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

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3
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1answer
773 views

What does it mean for a function to be bounded near $\infty$?

Suppose $f(z)$ is some analytic function which is bounded near $0$. Then $f(1/z)$ is bounded near $\infty$. What exactly does that last statement mean practically? Does it mean $|f(1/z)|$ is bounded ...
3
votes
0answers
357 views

Etymology of the word “pole”?

In his book Control System Design, Bernard Friedland writes (section 4.2, page 115): The roots of the denominator [of a rational function] are called the poles of the transfer function because $H(...
3
votes
2answers
346 views

Notation for covariant derivative

I'm reading John M. Lee's book " Riemannian Manifolds". On page 57, the covariant derivative of $V$ along a curve $\gamma$ is defined, where $V$ is a vector field along $\gamma$. It is denoted by $...
-1
votes
1answer
98 views

Meaning of a Logical Operator

Is it possible to know what those operator mean if they must be involved in this logicical condition? What is all the possible meaning of those two symbol if you don't know the symbol's meaning ...
11
votes
6answers
1k views

What's the difference between tuples and sequences?

Both are ordered collections that can have repeated elements. Is there a difference? Are there other terms that are used for similar concepts, and how are these terms different?
9
votes
3answers
1k views

Why were filters and nets in topology named filters and nets?

I am wondering why do mathematicians categorizes some structures and called them filters , Nets? In English, filter means: A porous material through which a liquid or gas is passed in order to ...
1
vote
1answer
168 views

Name of binary relation: if $(x, y)\in R$ then there is no $z$ such that $(y, z)\in R$

Is there a term for a binary relation $R\subset A^2$ on some set $A$ such that if $(x, y)\in R$ then there is no $z$ such that $(y, z)\in R$ ? Are there any examples of it? Are there any related ...
4
votes
1answer
133 views

What is the correct terminology to say that $\small f(x)=a+bx+cx^2+…$ can be expressed by $\small g(x)=A(1-x)+B(1-x)(2-x)+C(1-x)(2-x)(3-x)+… $

Hm, I do not even know the best formulation for my question in the header. It is not for the math but for the proper writing/terminology. I've come across the term "base change" recently but the ...
3
votes
0answers
139 views

The polynomial where only the terms in the multinomial series where each variable's exponent is $>0$ are kept?

I'm wondering if there's a special polynomial with a name out there with $x_1,x_2,\ldots,x_k$ as variables that's defined like this: $$ \sum_{\substack{i_1>0,i_2>0, \ldots,i_k>0 \\ i_1 +i_2+...
2
votes
1answer
122 views

Terminology for a property that holds in the finite but not infinite case?

(I apologize if this is a duplicate, but I don't know what terms to search for. Please feel free to close this if this has already been asked.) There are some properties of finite objects that don't ...
0
votes
1answer
2k views

Right and Left arrow notation in proof.

I'm studying vector spaces and I'm reading a proof where the authour uses the symbols $$(\Rightarrow)$$ and $$(\Leftarrow)$$ when proving a theorem. He doesn't use them in context, but rather ...
1
vote
1answer
235 views

What's are these index objects called? And $\mathrm{\LaTeX}$ \sum question

I want to refer to $$A_iB_jC_k$$ using $$\psi(ijk) = A_iB_jC_k$$ So that I can write out quite overwhelming-looking sums of ABC terms as sums of terms that look like 123, 231, 113, etc. If I am not ...
3
votes
0answers
77 views

Is there are a name for a simplicial complex that is homotopic to the clique complex of its 1-skeleton?

A hollow octahedron is a nice triangulation of the sphere, because once you know the edges, you know everything. The vertices are obviously the ends of the edges, and the faces are any collection of ...
8
votes
2answers
302 views

Explaining the motivation behind two different definitions of a generic point

This question is primarily regarding the definition of a generic point of a topological space that I came across in Qing Liu's Algebraic Geometry and Arithmetic Curves. First I will give the ...
0
votes
1answer
74 views

What should applying the Runge-Kutta-method 4 on a differential equation be called?

What should applying the Runge-Kutta-method 4 to a differential equation using a program be called? Does it qualify as "simulation"? I'm asking because I'm writing a document for school, and now I'm ...
3
votes
1answer
123 views

When are quantities considered mere numbers?

I don't understand how an angle (radians) is considered a mere number, while degrees (for example) aren't. I think that degrees are different in that they are defined arbitrarily, but I don't find ...
3
votes
3answers
8k views

why do we use 'non-increasing' instead of decreasing?

In english based math language it seems that non-increasing $\Longleftrightarrow$ less or equal (non-strict decreasing) decreasing $\Longleftrightarrow$ strict less ( strict decreasing) ...
4
votes
1answer
3k views

What does “relatively closed” mean?

Let $S\subset U$. What does it mean to say that $S$ is relatively closed in $U$? Also $U\subset\mathbb{R}^{n}$ is open and bounded, but I don't know if that's essential. Here follows an example from ...
27
votes
9answers
14k views

What's the difference between stochastic and random?

What's the difference between stochastic and random? I've read in the Portuguese Wikipedia that there's a difference, but I still didn't see this point on English Wikipedia.
13
votes
3answers
312 views

Is the thingie/cothingie distinction absolute?

Is there some inherent quality of a mathematical object that marks it as being "naturally" a thingie or a cothingie? Suppose, for example, that two mathematical concepts, say, doodad and doohickey, ...
15
votes
3answers
489 views

Etymology of “topological sorting”

This may be a dumb question, but what's "topological" about topological sorting in graph theory? I thought topology was related to geometry and deformations.
1
vote
0answers
96 views

Need terminology for components of pullback/pushout squares (or of limits/colimits)

Is there a name for the two morphisms $X\to Z$ and $Y\to Z$ that determine a pullback? Likewise, is there a name for the two morphisms $Z\to X$ and $Z\to Y$ that define a pushout? Also, is there a ...
2
votes
4answers
1k views

$y'''-y=x^{2}$ has solution — `“multiplicity”`?

The page 667 of the book (sorry not in English) claims $y'''-y=x^{2}$ to have the solution $$y(x)=C_{1}e^{x}+e^{-x/2}\left(C_{2} \cos \left( \frac{\sqrt{3}x}{2} \right)+C_{3} \sin\left(\...
2
votes
2answers
10k views

Complementary Solution = Homogenous solution?

I have calculated solutions to homogenous equations but is the complementary solution mentioned here the same as the homogenous solution? Let's take example $y''-3y'+2y=\cos(wx)$ and now ...
32
votes
6answers
5k views

Lemma vs. Theorem

I've been using Spivak's book for a while now and I'd like to know what is the formal difference between a Theorem and a Lemma in mathematics, since he uses the names in his book. I'd like to know a ...
4
votes
3answers
219 views

Probability Term for something that defies the odds.

I'm not a mathematician; I just wandered over here from Writers SE and am hoping you guys can help. I'm writing a novel in which the theme is characters beating the odds. (It's a future dystopia, the ...
1
vote
0answers
72 views

sheaf of hyperplanes

I've got a question on terminology. In 3d, a set of planes intersecting at a point is called a bundle of planes. A set of planes intersecting along a line is called a sheaf of planes. My question ...
11
votes
5answers
5k views

Del. $\partial, \delta, \nabla $: Correct enunciation

I've come across various different symbols being pronounced as "del". What is the internationally accepted del? If not internationally, then what's the English/American(specify which one if they are ...
3
votes
1answer
158 views

What's this type of chart called?

What's the name of this type of chart?
4
votes
2answers
147 views

Is there a name for a function that maps a set into a subset of itself?

Say $X$ is a set of subsets of some arbitrary set. Is there a name for a function $f:X\to X$ satisfying $f(A)\subseteq A$ for all $A\in X$? More specifically, is there a name for an $f:X\to X$ with $...
0
votes
2answers
37 views

Understanding the Lie algebra $o_{V,B}$

I am learning about Lie algebras and I do not understand the following subalgebra of $\mathfrak gl_{V}$. Let $V$ be a vector space and $\mathfrak gl_{V}$ be the Lie algebra of endomorphisms on $V$. ...
2
votes
1answer
103 views

What's the usual name for this kind of integration?

When I did further maths at college, we spent a couple of hours on a particular kind of integration, where the function was integrated with respect to the length of the path along the function, ...
8
votes
2answers
262 views

Terminology: center (of a group, of a ring, …)

What is the etymology of the word "center" as used in abstract algebra, e.g. the center of a group, or of an algebra? My best guess is that it might've come from matrix algebras, where often the ...
1
vote
2answers
245 views

When is a calculation undefined and when is it indeterminate?

I have the sense that f(x0,y0, ...) is indeterminate if the limit can be any complex number if we choose the right path to (x0, y0, ....). MathWorld and Wikedidia mention the subject, but it wasn't ...
8
votes
1answer
113 views

Does the subgroup $\{g\in G\,|\,o(\operatorname{Cl}(g))<\infty\}$ of $G$ have a name?

Let $G$ be a group. We can define $$F(G)=\{g\in G\,|\,o(\operatorname{Cl}(g))<\infty\},$$ where $o(\operatorname{Cl}(g))$ is the order (cardinality) of the conjugacy class of $g$ in $G$. This set ...
8
votes
1answer
770 views

Being isomorphic as representations of a group G

Let $G$ be a finite group. What is meant by two finite dimensional vector spaces (over $\mathbb{C}$) $V$ and $W$ being "isomorphic as representations of $G$"? To show that we have such an isomorphism, ...
2
votes
1answer
110 views

Is there a name for this homomorphism from $G$ to $\operatorname{Sym}([G:H])?$

Let $G$ be a group and $H$ its subgroup. Let $n=[G:H]$ be a cardinal number. Let $C=\{aH\,|\,a\in G\}.$ We have $n=\operatorname{card}(C).$ We define for any $g\in G$ the map $\phi_g:C\to C$ by the ...
1
vote
1answer
383 views

Turning a Product of Events into a Product of Conditional Probabilities

Is there a name for the following identity? $$ \begin{align*} & \Pr\left(\bigwedge_{i=1}^n A_i \mid B \right)\\ &= \Pr\left(A_1 \mid B \right) \cdot \Pr(A_2 \mid A_1 \wedge B) \cdot \Pr(A_3 ...
3
votes
1answer
759 views

Notation in linear algebra, what are $N(T)$ and $R(T)$

Working through some stuff I found on the web, I came across a notation that I haven't seen in my textbooks. In this problem, $ T: P_4(\mathbb R)\rightarrow \mathbb R^4 $ is a linear transformation, ...
3
votes
2answers
891 views

How to pronounce “tableaux”? [closed]

How do you pronounce Young tableaux? Does it sound just like its singular form?
9
votes
1answer
462 views

Why are modules called modules?

I know that a module is a generalization of a vector space, but I would like to know why are modules called modules? Thanks for your kindly help.
1
vote
1answer
97 views

How to mathematically formulate and illustrate the following statement?

English is not my native language and I'm trying formulate the following statement as simple and as mathematical as I can: A code is composed of a family name followed by n option(s):  &...
3
votes
4answers
163k views

What is the formula to calculate Profit Percentage?

Let cost price of an item be $C$, selling price be $S$. Assume the seller makes a profit. Then profit would be: $P = S - C$. Now, what is the formula for calculating Profit Percentage? $P \% = \...
0
votes
2answers
1k views

What is usually meant by logit scale or log scale?

This question is more about the math terminology than about the math itself. Say we have x = logit(p). If one says "logit scale" does he mean: the scale of p, or ...
2
votes
1answer
2k views

What do [] mean and what does it mean if it is used in an equation?

What do the square bracket symbols mean? Are they what I hear are "sets"? And when it is in an equation, how is it interpreted? Here is an example: $$\dfrac{dy}{dx}[2x2+y(x)2]=50x+2y(dy/dx)=0$$
3
votes
1answer
268 views

Extension and reduction of the structure group

Let $H\subset G$ be a subgroup and $\pi:P\to B$ be a principal $H$-bundle. $G$ has a left $H$ action and one can define a principal $G$-bundle $\pi':P\times_H G\to B$ where $P\times_H G$ is ...
4
votes
1answer
131 views

Ellipse: Name for the ratio $a/b$?

Given an ellipse with semi-major axis $a$ and semi-minor axis $b$, is there a "common" (or at least standard) name for either $\frac{a}{b}$ or $\frac{b}{a}$? I keep wanting to (informally) call it ...
1
vote
1answer
111 views

Point travels around curve

I wonder what does this mean: Point travels around curve. I try to figure out some math explanation in the book and I can't move forward because I can't understand these words. I can understand when ...
2
votes
0answers
436 views

Are derivative and differential the same thing?

(Sorry for bad English.) Let $f:\mathbb R^n\to\mathbb R^m$, $x\in\mathbb R^n$. What is a drivative $f'(x)$? It is the linear map $f'(x):\mathbb R^n\to\mathbb R^m$, $h\mapsto (f'(x))(h)=:f&...
0
votes
1answer
126 views

Planar graph constructed from the edges of another planar graph

Let $G$ be a planar graph. We construct a graph $H$ from $G$ in the following manner : The vertices of $H$ are interior points of the edges of $G$, one on each edge. Two vertices of $H$ are joined ...