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

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0
votes
1answer
34 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 ...
11
votes
7answers
268 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 ...
1
vote
1answer
33 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
0answers
21 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
vote
1answer
28 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
2answers
58 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? ...
6
votes
2answers
78 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
37 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 ...
3
votes
1answer
101 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 \| = \| ...
2
votes
0answers
42 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
12 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 ...
10
votes
3answers
7k views

What does “isomorphic” mean in linear algebra?

My professor keeps mentioning the word "isomorphic" in class, but has yet to define it... I've asked him and his response is that something that is isomorphic to something else means that they have ...
2
votes
1answer
35 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
66 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 ...
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 ...
3
votes
1answer
43 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
votes
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 ...
2
votes
0answers
170 views

Property similar to subadditivity

A function is called subadditive such that $f(x+y)\le f(x)+f(y)$ holds for any $x$, $y$ in the domain of $f$. (Let us say that, for example, the domain is some subset of $\mathbb R$ closed under ...
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 ...
6
votes
1answer
296 views

Difference between elementary submodel and elementary substructure

This is a really "elementary" question, forgive the pun. What is the difference between an elementary submodel and an elementary substructure (in first-order Logic)? Sincere thanks for help.
3
votes
1answer
43 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 ...
3
votes
0answers
172 views

Constructing a semigroup from a small category

The following was given as an example for a semigroup without an identity: Finite sets of matrices of varying dimensions, where the product $A*B=\{PQ \mid P \in A, Q \in B \text{ and } ...
66
votes
38answers
9k views

Unusual mathematical 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
75 views

What is a mathematical object? [closed]

What is a mathematical object? I read the definition on Wikipedia but it's really vague. How does something fall into the cathegory of being a mathematical object? How do we know they exist?
2
votes
2answers
56 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
1answer
49 views

Why does $ \frac {a}{b}$ of $c$ mean $ \frac {a}{b} \cdot c$ [closed]

When someone writes "$ \frac {a}{b}$ of $c$", why is the preposition "of" interpreted as multiplication of $c$ by $a/b$?
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. ...
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 ...
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 ...
6
votes
4answers
91 views

Is the logarithm of $\aleph_0$ infinite?

In classical mathematics $2^{\aleph_0}=\aleph_1$, right? So if $2^x=\aleph_0$, what does $x$ equal? In other words, can we define a logarithm for $\aleph_0$, and what should it be. Is it infinite? ...
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 ...
-1
votes
1answer
616 views

“Pythagoras Theorem” - Why is “theorem” or “theory” used rather than “law” in mathematics?

Why is Pythagoras Theorem a "theory" but not a "law"? I mean we use it many times in school and to build stairs etc. and it has been proven, however it is still called a theory. What are the ...
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
30 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
25 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) - ...
2
votes
1answer
139 views

What does it mean to “calculate in local coordinates” on a manifold?

In differential geometry textbook one sometimes reads "calculating in local coordinates, we obtain..." What does this expression mean? Say, $M$ is a smooth manifold and $h$ is a function on $M$; what ...
8
votes
4answers
269 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
22 views

Nomenclature for the function appearing in Carathéodory's criteria of differentiability

In my previous question Concerning Carathéodory's criteria of differentiability and a proof that differentiable implies continuous I stated the criteria as follows: There exists a function $\phi$ ...
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
1answer
43 views

Correct name for non-unit length 'hessian normal form' 3D plane.

A plane defined as 4 numbers (x,y,z,distance) is known as the hessian normal form, Where the xyz values are unit-length. However I've found its not necessary to ...
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 ...
2
votes
2answers
38 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.
6
votes
6answers
437 views

In what sense of “structure” do group homomorphisms “preserve structure”?

It is commonly said that group homomorphisms "preserve the structure of the group", e.g., from Wikipedia: The purpose of defining a group homomorphism as it is, is to create functions that ...
7
votes
0answers
111 views

Name of a certain set

I want to know if there is any already-standard way to refer to the sets described as follows. For a set $X$, let $-X = \{-x: x \in X \}$; call it the negative of $X$. Take the set of all primes in ...
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 $\mathbb{R}^N = \bigcup_{j\in\mathbb{N}} j \,B_{\mathbb{R^N}}$.
17
votes
4answers
8k views

What exactly does it mean for a function to be “well-behaved”?

Often in my studies (economics) the assumption of a "well-behaved" function will be invoked. I don't exactly know what that entails (I think twice continuously differentiability is one of the ...
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
39 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.