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

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1answer
9 views

Understanding terminology related to implementing the sobel edge detection algorithm

I'm trying to follow a scholarly paper that discusses a modified implementation of the sobel edge detection algorithm, but I'm not following the terminology 100%. The Sobel detector consists of ...
2
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4answers
99 views

I call them squares. They called them arrays. What do they mean?

So I was in C++, and we had third graders come today to play our programs. Whilst the others just drilled them with problems, my game was subtract a square. It was fun watching them discover that ...
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0answers
16 views

What's the name of this tensor product?

Fix $V$ to be a vector space over $\mathbb{R}$. For all $k \in \mathbb{N}$, let $L_k$ be the space of all $k$-tensors on $V$, and let $S_k$ be the set of all permutations of the set $\{1,\dots, k\}$. ...
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3answers
58 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 ...
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0answers
45 views

Mathematical principles and the0rems - what is the difference?

For me, intuitively, a mathematical principle is simply an influential theorem. Still, I am not clear on how and who decides (or decided) if a theorem/statement is a mathematical principle. Can you ...
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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: ...
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3answers
772 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 ...
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2answers
3k views

Relation between cross-product and outer product

If inner products ($V$) are generalisations of dot products ($ \mathbb{R}^n$), then are outer products ($V$) also related to cross-products ($ \mathbb{R}^3$) in some way? A quick search reveals that ...
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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. ...
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6answers
322 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 ...
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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? ...
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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.
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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
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1answer
48 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 ...
1
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1answer
93 views

After Exponentials

Look at this- $$f(a,b)=a+b$$ The next step would be to make a function $g$ such that $$g(a,b)=\underbrace{a + a + a \cdots}_{b\text{ times}}=a\cdot b$$ Then we made $h$ so that ...
1
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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?
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1answer
37 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 ...
2
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0answers
33 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 ...
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1answer
37 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 ...
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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? ...
6
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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
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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 ...
3
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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 \| = \| ...
2
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0answers
48 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 $n\times n$ ...
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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 ...
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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
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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
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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 ...
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3answers
41 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 ...
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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
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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
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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 ...
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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 ...
2
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0answers
172 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
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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
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1answer
300 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
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1answer
47 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
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0answers
173 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 } ...
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38answers
8k 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 ...
2
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2answers
59 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
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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 $a/b$?
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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
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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 ...
2
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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 ...
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4answers
95 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? ...
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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 ...
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1answer
632 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
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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
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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 ...
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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) - ...