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

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2answers
30 views

Is “foot of $X$” a common term in math? General questions about the foot?

I moved and started taking classes at a new university. One term that has come up several times in class is the "foot of $X$" which has notation similar to a bracket but with the top bits cut off. ...
1
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0answers
17 views

Is the translation of open and closed sets to some language non-antonym preserving?

Maybe more than one person though, before you were given the definition of closed set, that they were the sets that are not open, i.e. that the property of open and closed being antonyms were ...
0
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0answers
15 views

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 ...
0
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0answers
18 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
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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 ...
1
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0answers
30 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 ...
2
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1answer
42 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, ...
2
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4answers
58 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
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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 ...
0
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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: ...
0
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1answer
11 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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0answers
30 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
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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 $n=6$ ...
0
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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 ...
1
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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 ...
0
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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 ...
1
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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 ...
2
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2answers
30 views

Bilinear Map vs Inner Product

What is the difference between a Bilinear Map and a Inner Product?
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0answers
34 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
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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
73 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
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 ...
0
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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?
2
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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 ...
1
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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 ...
7
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5answers
352 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?
0
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0answers
27 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 ...
0
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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..
0
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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
votes
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 + ...
1
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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 ...
1
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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, ...
3
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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
votes
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 ...
1
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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?
11
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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 ...