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

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2answers
71 views

What's the name of the form $ai+b$ of a complex number?

Example: the number $0.5$ can be written as a fraction $\frac {1}{2}$. Is there an official name for writing a number in the form of $ai + b$? Complex numbers could also be written in this form $z = ...
1
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0answers
25 views

Composite residuosity statement.

Consider the following definition. A number $z$ is said to be $n$-th residue modulo $n^2$ , if there exists a number $y \in \mathbb{Z}_{n^2}^*$ such that $$z\equiv y^n \mod n^2$$ Let us take $n=6$ ...
0
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1answer
56 views

Monochromatic Solutions

I recently came across this paper: http://borisalexeev.com/pdf/foxgraham.pdf "On Minimal Colorings Without Monochromatic Solutions To a Linear Equation" Can someone explain in clearer terms what ...
0
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0answers
38 views

What is the proper term to describe algebraic techniques of equation manipulation?

Is there a term to describe the category of algebraic "tricks" that include: polynomial division completing the square quadratic formula partial fraction expansion etc. These are related since ...
1
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0answers
96 views

What is a Toy Model for the mathematician's practice? Definition and examples

Wikipedia says Toy model (physics): "In physics, a toy model is a simplified set of objects and equations relating them so that they can nevertheless be used to understand a mechanism that is also ...
3
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1answer
63 views

What is the name for a polynomial with all coefficients equal to 1?

I am looking for a good google search word for polynomials that have all coefficients equal to 1. An example of a such polynomial is: $$1+x^{23}+x^{57}+x^{101}$$ One such polynomial could also be ...
0
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1answer
18 views

What is the difference between self-avoiding and simple in FASS (space filling) curves?

Although it does not appear to be widely used, I occasionally see the acronym FASS used to describe certain curves that are space-filling, self-avoiding, simple, and self-similar. What is the ...
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2answers
41 views

Difference between equals/approaches/approximate

Consider the series $$\sum\limits_{k=0}^{\infty} \frac{1}{2^k} = 2$$ Is it correct to say "$\text{the series approaches 2 ?}$" if so, shouldn't we replace $=$ with $\approx$ ? Also Is it ...
2
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2answers
37 views

Bilinear Map vs Inner Product

What is the difference between a Bilinear Map and a Inner Product?
1
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1answer
42 views

Is there a name for a function such that $f=e^g$?

Let $X$ be a topological space. Let $f:X\rightarrow \mathbb{C}\setminus\{0\}$ be a continuous function. Is there a terminology to call functions $f$ such that $f=e^g$ for some continuous map ...
6
votes
1answer
75 views

Why are models in logic called models?

A model is an interpretation of a given formal language under which any wff in a given set of wffs of this formal language is true. Why are models called models? What's the reasoning behind the name? ...
0
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0answers
25 views

Compact hypersurface in $\mathbb{R}^n$

Let $S$ be an $(n-1)$ dimensional hypersurface in $\mathbb{R}^n$. If we say that $S$ is compact, does this necessarily mean that $S$ has no boundary? Eg. $S$ can be a sphere but not a sphere cut in ...
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2answers
16 views

What is the Term for the Center of Mass Equation Structure

What is the term for the generic structure of this form of equation: SUM(Mi * Xi) / SUM (Xi) It is the same as the center of mass calculation.
0
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0answers
29 views

What is a Serre presentation of a Lie algebra?

For example, as in: Give a Serre presentation of Lie algebra $\frak{g}$ of type $G_{2}$. Is it the presentation in terms of Chevalley generators, which satisfy Serre relations?
2
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0answers
31 views

What's a concise word for “the expression inside a limit”? Limitand?

In $\sqrt {f}$, $f$ is the radicand. In $\sum g_i$, $g_2$ is a summand. In $x \times y \times z$, $y$ is a multiplicand. In: $$\displaystyle \lim_{n \to +\infty} h_n(x)$$ or: $$h(x) \to \ell \quad ...
2
votes
1answer
69 views

If $R = \frac{P}{Q}$ is a rational function, does $f(R) := \deg (P) - \deg (Q)$ have a traditional name/notation?

Suppose $R : C \subseteq \mathbb{R} \rightarrow \mathbb{R}$ is a (univariate) rational function. Write $R=P/Q,$ where $P$ and $Q$ are polynomial functions $\mathbb{R} \rightarrow \mathbb{R}$. Is ...
1
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0answers
20 views

trail vs path in Graph Theory v/s Graphical Models

In my course on probabilistic graphical models, I learnt (quoting from page 36 of the book Probabilistic Graphical Models: Principles and Techniques by the same author) Path: We say that X1 , . . . ...
2
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0answers
31 views

Synonyms for “Theorem”

Some mathematical results, despite being formally proven, are not actually called "theorem". Examples include: Bertrand's postulate Pigeonhole principle Law of large numbers Do these names imply ...
3
votes
1answer
39 views

Variation on neighbourhood base

Suppose $\{\mathscr B(x) \mid x \in X\}$ is a collection of filters (or filter bases) on a set X, with each $x \in \cap\mathscr B(x)$. Then $$\mathscr T = \{U \subseteq X \mid (\forall x \in ...
1
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0answers
58 views

Does this lemma have a name or where can I find a proof?

Does the lemma at the bottom of this page have a name? Or could someone give me an idea of where I can find a proof? In case you can't access the link: Lemma $\ \ $ If $g$ is of class ...
7
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5answers
392 views

difference between nonpositive and negative numbers?

I am wondering if there is any difference between non-positive and negative numbers? I think that negative numbers mean "negative real numbers" and "Non-positive numbers" are negative real numbers ...
1
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1answer
52 views

What is a natural exact sequence?

I know what an exact sequence is, but I have searched for the definition of a natural exact sequence, and could not find it. Does "natural" perhaps mean some sort of preservation of structure? I ...
0
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0answers
30 views

Term for Multiple Functions that Share Critical Points?

Is there a term for when multiple functions share each other's critical points? Or, in general, when one function has a subset of the critical points of another?
0
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3answers
51 views

Is there a concept that describes the relationship between A and B where one is a subset of the other?

I feel like there must be a name for this. What is the relationship between A and B called if (A⊆B or A⊋B) is true?
2
votes
1answer
47 views

Why is the nuclear norm called so?

A simple question. Why is the sum of the singular values of a matrix called its nuclear norm? What is the origin of, and motivation for, this term? Apparently the term nucleus is sometimes used to ...
0
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0answers
53 views

What is the name of $\bigcap_{x\in G} xHx^{-1}$?

Let $G$ be a group and $H$ be a subgroup of $G$. What is the name of $\bigcap_{x\in G} xHx^{-1}$? I remember that there was a special name for this set but I forgot..
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1answer
19 views

Need help with finding if a function has a name.

I watched a first year senior year class in China and saw a function on the board. $$ H^n_x = x(x+1)(x+2)\cdots (x+n-1)$$ you can see a similar problem here in Chinese. I think this function ...
2
votes
2answers
50 views

What to call the relationship $\frac 1x + \frac1y = 1$

I've rediscovered the fun of geometry recently and found the beautiful and (to me at least) unexpected result that the two diagonal lengths of a regular unit heptagon are related by: $$\frac1a + ...
1
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0answers
17 views

Function 'result arity'

Given a map from $m$-tuples to $n$-tuples, $m$ can be referred to as the 'arity' of the mapping. What's the terminology for $n$? I feel like this should be brain-dead easy to find but my ...
1
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0answers
23 views

Is there terminology of the form “$n$-something form” that generalizes quadratic form and cubic forms?

By definition, a quadratic form is a homogeneous polynomial of degree $2$, and a cubic form is a homogeneous polynomial of degree $3$. Is there accepted terminology, like $n$-ic form, $n$-atic form, ...
2
votes
3answers
139 views

Is “=” an Operator?

I know that $+$, $-$, $\times$, and $/$ are all operators. But is $=$ an operator? For example, in the equation: $5 \times 5 = 25$ I know $\times$ is an operator, but is $=$?
7
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0answers
54 views

Is “slightly deform” a well defined concept in mathematical proof?

In topological proofs the phrase "slightly deform" is widely used. To me, although I can accept the idea intuitively, the phrase "slightly deform" does not sound like a strict mathematical concept. ...
2
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2answers
29 views

Origin of the term `quermassintegral'.

What is the origin of the term `quermassintegral'? I think this is a german word. What would be its literal translation in English? The definition of quermassintegrals from wikipedia: Let ...
1
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1answer
29 views

What is the name of logic which considers several distinct undefined objects?

Here is an example of a sentence of set theory written in first-order logic $\forall w_1\forall w_2\forall w_3\forall x \exists ! y\text{ } \phi(x,w_1,w_2,w_3)$ (where $\phi$ is a definable ...
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0answers
11 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
114 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 ...
0
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1answer
29 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
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)$a^{n+1}=aa^n$ ...
0
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0answers
21 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? $..., -7, -5, -3, -2, ...$
0
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1answer
27 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
30 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 ...
0
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1answer
17 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
27 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
69 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 ...
1
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1answer
24 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
48 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
64 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
votes
1answer
89 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
35 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?