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

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0
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1answer
19 views

Measures which are constant when not zero

Let $S$ be a finite set. I want to consider measures $\mu$ on $S$ which are constant only when not zero. As an example, let $S$ be $\{a,b,c,d,e\}$, and take the measure: ...
0
votes
1answer
13 views

Connectivity with minimal width

Suppose you have a land-estate $L \subseteq \mathbb{R}^2$. You want to be able to drive in your car from each point in $L$ to each other point in $L$. The width of the car is $w$. So, it is not ...
3
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0answers
19 views

About Special and Extra-special $p$-groups

A $p$-group $G$ is said to be special $p$-group if $Z(G)=[G,G]=$ elementary abelian. A $p$-group $G$ is said to be extra-special if $Z(G)=[G,G]=$ elementary abelian of order $p$. The ...
5
votes
1answer
73 views

Are the terms 'clan' and 'tribe' common in mathematics?

In the book 'Vector Measures' by Dinculeanu, he starts the discussion by talking about "classes of sets", and introduces two pieces of terminology I've never seen before, and can't find any evidence ...
4
votes
0answers
34 views

What do you call two groups with only trivial homomorphisms between them?

Suppose $G$ and $H$ are groups, and all group homomorphisms $G \to H$ and $H \to G$ are trivial. Is there a common term to describe such a pair of groups with? Like, “$G$ and $H$ are [...]”, or “$G$ ...
3
votes
2answers
468 views

Why are contravariant functors called contravariant?

I'm just now learning a bit of category theory, and there often seems to be a certain notion, like limits for instance, and if you inverse certain arrows, you obtain a co-object related to that notion ...
1
vote
1answer
19 views

Term for using a number as an exponent (complementing “raise to the power of …”)

If we have an equation we want to solve such as $\sqrt{x} = 3$, we can say something such as square both sides or "raise both sides to the power of 2", to arrive at $x = 9$. So $3 \rightarrow 3^2$ ...
5
votes
2answers
74 views

Probability: mathematically what does it mean to say “let $X$ be a random variable WITH a cdf/pdf”

I don't quite understand what people mean by let "$X$ be a random variable WITH a cdf/pdf". For example, there is a question that says: "Let X be a random variable with the 3-parameter Weibull pdf and ...
2
votes
0answers
23 views

Are there generic terms or names to refer to elements of the domain, codomain, and range of a function?

Say I have a function $f:A\rightarrow B$. Is there some generic term or name for $x\in A$? (Something like "input" maybe? My goal is just to see if there's any standard term that's more succinct than ...
0
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0answers
6 views

Parallel series systems defined in OR? Isomorphism to SP-graphs in graph theory?

The series parallel graph definition is inductive with respect to series operation and parallel operation in graph theory. In comparison to series parallel systems in OR (Operations Research) and ...
0
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0answers
9 views

Inversely Proportional and Inversely Related

Suppose that we have a formula like $y=\frac{1}{\sqrt{x}}$. Is it correct to say that y is inversely proportional to x? what about y is inversely related to x? If not, what other phrase should we use? ...
0
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1answer
68 views

“This statement is false” - Propositional Logic

In a text I am reading, the section on Propositional Logic says that a proposition is a statement that is either true or false, but not both true and false. Also, from this lecture online, the ...
0
votes
1answer
29 views

Terminology re Bijection elements vs. Relation elements

Suppose I have bijection $X \rightarrow Y$. Is there a specific term for an element of $X$, which conveys the fact that the element can only map to one element of $Y$? E.g. "key" ? Now suppose I ...
28
votes
2answers
2k views

What comes after length, area and volume? [duplicate]

The length of the unit is 1. The area of the unit square is 1. The volume of the unit cube is 1. The $\color{red}{???}$ of the unit tesseract is 1. The $\color{blue}{???}$ of the unit ...
1
vote
3answers
172 views

“This statement is false.” [duplicate]

In propositional logic, a proposition is a statement that is either true or false, but not both. In a text I am reading and in many others, "this statement is false" is not considered a proposition. ...
0
votes
0answers
48 views

The expression “back to the envelope calculation”, what does it mean?

I'm french and one of my teacher use often the expression : "back to the envelope calculation", but I don't find any satisfactory translation. If someone know the french, and a good translation of ...
0
votes
2answers
37 views

Growth of debt: exponential, logarithmic, or linear? [closed]

If I have increasing debt that I don't intent to pay off for a really long time, how would I prefer to have it grow? Exponentially, logarithmically, or linearly?
1
vote
1answer
24 views

What is the difference between to “draw” and to “describe”

Reading the famous book "The Elements of Euclid". And I found this: Draw [a dotted line] (post. I.), describe [a triangle], and produce [another line]. In here, the word "Draw" and the word ...
0
votes
1answer
25 views

Meaning of denseness in a $L^p$ spaces?

I am currently studyind Density theorems in $L^p$ - spaces. In that, I have encountered a theorem which goes like this - The space of integrable simple functions is dense in $L^p $(E, $\mathcal{A}$ ...
1
vote
1answer
71 views

Does the function $f(x) = \frac{x}{|x|}$ have a name?

Does the function $$f(x) = \frac{x}{\operatorname |x\ |}$$ have a common name in mathematics?
3
votes
0answers
45 views

Does the function $\log(1+\exp(x))$ have a conventional name?

Does the function $\log(1+\exp(x))$ (or the function $\log(1+\exp(-x))$) have a conventional or at least fairly common name? Alternatively, is it closely related to some reasonably well-known, named ...
1
vote
2answers
32 views

Problem in understanding definition of absolutely continuous?

Suppose $(E, \mathcal{A})$ is a measurable space. Let $\mu$ and $\gamma$ be two distinct measures of this space. Now we say that $\gamma$ is absolutely continuous with respect to $\mu$ if for every $A ...
2
votes
1answer
48 views

Is “the reals” a slang term for $\mathbb{R}^d$ where $d = 1$?

Often times I see people referring to certain functions as a mapping from $\mathbb{R}^d$ to "the reals", are they referring to $\mathbb{R}^d$ where $d = 1$? Sorry for the potentially trivial ...
1
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2answers
63 views

How to call a mathematical space “$(\mathcal S, f)$” consisting of set $\mathcal S$ and function $f : \mathcal{S \times S} \rightarrow \mathbb R$?

Is there a specific standard name for a mathematical space "$(\mathcal S, f)$" consisting of a set $\mathcal S$ and a function $f : \mathcal{S \times S} \rightarrow \mathbb R$; perhaps together with ...
0
votes
1answer
56 views

What is $K^n$ when $K$ is a field?

where I am not fully satisfied that $K^n$ is a field, rather $n$ pieces of fields under cartesian product such that $K\times K \times K \times \dots \times K$ where $n$ pieces of $K$. Also $K^n$ ...
1
vote
3answers
30 views

Meaning of the numbers in a sequence definition

The sequence $(a_n)$ tends to $+ \infty \iff$ given any number $C$, there's a number $N$ such that $n > N \implies a_n \ge C.$ Given a certain $N$ it's not difficult to prove the implication, ...
1
vote
1answer
32 views

Definition request: explicit definition of covering compactness in terms of set notation

Part of my confusion with covering compactness stems from the fact that it is a definition given almost completely in a high level manner (in English no less). When I look at: A set $A \subset ...
0
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1answer
30 views

Name of set with Jordan measure zero

In German we have a special work for sets with Jordan measure zero: "Jordansche Nullmenge". Does there exist a special name for such a set in English as well?
1
vote
4answers
51 views

Terminating each branch of a proof with $\square$

My question is a variation on this one. I have a proof which divides at the top level into a number of mutually exclusive cases, with further partitioning within that. Is it reasonable to place a ...
2
votes
0answers
43 views

What is the Name of the Function $f(x) = \frac{x + |x|}{2}$

I'm dealing with a function that can be written in all of the following forms: $$f(x) = \frac{x + |x|}{2} \\ = x\ \Theta(x) \\ = \int_{-\infty}^x \Theta(y) \operatorname{d}y,$$ where $\Theta(x)$ is ...
4
votes
4answers
164 views

Iff Interpretation

I understand that (1) "$A$ if and only if $B$" ($A\iff B)$ means that (2) "$A$ implies $B$ and $B$ implies $A$" $(A\implies B)\land (B\implies A)$. The phrase "$A$ if and only if $B$" sounds as ...
1
vote
1answer
11 views

Name for the maximum size of $f^{-1}(w)$

Let $X$ and $Y$ be sets, and $f:X\to Y$ be a function. Is there a name for the following quantity? $$\sup_{y\in Y}\ \big|f^{-1}(y)\big|$$ I was thinking the "maximal valence of $f$".
-4
votes
2answers
38 views

Is there any complex value for $x$ where $|x| < 0$?

What I'm really asking is if I get to a point in a calculation where I have $|x| = -4$, do I say There is no solution for $x$ or do I say There is no solution for $x ∈ ℝ$
0
votes
0answers
19 views

Equation with L2-distance of two single values

I am studying the equation which includes the L2-distance term $||a_n - b_n||_2$ (taken from http://caffe.berkeleyvision.org/doxygen/classcaffe_1_1ContrastiveLossLayer.html). Here, $a$ and $b$ are ...
2
votes
1answer
55 views

Discrete Mathematics Wording Difference Between “Show” and “Prove” [duplicate]

I just took a midterm for a Discrete Mathematics class. On couple of questions, it says "Show why this is true". For example, a sample question might have said "Show that five consecutive numbers is ...
0
votes
1answer
26 views

Particular name for the diagonal matrix with only one non-zero components

I need to deal with such matrices who are diagonal and with only one non-zero component. But, how should I call them? e.g, $$A=\begin{bmatrix}1& 0 &0 \\ 0 & 0& 0\\ 0 & 0& 0 ...
0
votes
2answers
80 views

Terminology: how to call this relation (inequality/inequation)?

dear native speakers, how would you call the relation like this? $$\ln(\sqrt{5})<\ln(5^2)$$ Is it inequality or inequation? Motivation for this question: In Czech we have different words for a ...
0
votes
1answer
17 views

Are Cartesian coordinates considered to be curvilinear coordinates?

In the wikipedia page on curvilinear coordinates it is said: "Well-known examples of curvilinear coordinate systems in three-dimensional Euclidean space (R^3) are Cartesian, cylindrical and spherical ...
150
votes
11answers
14k views

In simple English, what does it mean to be transcendental?

From Wikipedia A transcendental number is a real or complex number that is not algebraic A transcendental function is an analytic function that does not satisfy a polynomial equation However these ...
2
votes
1answer
52 views

Is foliation the right word?

Let say $C$ is a Jordan curve (rectifiable, closed with not self-intersections). Is there a term for the family $\{tC\mid t\in\mathbb R\}$? Is "foliation" the right word?
1
vote
1answer
42 views

Does this fact about concurrent lines have a name?

Let $ABC$ be a triangle. Pick $P$, $Q$, $R$ on sides $BC$, $CA$, $AB$, respectively, and then points $S$, $T$, $U$ on the sides $QR$, $RP$, $PQ$ of triangle $PQR$, respectively. Consider the ...
0
votes
1answer
52 views

$\cos(\theta) = \cos(-\theta)$ which means that the cosine function is (blank)?

I understand why $\cos(\theta) = \cos(-\theta)$ but I don't know what the specific property this question is asking for is - PreCalc homework. Likewise, another question is: $\sin(-\theta) = ...
1
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0answers
48 views

Terminology: What is the tuple $(x, x)$ called?

I need to write a few functions in PowerShell which operate on sequences, but I want to use accepted mathematical terminology if possible. I will be using the following terminology ($S$ and $T$ are ...
0
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4answers
96 views

Scientific name of square root of negative number [closed]

How do you call a number in the form: $\sqrt{-4}$ ? A non real number?
1
vote
1answer
27 views

Group morphism or group homomorphism?

I apologize for my question that might sound stupid, but i noticed that my lecturer in abstract algebra course uses always "group morphism" instead of "group homomorphism". In the books i see it ...
0
votes
1answer
29 views

What is the name for numbers using a comma for a decimal separator versus a dot

I am curious to know if there is a specific name for numbers that use a comma for a decimal separator and a dot for a thousands separator as opposed to numbers that are the reverse. For example: ...
49
votes
6answers
8k views

Why does the Cauchy-Schwarz Inequality even have a name?

When I came across the Cauchy-Schwarz inequality the other day, I found it really weird that this was its own thing, and it had lines upon lines of proof. I've always thought the geometric definition ...
0
votes
1answer
40 views

Is product topology of $X\times X$ is $X^2$?

I was wondering if we can write $X\times X$ (Product topology) as $X^2$. Or we can say that $X^2$ is with the product topology means that $X^2=X\times X$.
1
vote
1answer
27 views

What is the name of this function on group-ring modules?

Let $G$ be a finite group. Let $M$ be a $\Bbb{Z}G$-module. What is the name of the map $M\to M$ given by: $$ m \mapsto \sum_{g\in G} g m\, , $$ possibly divided by $|G|$? What is it used for? A ...
13
votes
3answers
892 views

What does “closed under …” mean?

What exactly is meant by "closed under fill in the blank"? Thanks.