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

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1answer
13 views

Difference between finite and discrete set of discontinuities

I am reading this paper. In page 395 and 396, theorem $1$ and $2$, there are terms 'finite' and 'discrete' set of discontinuities. May I know what is the difference? It would be a lot better if ...
4
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0answers
21 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 ...
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0answers
9 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 -> ...
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2answers
22 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 ...
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2answers
17 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 ...
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0answers
21 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 ...
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0answers
28 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 ...
0
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1answer
34 views

What does the term “perturb” mean?

I've been studying Calculus of Variations and I came a cross with the term "perturb" in my study material, but the term was not defined. The sentence where I read it from was: "Rigid extremals are ...
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0answers
43 views

What abstract structures allows us to describe “nets that converge toward each other”?

Topological spaces are equipped with a bare minimum of structure to allow for a formalization of the statement "the net $a$ converges to the point $x$." Actually this isn't strictly true, but its true ...
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3answers
59 views

What is a conventional name for a set of values having no properties except that values are distinct?

I know essentially nothing about math but I'm interested in very low-level concepts. I'm thinking of something like a finite or infinite set (although I'm not married to consider sets per se, maybe ...
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1answer
44 views

Wide equalizers

If $(f_i : A \to B)_{i \in I}$ is a family of morphisms in a category, we may declare their wide equalizer as a universal morphism $\iota : E \to A$ which satisfies $f_i \iota = f_j \iota$ for all ...
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1answer
42 views

Name of Inequality

Let $x_i, y_i$ be complex numbers for all $i$. Is there a name for the following inequality? $$\left| \sum_{i=1}^n x_i \right| \leq \sum_{j=1}^n |x_j| $$ In particular, is it a special case of this ...
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1answer
38 views

Can somebody explain with one example the concepts: Lemma-Hypothesis-Theorem-Assumption-Proof-Axiom-Thesis-Determination-Definition-Proof [on hold]

It would be great if someone can give me for each concept a simple explanatory example ! What is the difference between: Lemma Hypothesis (Hypothese) Theorem (Satz) Assumption (Annahme) Proof ...
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1answer
38 views

What is the difference from a theorem and a meta-theorem?

I'm confused about what a meta-theorem exactly is and if a meta-theorem can be used to prove a theorem. To illustrate my confusion i give an example. Given the three statements: Every vector space ...
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0answers
26 views

Is there a name for the inequality $\min(a+b,c+d) - \min(a,c) \ge \min(b,d)$?

Is there a name for the inequality $$\min(a+b,c+d) - \min(a,c) \ge \min(b,d)$$? And does anyone have any nice examples or applications, especially with an economic flavor? The transposed multivariate ...
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0answers
46 views

Does this family of special matrices have a name?

These are the bisymmetric matrices that are "pyramid" shaped as follows: $$f(14) =\begin{bmatrix}1&1&1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1\\1& ...
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0answers
15 views

Is there a name for the relation between Menger Sponge and Vicsek Fractal?

Both the Menger Sponge and the Vicsek Fractal in 3D can be constructed by starting with a cube, dividing it into 27 smaller cubes (3x3x3 grid), removing some of these cubes, and then applying the ...
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3answers
47 views

What is the difference between a counter-intuitive statement and a paradox?

In mathematics and logic, what is the difference between a counter-intuitive statement and a paradox? For example, what differs something like the Banach-Tarski theorem or Gabriel's horn from ...
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0answers
31 views

What is an omega model?

I went to a seminar and a side question was if a theory had an omega model, however from the context I could not deduce the exact meaning. Does an omega model have a general meaning in mathematical ...
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1answer
31 views

What does “$C^{\infty}$” convergence mean?

I'm studying first notions about several complex variables. As a consequence of the (generalized form) of the Cauchy esteem for holomorphic functions, the book says that in the space $\mathcal ...
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1answer
51 views

Meaning of the term “Sledgehammer”

I know a Sledgehammer is a special type of hammer, but I still do not quite get the exact meaning of the word in such a paragraphs as: The computational sledgehammer par excellence is the spectral ...
2
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1answer
26 views

What is the difference between coordinates transformation and change of coordinates?

In the context on 3D computer graphics, what is the difference between coordinates transformation and change of coordinates? It can just be a matter of notation, but my book makes a clear distinction ...
2
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3answers
83 views

How many $n$th roots does $0$ have?

Do we say that $0$ has $n$ $n$th roots, all nondistinct, or only one? I don't think it makes any difference, but I'm curious what the convention is.
3
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0answers
31 views

Terminology question : “half smooth, half topological” fibre bundle

First, I know (or I think I know...) the definition of fiber bundle, be it in the smooth or topological category. Here is my situation, which is kind of between the two: I have a smooth manifold $E$, ...
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2answers
48 views

Is the standard scalar product in a coordinate space basis independent?

Would you say that the standard scalar product in $K^n$, $\left< x,y \right>=\sum_i x_i y_i$, is basis-independent or not ? I would argue that it is, because we don't use the components of the ...
2
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1answer
63 views

Question about the wording of a topology problem.

I was asked to show that the topology $\mathcal{T}_{X\times Y}$ is the smallest topology for which the functions $$f_X:X\times Y \rightarrow Y , f_X((x,y))=x $$ and $f_y$ are continuous (where $f_Y$ ...
0
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1answer
48 views

Given a field extension $K\colon F$, $K$ is an $F$-vector space

I'm having a hard time understanding fields. Could someone help with the following I need to show that if $F$ $\subseteq$ $K$ are both fields and addition and multiplication on F are the ...
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1answer
29 views

Are maps and operators between two sets the same?

I have been reading on up on the definition of maps and operators, specifically reacting to sets (rather then the more restricted vector spaces) and their definitions seem to be identical. So are all ...
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6answers
3k views

What do mathematicians mean by “equipped”

I am a mathematical illiterate so I do not know what people mean when they say equipped. For example, I say that Hilbert space is a vector space equipped with a inner product. What does that ...
0
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2answers
37 views

Is there a non-ambiguous name for the “square of a function”?

Given a function $f$, I want to refer to $f \circ f$ other than by a formula. Is there any name for this other than square of $f$, which has the problem of being ambiguous? In analogy to the ...
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3answers
114 views

What is the element produced under a generic binary operation called?

For instance, for addition this is called the sum: $\underbrace{x+y}_{\text{summands}} = \underbrace{z}_{\text{sum}}$ But what is this called for a unspecified operation? $\underbrace{x\circ ...
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1answer
30 views

Small question: Name for the x of function f such that f(x)=x?

Background When doing maths and chemistry problems, I often came across things like $$x-\frac{x}{2}=\frac{x}{2}$$ It might seems trivial, but I found that it is often the presence of expressions like ...
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1answer
27 views

Why stronger norm defines weak local minimizer? [closed]

Why the stronger norm defines weak local minimizer, while the weaker norm defines strong local minimizer?
2
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0answers
21 views

Is this a bound variable?

If I write $\left \{\begin{array}{llll} & y = z \\ & z = x + 2 \end{array} \right.$ could I make the argument that $z$ is a "bound" variable. I've seen it referred to as a ...
2
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1answer
45 views

What exactly constitutes a 'term'?

From what I understand when I looked up the definition on wikipedia, a term is a monomial with a coefficient. However, I was taught in high school that a term could also be an expression depending on ...
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0answers
12 views

Is there a name/notation for coordinate-wise identical function?

Let's define $g: \mathbb{U}^n \rightarrow \mathbb{V}^n$ where $\mathbb{U}$ and $\mathbb{V}$ are arbitrary sets as $$g(u) = \left[f(u_1), f(u_2), \ldots, f(u_n) \right]^T$$ for some $f: \mathbb{U} ...
0
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1answer
20 views

Terminology for vectors in ''positive angle'' position

I would like to know whether there is a standard terminology for the following situation: Let $H$ be a complex Hilbert space and $\xi, \eta \in H$ are two vectors such that $(\xi, \eta)_H \ge 0$. Do ...
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2answers
47 views

Is there a name for a point on the circumference of a circle?

Is there an eloquent name for a point located on the circumference of a circle?
63
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38answers
8k views

A fan, a horn, and a snowflake - unusual math terms [closed]

From time to time, I come across some unusual mathematical terms. I know something about strange attractors. I also know what Witch of Agnesi is. However, what prompted me to write this question is ...
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2answers
41 views

Looking for the name of polynomials obtained as integrals over a simplex

I'm looking for the name of the following polynomials: $\mathrm{p}_1 = 1$ $\mathrm{p}_2 = x - \frac{1}{2}$ $\mathrm{p}_3 = \frac{1}{2} x^{2} - \frac{1}{2}x +\frac{1}{6}$ $\mathrm{p}_4 = \frac{1}{6} ...
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0answers
30 views

Name for a nowhere constant function?

Is there a pithy name for a function $f : \mathbb{R}^n \rightarrow \mathbb{R}^m$ such that there is no non-degenerate interval $I \subseteq \mathbb{R}^n$ such that $f$ is constant on $I$ (by '$f$ is ...
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0answers
20 views

Ask for the name of a condition on commutator of two operators

Let $T, S$ be two bounded linear operators on a Hilbert space. I wonder whether there is a standard way referring the following condition: $$ \text{The commutator $[T, S]$ is in the Hilbert-Schmidt ...
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4answers
230 views

Is there a name for the curve $t \mapsto (t,t^2,t^3)$?

Is there a name for the curve given by the parametrization $\{(t,t^2,t^3); t\in\mathbb R\}$? Here is a plot from WA. An another plot for $t$ from $0$ to $1$. This curve is an example of a ...
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4answers
61 views

Is $S$ a monoid, or is $(S,*)$ a monoid?

If I have a set $S$ with operation $*$ as a monoid. Would I say I have a monoid $S$ with the binary operation $*$ or would I say I have a monoid $(S,*)$ where the binary operation $*$ does ...
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1answer
36 views

Is there a name for these sequences of subsets of a commutative ring resembling the definition of a graded algebra?

(I am experimenting with writing arrows backwards.) Let $R$ denote a commutative ring. Is there a term for those sequences $A : \mathcal{P}(R) \leftarrow \mathbb{N}$ satisfying the following ...
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2answers
33 views

How should one rank a combination of positive and negative numbers from smallest to largest?

I thought size was the distance from zero, in which case ordering {-1, 2, -3} would be {-1, 2, -3}, but I saw it ordered as {-3, -1, 2}. Which method is correct?
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1answer
30 views

General name for interpolation and extrapolation

I would like to know if there is a technical term to cover both interpolation and extrapolation. The reason why I am asking is that I am writing a computer program to do interpolation and ...
0
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1answer
24 views

Area of set-difference of special sets

In a topological space, call a set $X$ special if it is equal to the closure of its own interior (is there a standard term for this?): $$X = \text{Cl}[\text{Int}[X]]$$ Let $X$ and $Y$ be two special ...
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1answer
53 views

Notation about cardinals

Does a cardinal $\mathcal{k}$ such that $2^\mathcal{k}=k^+$ have any special name? I never encountered any name for this property, but I think it is possible they have one.
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1answer
20 views

Meaning of a probability distribution being dominated by a measure

The following comes from Ghosh & Ramamoorthi (2003) Bayesian Nonparametrics. In terms of notations, $\Theta$ is a parameter space with Borel $\sigma$-algebra $\mathcal B(\Theta)$. For ...