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

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2
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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
369 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
657 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
839 views

How to pronounce “tableaux”? [closed]

How do you pronounce Young tableaux? Does it sound just like its singular form?
8
votes
1answer
440 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
95 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
143k 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: $$\dfrac{dy}{dx}[2x2+y(x)2]=50x+2y(dy/dx)=0$$
2
votes
1answer
241 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
127 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
107 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
430 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 ...
0
votes
1answer
121 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 ...
8
votes
2answers
395 views

What is an element of a rng called which is not the product of any elements?

Let $R$ be a non-unital ring. Let $F:R\times R\longrightarrow R$ be a function given by the formula $F(x,y)=xy.$ Let $r\not\in\operatorname{im}(F).$ Such elements can exists, for example $2\in ...
4
votes
1answer
4k views

Base ten is called “decimal”; what's the name of numbers in base 15?

Good afternoon all, I was wondering is there a table of names for the base x of numbers? For example, I know that numbers in base 10 are called "decimal", those in base 2 are called "binary", base 16 ...
1
vote
1answer
127 views

terminology: euler form and trigonometric form

Am I right, that the following is the so-called trigonometric form of the complex number $c \in \mathbb{C}$? $|c| \cdot (\cos \alpha + \mathbf{i} \sin \alpha)$ And the following is the Euler form of ...
2
votes
1answer
85 views

Other Names for Sierpinski Reals / Leaning Tower of L'viv

There is a poset constructed by combining in a certain way the usual order on the reals with any well-order on the reals (I can provide details if needed). I've heard it called the "Sierpinski Reals" ...
0
votes
2answers
104 views

What is this called? (Equations involving percentages)

I am trying to describe our formulas to our users, and have forgotten the basic math term for these 2 types. First one is: $$y=x+10\% $$ $$z=y+10\%$$ if $x$ was $10$, then $z$ would be $12.1$. Other ...
0
votes
1answer
43 views

Two terminology question about relations

Is there a name for constructing a set from a relation (or, more generally speaking, from a set of pairs that are tuples)? For example, let $R = \{(0, 1), (1, 2), (2, 3)\}$; if you collect all the ...
1
vote
0answers
86 views

What are variables with fractional powers called?

What are variables with fractional powers ( e.g. $x^{\frac{3}{4}}$) called in contrast to monomials for positive integer powers?
1
vote
1answer
189 views

What is an honest basis?

In a comment to this question, the commentator stated that "the monomials form an honest basis for your vector space". To be honest, I never heard of that. Is this something elementary?
0
votes
3answers
263 views

What do I call a unit vector parallel to a coordinate axis?

What do I call an arbitrary element of this set of vectors? $$ \begin{align*} \{&\langle 1, 0, 0 \rangle, \\ &\langle 0, 1, 0 \rangle, \\ &\langle 0, 0, 1 \rangle, \\ &\langle ...
6
votes
2answers
3k views

Generalization of variance to random vectors

Let $X$ be a random variable. Then its variance (dispersion) is defined as $D(X)=E((X-E(X))^2)$. As I understand it, this is supposed to be a measure of how far off from the average we should expect ...
1
vote
1answer
34 views

Range mapping process name

Does the process of mapping a random range, for example, [4; 55] to [0; 1] have a name? Maybe it's called normalization?
0
votes
2answers
304 views

How does mathematical coefficients differ from “physical coefficients”?

In the Talk page of Wikipedia Coefficient I read this comment: As far as I can tell, the mathematical definition should imply that coefficients are unitless, however, the physical sciences have ...
60
votes
5answers
3k views

Why “characteristic zero” and not “infinite characteristic”?

The characteristic of a ring (with unity, say) is the smallest positive number $n$ such that $$\underbrace{1 + 1 + \cdots + 1}_{n \text{ times}} = 0,$$ provided such an $n$ exists. Otherwise, we ...
3
votes
1answer
121 views

A poset that's the union of the lower sets

Let $(P,\leq)$ be a poset, and let $\downarrow\! p = \{ x\leq p\}\subseteq P$. Let $M\subseteq P$ be the subset of all maximal elements of $P$. Question: is there a specific term for a poset ...
3
votes
1answer
228 views

What's the correct name for a geometric solid that's a beanbag?

enter image description hereMy daughter is in the first grade, and I'm having a good deal of fun trying to determine the shapes of irregular geometric solids. I'm stuck on the good, old beanbag. ...
1
vote
1answer
157 views

Using two or more “such that”.

I'm wondering if it's right (and not abusive or ugly) the use of two, or more, "such that" in a definition, and in the dealing with mathematical objects. I know that I could find equivalences for such ...
5
votes
1answer
2k views

Function theory: codomain and image, difference between them

Can't figure out the difference between them. I have read wiki article about codomains and images, but what is the difference? It seems confusing the examples part in codomain article. How can we ...
3
votes
0answers
188 views

Constructing a semigroup from a small category

The following was given as an example for a semigroup without an identity: Finite sets of matrices of varying dimensions, where the product $A*B=\{PQ \mid P \in A, Q \in B \text{ and } ...
5
votes
3answers
514 views

Generic Elements of a Set.

Mild Motivation: In writing a post about the Baire Category Theorem, I learned the neat fact that a "generic" $f\in C^{0}([a,b], {\mathbb R})$ was nowhere differentiable and not monotone on any ...
0
votes
1answer
159 views

Is topological perimeter not defined anywhere in the literature?

I don’t understand why I have never seen topological perimeter defined anywhere in the literature. Is it not a useful/interesting notion? Let’s consider the following example. Suppose that $M$ is the ...
3
votes
3answers
277 views

Is there a name encompassing both limit inferior and limit superior

Is there a mathematical term which would include both liminf and limsup? (In a similar way we talk about extrema to describe both maxima and minima?) The only thing I was able to find was that some ...
3
votes
1answer
5k views

Relationships among the terms “slope”, “parameter”, and “coefficient”?

In $y=mx$, is $m$, are there different implications of referring to $m$ as a "slope", a "coefficient", a "parameter"? Or perhaps the "slope coefficient" or "slope parameter"? For context, I am ...
1
vote
2answers
974 views

Is there actually a difference when we say 'perpendicular' vs 'tangent'

I find myself often getting these two words mixed up a lot. So let's say I have a simple graph of $y = t^2$ and $x = t$. If a line is tangent to the curve at the origin, it would only be the line y ...
3
votes
2answers
119 views

What's the most concise way to refer to this shape?

What would you call this shape? Not the shape in green, I mean the entire object.
3
votes
3answers
3k views

Definition of “maximal” and “minimal” [duplicate]

Possible Duplicate: difference between maximal element and greatest element When I first encountered the terms maximal and minimal, I confused them with maximum and minimum. Many of my ...
-1
votes
3answers
110 views

Is there a name for this type of groups?

A group having more than one elements with only one element as inverse of each element in the group. Is there any name for that? Let me explain my question: $(\{0\}, +)$ is a trivial group with ...
25
votes
6answers
15k views

Is there any difference between mapping and function?

I wonder if there is any difference between mapping and a function. Somebody told me that the only difference is that mapping can be from any set to any set, but function must be from $\mathbb R$ to ...
4
votes
3answers
196 views

Does this generalisation of Latin squares have a name?

I am interested in looking at $n\times n$ tableaux (or matrices) in which (WLOG) each integer in $\{ 1, 2, \ldots, n \}$ occurs exactly $n$ times. This is a generalisation of a Latin (or even ...
1
vote
2answers
155 views

Is $i\in n\Leftrightarrow i\in\{0,\ldots,n-1\}$ a common knowledge?

Is $i\in n\Leftrightarrow i\in\{0,\ldots,n-1\}$ for every $n\in\mathbb{N}$ a common knowledge? I am to publish a research article which uses this notation for convenience. The question: Should I ...
0
votes
3answers
3k views

What do these terms mean: commutative, associative, distributive

I am reading a book, and I am trying to understand what the writer really mean by the following terms. I would like to understand what these words mean in relation to the examples. In regular ...
2
votes
0answers
57 views

terminology clarification needed: projection of a measure to an open set

I'm reading in Doobs "Classical Potential Theory and its Probabilistic Counterpart" and I'm having trouble with terminology. Specifically, in Part I chapter 6, he talks about the projection of a ...
1
vote
0answers
120 views

Is there a name for a number whose factors' exponents are all prime?

For instance, 864, whose factorization is 2^5 x 3^3.
11
votes
0answers
150 views

Why are parabolic subgroups called “parabolic” subgroups?

I used to think that things called "parabolic" must have something to do with parabolas or their defining quadratic equations. In fact, terms like parabolic coordinate, parabolic partial differential ...
15
votes
5answers
4k views

What do you call numbers such as 100, 200, 500, 1000, 10000, 50000 as opposed to 370, 14, 4500, 59000

There are different categories of numbers that we use every day. Integers that written in decimal notation have 1, 2 or 5 as the leading figure, followed by none, one or more zeros. These are very ...
2
votes
3answers
137 views

Name for a bipartite graph in which one vertex set has maximal degree 1?

I'm looking for a specific name for a bipartite graph $(U,V,E)$ in which there is at most one edge incident to each vertex $u \in U$. That is, $|E_u| \le 1$ for all $u \in U$, where $E_u = \{(u,v) \in ...
4
votes
4answers
902 views

Name for “decimals” in other bases?

In grade school, numbers that use a positional notation along with a decimal point (to delimit integer and fractional parts of a number are called "decimals". This "point" notation is easily ...