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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2answers
29 views

Is there any standard terminology for this property?

Let $f$ be a map whose domain is $X$. If $f$ satisfies the property that for all $x\in X$, $$f(f(x))=f(x)\text{,}$$ is there any standard name for such a function? Not sure if "projection" is the ...
0
votes
1answer
22 views

What does “exponent 2 nilpotency class 2” mean?

According to the book The Symmetries of Things, p. 208, the number of groups of order 2048 "strictly exceeds 1,774,274,116,992,170, which is the exact number of groups of order 2048 that have ...
1
vote
1answer
42 views

Is there a name for this result in planar geometry?

I found out that the following statement is fairly easy to prove: Let $A$, $B$ and $C$ be thee distinct points in the plane. Let $S_{AB}$ be the circle that has the line segment $AB$ as a ...
-4
votes
1answer
64 views

How to describe the Cartesian product $\mathbb{R} × \mathbb{R}$?

I am taking a discrete mathematics course in the spring and in an attempt to fully understand the material I am reading ahead. I came across this statement Let $\mathbb{R}$ denote the set of all real ...
3
votes
1answer
30 views

Is there any significance to complex function “monotone in norm?”

So, I was reading a question earlier where someone asked if something would be strictly monotone in the complex plane, and the comment was that this would be meaningless, since the complex numbers ...
3
votes
2answers
39 views

Definition of totality in relations

I see two apparently different definitions for totality which don't seem to be equivalent. Definition 1. A relation $R \subset X \times Y$ is total if it associates to every $x \in X$ at least one $y ...
2
votes
2answers
51 views

What is a non-decreasing sequence of sets?

What is a non-decreasing sequence of sets and how come it can have a limit? It appear in a probability theory book
1
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2answers
42 views

Is there a good short phrase for a point where a function is continuous but not smooth?

Given a point $x_0$ where a function $f$ is $C^0$ but not $C^1$, how could one call this point intuitively? I am not looking for a technically precise term (like a point where $f'$ is ...
3
votes
1answer
64 views

What does “versin” mean?

$$\newcommand{\versin}{\operatorname{versin}}2\versin A+\cos ^2 A= 1+\versin ^2 A$$ I don't understand the word 'ver' in this equation. What does it mean?
3
votes
0answers
24 views

How is a part of eulerian path called?

An eulerian path in a graph is a path that visits every edge in the graph exactly once. If there is a path that has a similar property that it visits an edge at most once (e.g. a part of an eulerian ...
2
votes
1answer
52 views

What format is this?

I was given a snippet and can't seem to parse it myself, what's the name of this format and is there a tool that will render it like latex or mathML like this site does? ...
2
votes
2answers
58 views

Opposite of a function being bijective?

A function is bijective if it is both surjective and injective. Is there a term for when a function is both not surjective and not injective?
1
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0answers
34 views

Name for matrices with $a_{ij} + a_{ji} = 1$?

Do you know of any commonly used name for square matrices $A$ having the property that $$ a_{ij} + a_{ji} = 1$$ for all $i,j \in \{1,\dots, n\}$, where $n$ is the dimension of $A$?
2
votes
1answer
47 views

Can there be a bijection between a countably infinite set and an uncountably infinite set?

I suppose the answer is trivially no, but I haven't actually seen it stated precisely this way in the general. I've only seen specific cases, such as the proof by Cantor's diagonal argument that ...
0
votes
0answers
54 views

Is it normal (correct) to calculate a probability without knowing the sample space?

Is it normal (correct) to calculate a probability without knowing the sample space? Background: I have finished a probability calculation $\mathbb{P}(E)$. I want to do some simulations. ...
0
votes
0answers
40 views
+50

Generalized semilattice morphism

Join-semilattice morphism from a join-semilattice $\mathfrak{A}$ to a join-semilattice $\mathfrak{B}$ is a function $\alpha$ conforming to the formula $\alpha(X\sqcup Y) = \alpha X\sqcup\alpha Y$ ...
2
votes
1answer
52 views

What do you call 'perpendicular but skew' lines?

For example, the seat tube and rear axle of a bicycle or motorcycle. That is, when viewed from above, the seat tube would appear 'perpendicular' to the rear axle. But in 3d reality, the lines are ...
1
vote
2answers
57 views

Terminology question: what does a natural isomorphism do to maps?

Suppose I have categories $C$ and $D$ and naturally isomorphic functors $F,G\colon C \to D$. (I do. Trust me.) Now name the natural isomorphism $\theta$; then for any arrow $f\colon x \to y$ in $C$, ...
3
votes
2answers
23 views

Terminology for orthogonal projections

Let $H = X \oplus Y$ a Hilbert space. Then, the map $p(x + y) = x$ is called the orthogonal projection onto $X$ along $Y$. Why is it necessary to mention along $Y$? Of course if a space has a ...
2
votes
1answer
25 views

Terminology in Viro et al.

I'm working through this book (Elementary Topology) and skimming the first section to make sure I'm not missing anything important to begin an independent study in algebraic topology, and I've come ...
0
votes
1answer
12 views

Meaning of “within a constant factor from”?

When a quantity $A$ is said to be "within a constant factor from" another quantity $B$, does it mean that there exists a posiitve constant $C$, so that $A \leq C B$? does it assume $A$ and $B$ ...
1
vote
2answers
22 views

What does it mean when two variables are said to be proportional?

Assume we are dealing with two variables i.e. $x$ and $y$. And suppose that $x$ starts increasing and to a certain value of $x$, say $a$, $y$ is $Zero$ but starts increasing when $x>a$ and a ...
0
votes
1answer
21 views

Relaxing Monotonicity of a Function $f:\mathbb{Z}\rightarrow \mathbb{R}$

Suppose a function $f:\mathbb{Z_+}\rightarrow \mathbb{R}$ fails monotonicity, but not by much. For example $f(2)= .3$ and $f(z)=1/z$ otherwise. Here there exists a single point where the function is ...
0
votes
2answers
43 views

What does non-zero integer mean?

The definition for the Rational Number is given as Numbers that can be expressed as a fraction of an integer and a non-zero integer. at ...
1
vote
0answers
17 views

How to describe homomorphism in terms of operations

I'm writing a paper, and in one section I discuss homomorphisms. As an example, I talk about the absolute value function as a homomorphism between the set of real numbers and the set of nonnegative ...
1
vote
2answers
51 views

What is the term for a component of a quantity's units?

Imagine a company pays for a service for each employee. The service costs $10/employee/month. Written another way, the cost is "10 dollars per employee per month." My question focuses on 10 dollars ...
14
votes
5answers
1k views

In plain language, what's the difference between two things that are 'equivalent', 'equal', and 'identical'?

In plain language, what's the difference between two things that are 'equivalent', 'equal', 'identical', and isomorphic? If the answer depends on the area of mathematics, then please take the ...
0
votes
1answer
37 views

Riemann Mapping Theorem, the concept of a Riemann mapping

If I construct a composition of mappings that map the upper half of the unit disk conformally to the entire unit disk, then this mapping is a Riemann mapping, by the Riemann Mapping Theorem, since ...
1
vote
0answers
27 views

Complete lattice without greatest element

Is there any term for "complete lattice without greatest element" (because the lattice is too big to have the greatest element). A typical example would be the lattice of all small (in Grotendieck's ...
1
vote
2answers
29 views

What is “the crossing number inequality”?

Could someone explain to me what "The crossing number inequality" is? How is it different from the crossing number of a graph?
0
votes
0answers
16 views

What is a nice way to call continuants?

I'm reading this paper : http://www.numbertheory.org/pdfs/continuant.pdf and here is a definition for continuant : http://en.wikipedia.org/wiki/Continuant_(mathematics) Let $\{a_n\}$ be a ...
-1
votes
0answers
13 views

Are the diagonals of cube subset of it?

The intersection of a cube and one of its diagonals is what? 1) This diagonal 2) two of its vertices
0
votes
1answer
23 views

Given an element $y$ name inEnglish of $x$ such that $f(x)=y$

My question is about English wording. For an application $f$ and an element $y$ in the image of $f$, what is the name of an element $x$ such that $f(x)=y$? In French we say that $x$ is un antécédent ...
1
vote
1answer
25 views

English wording around equivalence relation

What is the English word to mean an element of an equivalence class of an equivalence relation? In French we say "représentant".
2
votes
1answer
44 views

Is there a term for “finite and non-zero”?

People sometimes use the term "finite" to mean "non-zero" or "non-infinitesimal". For example, physicists often say "finite temperature" to emphasize that the temperature under consideration is not ...
0
votes
1answer
35 views

Category defined by a finite commutative diagram

What is the name for a category defined by a finite commutative diagram? Maybe category "induced" by a commutative diagram? or category "defined" by a commutative diagram? Also, what is the exact ...
1
vote
1answer
45 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. ...
3
votes
1answer
21 views

Terminologies for $nA=0$

Let $A$ be a matrix over a ring. Suppose $nA=0$ for some $n\in\mathbb{Z}$. I wonder if there are terminologies for such A and $n$.
3
votes
1answer
56 views

What are you if you specialize in combinatorics

If you specialize in number theory or in computer science (this for cryptology) you are a number theorist, a computer scientist, a cryptologist. But how do you call someone who specializes in ...
0
votes
2answers
85 views

Why “thin groupoids” are not ubiquitous?

Google search for "thin groupoid" finds surprisingly few (namely 7) pages. But "thin groupoid" is a term to denote an important notation of a groupoid with every loop being the identity. I met it ...
0
votes
1answer
25 views

Function linear in its arguments

What does it mean to say that a function is linear in [some of] its arguments? I tried to Google it and nothing came up.
5
votes
1answer
118 views

What does “adic” mean?

The word "adic" is often seen in books of algebra and number theory. I don't know what does this word mean, so I look it up in a dictionary, called Oxford Dictionary of English. But it does not appear ...
2
votes
1answer
29 views

Name for sum of reciprocals

I have often run into the equivalent equations $\frac{1}{a} + \frac{1}{b} = \frac{1}{c}$ and $c = \frac{1}{\frac{1}{a} + \frac{1}{b}}$ (e.g. focal length, equivalent resistance, etc). Does this ...
0
votes
0answers
25 views

Hyper $n-$ torus cohomology group?

I don't know if this interpretation is correct. Is $S^{n_1} \times S^{n_2} \times \dots \times S^{n_k}$ some sort of hyper torus of dimension $1 + \sum_{k = 1} n_k$ (see here for calculation)? Let's ...
0
votes
0answers
66 views

Math multiplication tricks/identities

There are some multiplication tricks, especially used in Calculus, which help to prove or solve problems. For example: $$ \frac{1}{n \cdot (n + 1)} = \frac{1}{n} - \frac{1}{n+1} $$ These are mostly ...
0
votes
0answers
20 views

Method's name/Theory: Equivalence of complex and real matrices of double dimension

I remember reading a document where it was explained, how complex matrices are equivalent to real matrices of double size, according (as far as I remember): Let $C$ be a complex matrix, then $D = ...
1
vote
1answer
54 views

Subsets of a monoid closed under left-multiplication by elements of a submonoid

Let $M, T$ be monoids (or, semigroups) with $M \subset T$. Then we can consider subsets $S$ of $T$ that are closed under left-multiplication by something in $M$, i.e. $$ a \in S, m \in M \implies ma ...
2
votes
1answer
36 views

Does the concept of “dynamic average” makes any sense?

While making an excel table about how many times an event happens per day I thought that it could be interesting to see what is the growth rate of those events. If in $2$ days the event happens two ...
1
vote
1answer
27 views

What exactly is $k\left(T_{n}\right)_{n\in\mathbb{N}}$?

Let $k$ be a field and $T_{n}$ indeterminates over $k$. Is $k\left(T_{n}\right)_{n\in\mathbb{N}}$ the field of fractions of the form $x=\frac{p}{q}$, where $p\in k\left[T_{i}\right]_{i\in\mathbb{N}}$ ...
2
votes
0answers
36 views

Why are there so many different symbols to represent the Heaviside (unit step) function

In signal processing, the unit step function is typically written as $u(t)$. In other references though I have seen it represented as $H(t)$ and even $\theta(t)$. The unit impulse is fairly ...