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

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3
votes
1answer
54 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
22 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
50 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? ...
3
votes
2answers
48 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?
0
votes
0answers
37 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 $\alpha(X\sqcup Y) = \alpha X\sqcup\alpha Y$ ...
1
vote
0answers
33 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. ...
54
votes
10answers
3k views

Is $1$ a prime number?

Is 1 classified as a prime number? And if so, why? If not, why not?
3
votes
2answers
16 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
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
55 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 $C$, ...
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 ...
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 ...
6
votes
5answers
3k views

Is there a formal name for an equation that has no solution?

I was wondering if there is a formal name for the equations which don't have any solution? For example consider this equation in $m$ : $$ -2(3-m)+15=6m-4(m-20)$$ If we do the algebra we will get ...
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 $B$ ...
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 ...
3
votes
4answers
71k views

What is the formula to calculate Profit Percentage?

Let cost price of an item be $C$, selling price be $S$. Assume the seller makes a profit. Then profit would be: $P = S - C$. Now, what is the formula for calculating Profit Percentage? $P \% = ...
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 ...
0
votes
1answer
171 views

definition from mathematics translated in english language

guys this question is more specific related to english and math together then math only,i am studying GRE tasks(quantity variant) and want to be acquainted every term and trick related to ...
0
votes
2answers
42 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 ...
6
votes
1answer
288 views

Is the kernel of any ring homomorphism a subring, according to this definition?

This is an exercise taken verbatim from Birkhoff and MacLane, A Survey of Modern Algebra: Show that if $\phi: R \rightarrow R'$ is any homomorphism of rings, then the set $K$ of those elements in ...
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
26 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 ...
2
votes
2answers
277 views

probability terminology for parameter in a Markov process

Suppose $$P(\text{feature present at time} \ t \ \text{and} \ t+\Delta t) = \beta^{2}+\beta(1-\beta) \exp(\Delta t/\tau)$$ where $\tau = 1/(\pi_{01}+\pi_{10})$. What is $\tau$?
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 ...
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".
-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
2
votes
7answers
374 views

When does it make sense to say that something is almost infinite?

I remember hearing someone say "almost infinite" on one of the science-esque youtube channels. I can't remember which video exactly, but if I do, I'll include it for reference. As someone who hasn't ...
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 ...
0
votes
1answer
15 views

What is the difference between self-avoiding and simple in FASS (space filling) curves?

Although it does not appear to be widely used, I occasionally see the acronym FASS used to describe certain curves that are space-filling, self-avoiding, simple, and self-similar. What is the ...
0
votes
1answer
34 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 $n$.
1
vote
1answer
52 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 ...
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 ...
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 ...
1
vote
2answers
42 views

Name for shape defined by volume between two concentric spheres

Is there a proper name for a shape defined by the volume between two concentric spheres? My understanding is that, formally, a "sphere" is strictly a 2D surface and there's a formal term for volume ...
5
votes
1answer
117 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 ...
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.
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
1answer
49 views

Monochromatic Solutions

I recently came across this paper: http://borisalexeev.com/pdf/foxgraham.pdf "On Minimal Colorings Without Monochromatic Solutions To a Linear Equation" Can someone explain in clearer terms what ...
0
votes
0answers
65 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 = ...
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 ...