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

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-3
votes
1answer
66 views

what do these complex analysis terms mean?

I'd like to know the definition of the following terms I'm not familiar with... and to know if my understanding is misguided or in the right direction. In the brackets is what I believe it to be - ...
1
vote
2answers
66 views

Is definable $\emptyset$-definable?

A set $A$ is $X$-definable in an $L$-structure $\mathcal{M}$ with a domain $M$ iff there are an $L$ formula $\phi(a,\bar x)$ and $\bar x \in X^n$ such that $A=\{a \in M^m | \mathcal{M} \models ...
0
votes
1answer
37 views

Name of the difference between an asymptote and the curve that approaches it

Consider a function, say a hyperbola, and its asymptote. Is there a specific term for the difference between the two? Answers specific to hyperbola, as well as answers about general terminology, are ...
4
votes
3answers
435 views

What is this property called for a function? $f(f(x))=f(x)$

I am looking for a name for the following types of functions. Suppose that for function f, we have: $$f(x)=y_x$$ and $$f(f(x))=y_x$$ Is there any name for this property?
1
vote
1answer
35 views

The name for numbers with a certain digit sum.

What is the term for a number that has a certain digit sum? For instance 12 is the "digit sum" of 84, 138, 525 and so on. But what kind of number is 84, 138 and 525 to the number 12? Is there a term ...
2
votes
1answer
38 views

Dot product equivalent for complex numbers

NB I'm not asking about the dot product for complex vectors, but rather something much simpler. For vectors, a dot product is obtained as follows: $$ \left<1,2\right> \cdot ...
0
votes
1answer
34 views

What is a signed number?

When is the meaning of "signed number"? A signed number simply means a number that is negative, correct? Sorry if this seems like a stupid question but I'm just starting to get deep into ...
0
votes
1answer
42 views

What does the square-zero ideal means

I tried to study why Krull's intersection theorem won't work in non-Noetherian rings. It was said here that the example written by user2035 works by taking some kind of square-zero ideal. How do one ...
1
vote
1answer
50 views

What is the term for an undirected graph that's not a tree?

What is the term for an undirected graph in which a path can start from node $A$ and return to $A$ without traversing any edge twice? My first guess would be to call it a "cyclic" graph, but that ...
2
votes
1answer
35 views

Is it correct to say that a Riemann integral converges?

I got into an argument with a friend of mine. He argues that it's correct to say that a Riemann integral converges, like improper integrals, as the result is always a number. I said that a Riemann ...
2
votes
2answers
106 views

Is there a name for: (p => q) => ((p and r) => q)?

Is there a name for the following inference rule?: If (p => q), then we infer [for all r]: (p and r) => q If so, what is it? I use the above inference ...
-1
votes
2answers
53 views

What are the definition of an algebra and $\sigma$-algebra and the proof of this theorem?

Suppose that $\Omega$ is an infinite set (countable or not), and let $\mathcal{A}$ be the family of all subsets which are either finite or have a finite complement. Show that $\mathcal{A}$ is an ...
1
vote
3answers
81 views

Which is correct: negative infinity or 'does not exist'?

For the $\lim_{x\to 10^-} ln(100-x^2)$, which is more correct? $\lim_{x\to 10^-} ln(100-x^2)$ = negative infinity $\lim_{x\to 10^-} ln(100-x^2)$ = DNE (Does not exist) Graphically, $x$ ...
0
votes
0answers
35 views

Need help identifying PDE with terms of the form $\frac{\partial^2 u1}{\partial x^2 }+\frac{\partial^2 u2}{\partial y^2} \cdots$

So while reading this and some other lecture notes on PDE solving methods, I learnt about Semilinear 2nd order PDEs and briefly got a taste of solving them using the Method of Characteristics ...
3
votes
1answer
145 views

The functor $\mathbf{D} \rightarrow \mathbf{Prof}$ obtained by “splitting” $F : \mathbf{C} \rightarrow \mathbf{D}$ at each object of $\mathbf{D}.$

(Write $\mathbf{Prof}$ for the category whose objects are categories and whose arrows are profunctors.) I'm pretty sure that every functor $F : \mathbf{C} \rightarrow \mathbf{D}$ yields a ...
3
votes
1answer
26 views

What is part / whole?

For example, $$\frac{\text{part}}{\text{whole}} \cdot 100 = \text{percentage}$$ Example $$\frac{1}{4} \cdot 100 \%$$ What is the quantity $\frac{\text{part}}{\text{whole}}$ called? From the above ...
1
vote
1answer
43 views

Terminology: Probability “with respect to a measure”

The following excerpt is taken from Shen and Wasserman (2001). I have difficulty understanding some terminologies. On line 4, [...] each $P_\eta$ is a probability on $(\mathscr Y,\mathscr ...
0
votes
1answer
34 views

Names for left- and right-total relations

Let $X$ and $Y$ be finite sets. I am interested in subsets $r \subseteq X \times Y$, which contain each $x \in X$ and each $y \in Y$ at least once: $$ \forall_{x \in X} \exists_{y \in Y} (x, y) \in r ...
0
votes
0answers
14 views

Is “quantum” a correct term for the subsets used by a quantization function?

A quantizer is a many-to-few map. Its domain then is sets. I've heard those sets referred to as quanta (the plural of quantum). That usage seems to agree with what I understand to be the ...
0
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0answers
15 views

What is the term for the value from the set of values in a quantum that is closest to the aliased value of the quantum?

Signal quantization results in aliasing of the quanta. Is there a term for the value in the quantized set that is closest to the aliased value of the quantum? Something like "nearest neighbor" or ...
3
votes
3answers
93 views

Does $1/4=2/8$ in statistics? [closed]

What is the difference between practice and theory? Is "one in four" the same as "two in eight''? In theory, these are the same number. But in practice, it seems that "two in eight" implies eight ...
0
votes
0answers
34 views

Is there always a unit in topological rings?

I'm reading Qing Liu's Algebraic Geometry and Arithmetic Curves, http://176.58.104.245/ALGANT/TONG/Liu-1-4.pdf . On the first page he wrote that "Unless otherwise specified, all rings is this book ...
1
vote
1answer
71 views

Difference between locally and globally defined function

What is the difference between a function defined locally at $0$ and globally at $0$ on a set $S$? My textbook keeps referring to these things, but I couldn't find any definition about it anywhere. ...
0
votes
0answers
22 views

Partition of unity and coordinate patches

I have a question related to terminology. Assume that $M$ is a $k$ manifold. What does it mean to say that the partition of unity $f_1,f_2,...f_n$ on $M$ is dominated by the collection of all ...
1
vote
1answer
36 views

Math terminology: What are rules regarding hyphens? (Nonzero vs. non-zero)

This question is geared toward clarifying terminology in writing math. Which terms are correct and why? A set $E$ is non-empty. A set $E$ is nonempty. The number $x$ is non-negative. The ...
0
votes
0answers
43 views

Why “cylinder sets”?

If $I$ is any set of indexes, we define $E^I=\{(x_i)_{i\in I}:x_i\in E\,\,\forall i\in I\}$, $E$ being any set. Subsets of $E^I$ of the form $C_J=\{x_i\in B_i\,\,\forall i\in J\}$, where ...
1
vote
1answer
30 views

How do we say in English that pyramid is not skewed?

I would like to know if there is a term kind of "straight pyramid"? I mean, is there a word for a pyramid such that the line segment from the apex to the center of the base is perpendicular to the ...
3
votes
0answers
52 views

Intuitive meaning of benign subgroup

I've been studying a proof of Higmann's Embedding Theorem which makes use of the notion of a "benign subgroup". The definition is quite straight-forward: $G\leq H \ is\ benign\ in\ H \Leftrightarrow$ ...
3
votes
4answers
467 views

What does it mean to solve or find solutions in mathematics?

Something that has been really confusing me lately is that this equation has four solutions $$3x(x+1)(x^2+x+2)=16x(x+1)(2x+1)$$ But what does that mean? Until now solutions to me has meant, what are ...
0
votes
1answer
22 views

Need help with some regular polygon terminology.

I'm looking for the names of three different measures of a regular polygon. The name for the line between the centerpoint of the polygon, and any of its vertices. The name for the line between the ...
2
votes
2answers
40 views

What's the difference between an axiomatization and a characterization of a structure?

Regarding structures such as the natural numbers, complex numbers, groups, etcetera. Would it make sense to say that a collection of properties is a characterization of sets? I know that there are ...
1
vote
3answers
44 views

Basic question about terminology, notation and definitions in calculus

When reading stuff about differential equations I'm coming across some strange (for me) notations/terminology. For example, when coming across something like this: $$\frac{dy}{dt}=f(y,t)$$ or ...
4
votes
2answers
127 views

Why is Zorn's Lemma called a lemma?

By convention a Lemma is a technical intermediate step which has no standing as an independent result. Lemmas are only used to chop big proofs into handy pieces. (Quoted from here) I am wondering why ...
0
votes
0answers
20 views

Is there a term to designate the “complexity” of a complex number

The simplest way to explain my question is using an analogy: When classifying integers as odd and even, we speak of parity. Is there an equivalent term when speaking of the "complexity" of a number? ...
2
votes
0answers
62 views

What is a fewnomial?

I came across the theory of "fewnomials" (by Khovanskii), which (I guess) are related to polynomials. However, I was surprised that there is no single question on stackexchange concerning fewnomials, ...
0
votes
3answers
80 views

How is the relation between $y$ and $x$ called in $y = 1/x$?

Probably a very simple question for most of you, but how is the relation called between $x$ and $y$ if $y = 1/x$? As in, if I want to say: $y$ is .... related to $x$, what should go on the dots? ...
0
votes
1answer
26 views

Difference between cofinal map and cofinal

In this note I read, the cofinal map is defined as, Let $\mathbb D´$ and $\mathbb D$ be two directed sets, $f: \mathbb D´ \to \mathbb D$ is a cofinal map, if $M$ is cofinal in $\mathbb D´$, then ...
0
votes
1answer
48 views

Equivalent definitions of a quasi-affine variety?

I have a concern about a definition of a quasi-affine variety. I had a professor who defined a quasi-affine variety to be an intersection of an open set and a closed set in some affine space ...
0
votes
0answers
21 views

Name of this theorem? (Generalization of the class equation)

Let $X$ be a nonempty finitr set and $G$ be a finite group acting on $X$. Let $G.x_1,...,G.x_n$ be the distinct orbits of $G$. Define $F(X)=\{x\in X : \forall g\in G, g.x=x\}$. Then ...
1
vote
1answer
26 views

Let $f: \mathbb R \times \mathbb R^n \rightarrow \mathbb R^n$ given as $f(t,y)$. How I understand:“$f$ has continuous partial $y$-derivatives”?

Suppose I have a function $f: \mathbb R \times \mathbb R^n \rightarrow \mathbb R^n$ given as $f(t,y)$. Then how should it be understood "$f$ has continuous partial $y$-derivatives" ? Should it be ...
2
votes
0answers
24 views

Exponents for Hölder functions on metric spaces

Sometimes people talk about Hölder functions on metric spaces without mentioning the allowed range for the exponent. On manifolds, it's traditional to assume an exponent in $[0, 1]$, since all ...
0
votes
2answers
37 views

What's the name of this law in Boolean algebra?

I forgot the name of a law in Boolean algebra, and I can't think of how to ask this question to a search engine. It's the law that states that the disjunction of a variable with the conjunction of its ...
1
vote
1answer
24 views

Difference between finite and discrete set of discontinuities

I am reading this paper. In page 395 and 396, theorems $1$ and $2$ use the terms 'finite' and 'discrete' to refer to sets, in this case sets of discontinuities. What I don't understand is: what is the ...
4
votes
1answer
56 views

Is there a name for this special, “most parallel” ultraparallel line in hyperbolic geometry?

Suppose you're in the hyperbolic plane, and you have a line L and a point P not through L. There are an infinite number of lines parallel to L that go through P. However, there's one line M which is ...
0
votes
0answers
12 views

What is the proper name of a model that takes as input the output of another model?

Thanks in advance for the help. I am writing a paper and for the life of me can't remember the proper term for a model that works as follows. rawData -> model1 -> outputModel1 -> model2 -> ...
1
vote
2answers
27 views

What's the term for antisymmetry where equal elements are not in the relation?

The most common definition of antisymmetry of a relation $R$ on a set $S$ is $$ \forall a, b \in S, R(a, b) \land R(b, a) \to a = b. $$ However, this doesn't cover a relation such as $<$, for ...
0
votes
1answer
240 views

What is the line of greatest slope on a plane? [closed]

Let $P$ be a plane in $\mathbb{R}^3$ that is inclined (neither horizontal nor vertical). When considering lines lying on $P$, it is sometimes said "$L$ is a line of greatest slope of $P$". What is ...
3
votes
2answers
19 views

What's the name of a solid that results from extruding an area straight along an axis?

If you have any kind of 2D shape and move it up into the third dimension, what do you call it, because it seems like prism is used only if the base is a polygon. It also seems like extrusion is a ...
0
votes
0answers
27 views

Name for problems where the constraints are on inner products

I have a problem with a lot of dot-product constraints like $V_1 \cdot V_2 = 0$ or $V_1 \cdot V_3 = V_2 \cdot V_4$. However, I don't know what these types of problems are called so I can't look up ...
0
votes
0answers
37 views

“Absolute retracts” in arbitrary category

Is there a standard notion of something like "absolute retract" in arbitrary categories that generalizes absolute retracts in topology? I am mostly interested in categorical approach to Hausdorff ...