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

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What is the correct term (and symbolic representation) of specific “un-modded” values?

Given $x \in \mathbb{R}$ such that $x \equiv x+k\cdot(b_u-b_l),\,\forall k\in\mathbb{Z}$, are there terms to describe the functions $$f:[b_l, b_u) \to[b_u, b_u+(b_u-b_l)):x\mapsto x+(b_u-b_l)$$ and ...
1
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1answer
14 views

What is “subordination” with respect to stochastic processes?

I'm building a model for a panel of counts, $\{n_{kt}\}_{k,t}$. As I read about regression methods for count models and the stochastic processes behind them, the concept of one random variable being ...
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0answers
17 views

Uniform vs variable geometries

Euclidean, elliptic and hyperbolic geometry are all different. But they do share a common property: every part of space is "the same". There are no distinguished points that have different properties. ...
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0answers
19 views

Spherical geometry vs elliptic geometry

Wikipedia says that "spherical geometry" and "elliptic geometry" are both the geometry of the surface of a sphere. It also asserts that these two geometries are not the same — but neglects to ...
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0answers
29 views

Is there a name for those relations that behave a bit like $<$?

Consider a fixed but arbitrary preordered set $X$. Is there a name for those binary relations $R$ on $X$ satisfying the following? They seem to show up a lot. (Note that every such $R$ is necessarily ...
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1answer
40 views

What is the name of this terminology?

Let $G$ be the group generated by a set $X=\{x_1,\cdots,x_n\}$. Then each element can be (not necessarily uniquely) written as a product of the form $x_{j_1}^{e_1}\cdots x_{j_k}^{e_k}$, where each ...
4
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1answer
48 views

Definiton of No Tear and No Paste

Topologists often mention an example beginning by "If there is no tear and no paste, then ...". As a student, I am confused with this "term", and I want to know the exact mean of it. First of all, ...
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4answers
57 views

What does it mean to say breaking RSA generically is equivalent to factoring?

I am giving a one hour presentation on the RSA crypto-system as one of the requirements for Masters degree. I just want to get some facts straight here. I was told casually by a professor that RSA is ...
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1answer
14 views

periodic free resolution

I am reading A Course in Hom.Algebra by Hilton & Stammbach He is using a term periodic free resolution with out saying what it is... I know what is a free resolution but i am not sure what is a ...
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1answer
14 views

Don't understand question: correlation w.r.t.

This is related to pattern recognition, specifically augmented neural networks. I do not understand what a correlation "w.r.t." is, or what it stands for. Anyone? Here is the question in full: ...
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1answer
10 views

reintepreting n-dimensional spaces as k-dimensional spaces of (n-k)-dimensional subspaces

Say you have defined a 3D space, which consists of 0D points. What is it called when you reinterpret it as a 1D space, in which each "point" is a 2D subspace of the original 3D space?
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29 views

What's the name of the form (123i + 321)

Okay, so $0.5$ 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 be written in this form $z = a\ e^{i ...
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0answers
24 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 $n=6$ ...
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0answers
36 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 ...
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0answers
83 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 ...
2
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1answer
51 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 ...
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0answers
10 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
34 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 ...
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0answers
33 views

Why is a linear order called linear?

Why does the definition of linearly ordered set imply that we can make a diagram of this set as a line in which a < b if and only if a is to the left of b?
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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
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1answer
72 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? ...
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0answers
20 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.
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0answers
27 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?
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0answers
29 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
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1answer
60 views

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

Suppose $R : C \subseteq R \rightarrow \mathbb{R}$ is a (univariate) rational function. Write $R=P/Q,$ where $P$ and $Q$ are polynomial functions $\mathbb{R} \rightarrow \mathbb{R}$. Is there a ...
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0answers
16 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
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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
56 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 ...
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5answers
351 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
48 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 ...
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1answer
31 views

Difference of 2 numbers [closed]

My question: Can the difference of 2 real numbers A and B, be negative? For example: A = 2, B = 4. Is the difference between A and B -2 or 2?
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0answers
26 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?
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3answers
50 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
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1answer
40 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 ...
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0answers
52 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
18 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
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2answers
48 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 + ...
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0answers
15 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 ...
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0answers
22 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, ...
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3answers
125 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
48 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
28 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 ...
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1answer
25 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
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?
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0answers
105 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
109 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)$a^{n+1}=aa^n$ ...