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

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4
votes
1answer
220 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.
0
votes
1answer
9 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 ...
2
votes
1answer
32 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 ...
0
votes
0answers
16 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. ...
1
vote
0answers
18 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 ...
1
vote
0answers
19 views

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

Question. Consider a fixed but arbitrary preordered set. Is there a name for those binary relations $R$ on that set which, like "$<$", satisfy the following conditions? Such relations seem ...
4
votes
1answer
47 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, ...
7
votes
5answers
2k views

difference between theorem, lemma and corollary

Can anybody explain what is the basic difference between theorem, lemma and corollary. We have been using it for a long time but I never paid any attention. I am just curious to know.Thanks a lot.
2
votes
4answers
56 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 ...
0
votes
1answer
13 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 ...
0
votes
1answer
13 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: ...
0
votes
1answer
9 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?
17
votes
3answers
25k views

Difference between axioms, theorems, postulates, corollaries, and hypothesis

I've heard all these terms thrown about in proofs and in geometry, but what are the differences and relationships between them? Examples would be awesome! :)
1
vote
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 $n=6$ ...
0
votes
0answers
28 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 ...
1
vote
0answers
81 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 ...
0
votes
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 ...
2
votes
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 ...
8
votes
3answers
7k views

Why does a limit at infinity not exist?

I read in Stewart "single variable calculus" page 83 that the limit $$\lim_{x\to 0}{1/x^2}$$ does not exist. How precise is this statement knowing that this limit is $\infty$?. I thought saying the ...
1
vote
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)$a^{n+1}=aa^n$ ...
0
votes
0answers
9 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 ...
2
votes
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 ...
1
vote
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 ...
0
votes
1answer
17 views

Nomenclature for the function appearing in Carathéodory's criteria of differentiability

In my previous question Concerning Carathéodory's criteria of differentiability and a proof that differentiable implies continuous I stated the criteria as follows: There exists a function $\phi$ ...
1
vote
1answer
174 views

What is the purpose of the characteristic exponent?

I just came across the term "characteristic exponent" of a field $\Bbbk$. Apparently, it is equal to $1$ if $\DeclareMathOperator{\c}{char}\c(\Bbbk)=0$ and it is equal to $p=\c(\Bbbk)$ otherwise. ...
-2
votes
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?
1
vote
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
71 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
votes
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
votes
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 ...
2
votes
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 ...
0
votes
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?
2
votes
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 ...
7
votes
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 ...
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
vote
0answers
15 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
votes
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 ...
1
vote
4answers
3k views

What is a fraction in which the greatest common factor of the numerator and the denominator is 1?

What is this fraction: A fraction in which the greatest common factor of the numerator and the denominator is 1?
11
votes
0answers
103 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 ...
1
vote
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 ...
0
votes
1answer
69 views

Is there a name for a lattice that is isomorphic to its dual?

If we have a lattice and we invert the order, we again obtain a lattice, called the dual lattice. Is there a name for a lattice that is isomorphic to its dual lattice?
1
vote
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 ...
48
votes
8answers
3k views

Is $1$ a prime number?

Is 1 classified as a prime number? And if so, why? If not, why not?
7
votes
1answer
227 views

Maximal volume for given surface area of an $n$-hedron

Is there a term for a polyhedron with $n$ faces (or, similarly, $n$ vertices) that maximises the enclosed volume for a given surface area (equivalently, minimises the surface area for a given volume)? ...
6
votes
2answers
282 views

If $f''(x)=0$ but is not an inflection point, what is it called?

If the second derivative of a function $f(x)$ equals zero at point $x_0$ ( $f''(x_0)=0$ ), the point is an inflection point if the concavity changes. Here's an example of an inflection point. ...
-3
votes
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?
0
votes
1answer
96 views

“componentwise constant”?

This is a trivial vocabulary question. It seems to me that "constant on every connected component of the domain" would be a reasonable definition of the term "componentwise constant", provided that ...
0
votes
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?
85
votes
5answers
7k views

What is the Riemann-Zeta function?

In laymen's terms, as much as possible: What is the Riemann-Zeta function, and why does it come up so often with relation to prime numbers?
0
votes
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?