
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0answers
20 views

Matrices with Continuous Indices

The components of a matrix $A$ can be written as $a_{ij}$. In Quantum we're starting to talk about a generalization where the indices are not elements of $\Bbb N$, but are instead continuous. Our ...
46
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3answers
4k views

Do we have negative prime numbers?

Do we have negative prime numbers? $..., -7, -5, -3, -2, ...$
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1answer
26 views

Name for the set {Mv : |v| = 1}

Let $M$ be a matrix on a normed vector space. Is there a name for the set $\{Mv : |v| = 1\}$?
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2answers
29 views

X and Y have the same cardinality if and only if bijection from X to Y? [duplicate]

My textbook says "Let X and Y be sets. We say X and Y have the same cardinality if there is a bijection f: X --> Y." I was wondering why the text does not say "if and only if." A bijection implies ...
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1answer
15 views

Codomain confusion

I'm confused about the codomain of a linear transformation. If we have a linear transformation which maps from $\mathbb{R}^n$ to $\mathbb{R}^m$ and the range of the linear transformation is only the ...
0
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0answers
26 views

Upto which number of vertices does every graph have a name?

I have heard of many families of graphs and also many famous graphs named after persons who intensively studied it. But I did not find a complete list with the names of the graphs to, lets say, ...
5
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2answers
67 views

Nuances of the word “proposition” (versus “theorem”) in mathematical writing

In mathematical writing, the word "Proposition" is often used to label lesser theorems. However, I tend to feel that there's a further difference in the way the words "Proposition" and "Theorem" are ...
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1answer
22 views

(Partial) symmetry order for matrices

Does there exists commonly used ( possible partial) orderings which would rank matrices as a function of their "degree of symmetry"? I am thinking one could for instance have $\succeq_{SYM}$ defined ...
1
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1answer
46 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 $\mathbf A(\Omega)=\int_\Omega\hat n\,\mathrm dA$. We may call this the "directed area" of the surface because, when $\Omega$ ...
1
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1answer
62 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 $m=3$ ...
3
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1answer
83 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\ ...
2
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0answers
32 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?
0
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1answer
17 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 ...
0
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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 $s_p$?
1
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1answer
44 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 ...
0
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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. ...
0
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1answer
30 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? ...
4
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2answers
122 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
24 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
22 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 ...
1
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1answer
28 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 ...
0
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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 ...
2
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2answers
35 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 (???) ...
0
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1answer
83 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, ...
2
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2answers
42 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
62 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 ...
1
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0answers
29 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 $T_\alpha: \mathbb{F} \to \mathbb{F}$ ...
1
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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
35 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?
5
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0answers
65 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 ...
4
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6answers
581 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.
0
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1answer
30 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 ...
0
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0answers
12 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 $M$ ...
0
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0answers
11 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 ...
1
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1answer
43 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 ...
0
votes
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 ...
2
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2answers
20 views

Origin of the words arithmetic and geometric progression

Why are arithmetic progression and geometric progression called arithmetic and geometric respectively?
0
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0answers
19 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 $z\in P$ ...
2
votes
1answer
38 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 ...
1
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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
30 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 ...
0
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2answers
93 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"??