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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3answers
46 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 ...
3
votes
2answers
15 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 ...
4
votes
0answers
123 views

How do you call functions that fulfill $f(x)=\pm f(\pm 1/x)$?

A function $f(x)$ that fulfills $f(x)=\pm f(-x)$ is called (a)symmetric even/odd. How do you call functions that fulfill $f(x)=\color{blue}\pm f(\color{red}\pm 1/x)$? ...
0
votes
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 ...
0
votes
1answer
31 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 ...
0
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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 ...
1
vote
0answers
30 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 ...
2
votes
3answers
57 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 ...
3
votes
1answer
43 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 ...
3
votes
1answer
41 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 ...
63
votes
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 ...
0
votes
1answer
36 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 ...
1
vote
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 ...
1
vote
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 ...
2
votes
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& ...
3
votes
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 ...
1
vote
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 ...
0
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0answers
146 views

Terminology, mapping a tree to a tree

I have stumbled upon a problem; unfortunately, I do not know the proper terminology to be used which hinders me in thinking about the problem and explaining the problem. I am not even sure this is the ...
1
vote
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 ...
1
vote
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 ...
2
votes
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 ...
0
votes
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
votes
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 $f_Y$ ...
24
votes
4answers
4k views

What does it really mean for something to be “trivial”?

I see this word a lot when I read about mathematics. Is this meant to be another way of saying "obvious" or "easy"? What if it's actually wrong? It's like when I see "the rest is left as an exercise ...
2
votes
3answers
82 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.
1
vote
2answers
43 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 ...
3
votes
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 $E$, ...
34
votes
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 ...
1
vote
1answer
120 views

What is the sigmoid *squashing* function?

I've just read the following The basic unit ("neuron" i) performs the following computation to update its state $y_i$: it computes a weighted sum $v_i$ of its inputs $x:j$ which is passed ...
0
votes
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 ...
2
votes
3answers
126 views

What is a non-degenerate module?

I know what a non-degenerate bi-linear form is, but what does it mean for say a left $R$-module $M$ to be non-degenerate? (Here $R$ is a ring without unit$) I came across a module being called ...
1
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4answers
4k views

What is a fraction in which the greatest common factor of the numerator and the denominator is 1?

What is this fraction: A fraction in which the greatest common factor of the numerator and the denominator is 1?
16
votes
6answers
5k views

Operator vs function

Could someone please explain the MATHEMATICAL difference between an operator and a function? I am not talking about these in terms of coding but rather the mathematical difference. Is operator also a ...
0
votes
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 ...
3
votes
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 ...
6
votes
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 ...
0
votes
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 ...
1
vote
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
votes
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 ...
0
votes
1answer
54 views

Overall percentage difference

In a corpus of text the expected letter frequency might be: e = 30% t = 30% a = 20% o = 20% Actual recorded frequency: e = 90% t = 10% a = 0% o = 0% I want to know the OVERALL percentage ...
2
votes
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 ...
1
vote
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} ...
-2
votes
1answer
60 views

What is the difference between helix and spiral? [closed]

The words spiral and helix are both used for curves that "wind around". For example, both searches "DNA spiral" and "DNA helix" (with quotation marks) result in many thousands of Google hits. Is ...
1
vote
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 ...
0
votes
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 ...
2
votes
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?
1
vote
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} ...
1
vote
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 ...
1
vote
1answer
59 views

Name of Legendre symbol?

This may seem stupid question, but I'm curious about this. Generally, $(a/p)$ is called "the Legendre symbol" where $p$ is an odd prime, but I don't like this naming since this naming is not formal. ...
2
votes
2answers
279 views

probability terminology for parameter in a Markov process

Suppose $$P(\text{feature present at time} \ t \ \text{and} \ t+\Delta t) = \beta^{2}+\beta(1-\beta) \exp(\Delta t/\tau)$$ where $\tau = 1/(\pi_{01}+\pi_{10})$. What is $\tau$?