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

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6
votes
2answers
95 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
41 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
49 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
14 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
67 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
63 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
72 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
56 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
125 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
50 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
7 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
34 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
55 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
61 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
27 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
42 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
40 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
40 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
43 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
35 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
29 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) - ...
53
votes
6answers
3k views

Why is a geometric progression called so?

Just curious about why geometric progression is called so. Is it related to geometry?
0
votes
1answer
25 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
50 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
46 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
47 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
32 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
21 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
20 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
46 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.
-1
votes
1answer
44 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
779 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
29 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
15 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
39 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
68 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
44 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 ...
1
vote
0answers
17 views

What is the meaning of “mass defect” in measure theory?

What does the term "mass defect" mean in measure theory? I stumbled upon it in the context of weak convergence and the dominated convergence theorem, but I haven't seen it defined anywhere.
1
vote
1answer
99 views

Is there a well-known type of differential equation consisting of $y$, $y'$, and $y''$ multiplied together? [closed]

Is there some sort of well known type of differential equation consisting of first and second derivatives multiplied together? For example (I just made this up): $$y''(y')^2-y-x^2=0$$ Edit: Are ...
1
vote
1answer
49 views

Some weaker axiom than “no nontrivial zero divisors.”

I would like to know if there a standard term for or well-known applications of the following axiom for rings or semigroups with zero (which is weaker than the "no nontrivial zero divisors" axiom): ...
3
votes
1answer
44 views

Is there a special name for matrices $A^T A$ and $A A^T$?

I'm looking for a special name for matrices $A^T A$ and $A A^T$. "Symmetric" and "Positive semi-definite" are too general terms. These matrices have special properties, so they should have a special ...
1
vote
3answers
46 views

how to call a and b when a+b=1?

I guess it's a simple question, but it really escaped my memory. If $a + b =1$, then how can I call those $a$ and $b$ numbers? $a$ is not an inversion of $b$, and it's not reciprocal of $b$.. but ...
2
votes
1answer
51 views

Well-posed vs Well-conditioned

What's the difference between a well-posed (ill-posed) and well-conditioned (ill-conditioned) problem ?` Here is my finding up to now: "Even if a problem is well-posed, it may still be ...
1
vote
0answers
51 views

Mathematical structures with name reffering to a country

I am looking for a list of mathematical structures (not theorems) that refer to a country or nationality. I only know of Polish spaces and Polish groups. Does anyone have other examples? Note: many ...
1
vote
1answer
46 views

Why did mathematicians name a functional that assigns number to function as a “distribution”?

Why did people name it as a "distribution"? I don't see the reason. My instructor told us don't bother with this strange name, but I guess maybe I will have a better understanding if I know the ...
4
votes
0answers
21 views

Terminology: order vs. degree (in general)

The word degree comes from Latin degradus (through French), which means something like step down. The word order comes from Latin ...
5
votes
5answers
525 views

Is there an intuitive, not-too-mathematical way of thinking about limit points? [duplicate]

so I know this question has been asked sooo many times. But I just have a few questions in particular, which despite searching, I haven't found an answer to. I appreciate any help. Book's definition: ...
6
votes
4answers
104 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? ...
0
votes
2answers
23 views

Comparing Open Bases and Covers

In Topology, I see a resemblance and similarity between open bases and open covers. Although this is a short question, what is the defining difference between the two that sets them apart? ...
2
votes
0answers
35 views

Rings where action of automorphisms on maximal ideals is transitive

If $R$ is a commutative ring, $\alpha: R \to R$ an automorphism of $R$, and $M$ a maximal ideal of $R$, then $\alpha(M)$ is also a maximal ideal of $R$ with the same quotient field. So the group of ...