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

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3answers
51 views

Is zero “finite” - Terminology

edit: This is usually done by physicists, engineers, etc. And it refers to a numerical value, not a set. It is used for cases the numerical value of $0$ is not allowed as well. Infinity, is clearly ...
9
votes
3answers
767 views

Why lower case “a” for “abelian group” and upper case “C” for “Cauchy sequence”?

This has been bugging me. Why is the lower case letter "a" used to spell "abelian group" when upper case letters are used to spell the terms, "Gaussian Integral", "Cantor set" or "Cauchy ...
1
vote
1answer
40 views

Mathematical symbol for Symbolic Replacement

(Posted at mathematica.SE, as it might be better there) I'm searching for a mathematical symbol, that describes the symbolic replacement done for instance in Mathematica: ...
0
votes
2answers
43 views

What type of angle is $3+ \frac{1}{6}$ of a complete rotation?

Angle less than $90$ deg is acute, angle greater than $90$ and less than $180$ is obtuse and angle greater than $180$ deg is reflex. Now, what if an angle is a $3+\frac{1}{6}$ of a complete rotation? ...
8
votes
6answers
1k views

What is an adjective for “weaker than weak”?

I defined a notion (say, some kind of equivalence) in three forms, the first implies the second, which in turn implies the third. I would like to use "strong", (nothing), and "weak" to describe them. ...
1
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1answer
26 views

What does “2- place real function” mean?

What does "2-place real function" mean? This comes up in the context of copulas, as here.
3
votes
1answer
76 views

Origin of the term dual space?

Basically, why is a dual vector space called as such? Is the reason for the term "dual" simply because the two vector spaces are related by a one-to-one mapping, or is there something more to it? ...
1
vote
1answer
69 views

What is the name of this geometric shape?

#1 I am trying to find the name for this when $d1 = d2$ What is the name of this object? #2 Assume d1 is different than d2. What is the name of this kind of object?
11
votes
6answers
318 views

What is the significance of using “$a$” vs “$x$” in this text?

I'm a web development guy currently learning Calculus and am having some trouble understanding the seemingly unwritten rules of variable naming conventions in mathematics. I've read several other ...
2
votes
0answers
32 views

Relation of ideals in probability with other kinds of ideals?

It seems that there are at least 5 kinds of ideals in maths: Ideals in number theory (Kummer, Dedekind) Ideals in abstract algebra (Dedekind, Noether), as kernels of homomorphisms Ideals in order ...
1
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1answer
35 views

“Inverse” of nondecreasing, right-continuous function?

Suppose $F : \mathbb{R} \to \mathbb{R}$ is a nondecreasing and right-continuous function. Define $G : [\inf F,\sup F] \to \overline{\mathbb{R}}$ by $G(p)=\inf \{ x : F(x) \geq p \}$, with the ...
1
vote
1answer
34 views

Mathematical terminology for primes $(q+1)/2$ such that $q$ is also prime

So I know that if both $p$ and $2p + 1$ are primes, then $p$ is a Sophie Germain prime from the Prime Glossary. My question is this: How do we call a prime $r=(q+1)/2$ such that $q=2r-1$ is also ...
1
vote
1answer
47 views

Does a $K_n$ with $n$ pendants have a name?

Consider the graph we get by taking the complete graph on $n$ vertices, and then attaching a pendant vertex to each of the $n$ vertices by an edge. Does such a graph have a name, i.e. do such graphs ...
6
votes
2answers
83 views

Name for the reals augmented with an $x$ such that $x^2 = x$

If you add an $x$ such that $x^2=-1$ to the reals, you get the complex numbers. If you add an $x$ such that $x^2=0$ to the reals, you get the dual numbers. If you add an $x$ such that $x^2=+1$ to the ...
2
votes
1answer
38 views

Is there a name for this kind of space?

Assume a Riemannian symmetric space $G/H$ where the decomposition of the Lie algebra of $G$ is $\mathfrak{g} = \mathfrak{h} \oplus \mathfrak{m}$. It is a known fact that if $\mathfrak{h}$ is the Lie ...
2
votes
0answers
47 views

Is there a name or symbol for the matrix division resulting in a scalar?

I am not talking about the inverse matrix, $A^{-1}$ which gives $A\times A^{-1}=I$, but rather the operation $\frac{1}{n}tr(\space\cdot \times A^{-1})$, which gives 1 when applied to a $n\times n$ ...
1
vote
0answers
13 views

What is the name of this similarity measure for sets?

just a quick question. Suppose I have two sets A and B. Is there a specific name for the following similarity measure? It is slightly different from the Jaccard coefficient, but I can't find the ...
1
vote
2answers
62 views

Are there names for these subsets of rational numbers?

Rational numbers can be defined as: $$\left\{ \frac{p}{q} | p \in \Bbb{Z}; q \in \Bbb{Z}; q \neq 0 \right\}$$ Are there conventional or existing names for the sets where $q$ is a particular number? ...
2
votes
1answer
44 views

What do we call well-founded posets whose elements have a unique height?

What do we call those well-founded posets $P$ with the property that for every $x \in P$, all maximal chains in the lowerset generated by $x$ have the same length? Examples: The set of all finite ...
3
votes
1answer
69 views

left adjointable functors

When a functor $F$ is left adjoint to some functor $G$, then one usually says that "$F$ is a left adjoint". Is this grammatically correct? Wouldn't it be more accurate to say that "$F$ is right ...
0
votes
3answers
39 views

Difference between variables, parameters and constants

I believe the following 4 questions I have, are all related to eachother. Question 1: Of course I've been using constants, variables and parameters for a long time, but I sometimes get confused ...
3
votes
1answer
119 views

A name for the property $ \| x \star y \| = \| x \| \| y \| $.

Suppose that $ \star: V \times V \to V $ is some binary operation on a vector space $ V $. Should it hold, is there a name for the following property? $$ \forall x,y \in V: \quad \| x \star y \| = \| ...
3
votes
1answer
48 views

What is a differential equation?

Some definitions says a differential equation is a mathematical equation that relates a function with its derivatives Some say that it is just an equation involving derivatives of a ...
0
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0answers
6 views

Implied meaning of “existence” of inner products

I read somewhere that the inner products of the eigenfunctions of an operator with a discrete eigenvalue spectrum are guaranteed to exist. Does existence here just mean that they can be defined or ...
0
votes
1answer
30 views

Notation about factors

What is the name (if there is one) of the "full factorization representation" of a number, in which also the powers of the factors are (recursively) decomposed until all the numbers used in the ...
3
votes
1answer
46 views

What does “up to a subsequence” mean?

English is my second language. Now I have to read papers written in English, and I can't understand the phrase. Well, I get a vague idea, but that's all. What have I done? I Googled with ...
2
votes
2answers
58 views

Why is Cumulative “Density” wrong?

CDF stands for cumulative distribution function. However, it is "loosely" referred to as Cumulative Density many times. As i write this question, I have a suggestion toolbar on this page that lists ...
0
votes
0answers
26 views

Multiply vector by number that rescales to integers - what is the name?

What is the name of the number that rescales a set of rational numbers s.t. they are all integers? E.G., 1,000 in the following example. ...
2
votes
1answer
40 views

What is the line $y=x$ and $y=-x$ called?

I know that some non-english mathematicians use first median to mean the identity line $y=x$ (i.e. line considered in $\mathbb R^2$) and second median to mean the line $y=-x$. I don't suppose this is ...
4
votes
1answer
39 views

What is the name of the technique for showing that $\mathbb{N}^2$ is countable?

In order to show that $\mathbb{N} \times \mathbb{N}$ is countable, we can define a bijection $f : \mathbb{N} \rightarrow \mathbb{N} \times \mathbb{N}$ like this one: $0 \rightarrow (0, 0)$ $1 ...
1
vote
0answers
32 views

MTL algebra 'prelinearity' condition etymology

According to wikipedia the prelinearity condition of a monoidal t-norm logic is expressed as $(x\implies y) \vee (y\implies x) = 1$. As far as I know, the 'pre' prefixed version of a rule or ...
2
votes
0answers
33 views

Geometric, Arithmetic, and Harmonic

I'm curious as to the origin of the words "geometric", "arithmetic", and "harmonic" means. What's so "geometric" about the geometric mean? How is the arithmetic mean more "arithmetic" than the other ...
0
votes
2answers
32 views

Real (Valued) Functions in German

I just realized something that was left unnoticed by me for many years. Apparently, among German speakers reelle Funktion (literary also translated word by word as "real functions") has both domain ...
1
vote
1answer
27 views

Measuring the “flatness” of a function

In some work I am doing, for a function $f$, I want to measure the average difference between two function values $|f(x_1) - f(x_2)|$ over the entire data distribution, $\int_X \int_X |f(x_1) - ...
0
votes
1answer
23 views

Need of proper concept of inverse function in sets

A function $X ∶ (\Omega_1, \{ \Omega_1 , \varnothing\}) \to (\Omega_2 , \{\Omega_2,A,A^c,\varnothing\})$ is given and $A$ is some non empty subset of $\Omega_2$. Now since I am new to measure theory a ...
1
vote
1answer
46 views

What is the name of this (circumscribed) triangle?

I am meeting the following triangle more and more in my investigations of ideal triangles in the Beltrami Klein model of hyperbolic geometry. That made me wonder: is there a name for it? (And does it ...
2
votes
1answer
27 views

Is there a standard term for this generalization of the Euler totient function?

Let $\phi_k(n)$ be the number of integers $m$ in $1\le m\le n$ for which $\gcd(m,n) = k$. Then $\phi_1(n) =\varphi(n)$, the standard totient function. This function arises in the analysis of the ...
2
votes
2answers
39 views

Is there a measure for how thin or squat a triangle is?

Is there a measure for how thin or squat a triangle is? Similar to eccentricity for ellipses.
1
vote
1answer
29 views

What do you call a frequency that varies by a function?

I have a concept that I need to learn more about, but I don't know what it's called so I'm not sure what search terms to use to look for it. I apologize in advance that while I'm comfortable with ...
0
votes
0answers
19 views

Name for space which is countable union of compact sets

Is there a name for a (topological) space which is the countable union of compact sets. For example $\mathbb{R}^N = \bigcup_{j\in\mathbb{N}} j \,B_{\mathbb{R^N}}$.
1
vote
1answer
17 views

Non-ordered n-tuple?

In many mathematics texts I've seen "ordered n-tuple" appear, and in such texts, there isn't any mention of just "n-tuple". So I'm wondering: are there really cases where one writes "n-tuple" and ...
3
votes
3answers
40 views

What is the area leftover from an inscribed circle called

What are the little triangle things called (displayed as red in the picture)? If the ones on the corners and the ones on the sides are different, then I would like to know those names too.
0
votes
0answers
23 views

Would my paper be considered Diophantine?

From Wikipedia In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is ...
-1
votes
1answer
40 views

What is the name of the measurement along a 4th dimensional axis?

Given that measurement along the X, Y and Z axes correspond to the terms "width", "height", and "depth", is there an accepted term for spatial measurement along the W axis when dealing in four ...
4
votes
3answers
753 views

What do we call the front part of a decimal number? [duplicate]

I have the following number. 23.45 There are two parts of this number. 23 and 45. What is the mathematical name of the 23 part?
2
votes
1answer
28 views

How are fields (algebra) related to vector/scalar fields?

Is there a reason as to why they both have similar etymologies? If not, is there a big book of mathematical etymologies? Please include sources, thanks!
1
vote
0answers
12 views

Term to describe breaking a number into its constituent digits?

I'm writing a program, and in this program is a method that takes a number (say, 1,337), and returns its digits (1, 3, 3, and 7). Is there a mathematical term that describes this process? If not, is ...
0
votes
0answers
34 views

Differentiate between Fourier analysis and Fourier decomposition

I am a beginner. I am confused between two terms i.e. Fourier analysis and Fourier decomposition.I don't understand when to use Fourier analysis term and when to use Fourier decomposition term. It ...
6
votes
1answer
66 views

When vectors act on scalars.

Background. I've been struggling through an introduction to differential geometry this semester. Recently, a tiny part of what we've been learning "clicked" for me, and to solidify this, I'd like ...
2
votes
1answer
36 views

Is a Linear Transformation a Vector Space Homomorphism?

I see the terms linear transformation and (vector space) homomorphism used more or less interchangeably, and the set (space) of linear transformations from V to W referred to as Hom(V, W) or ...