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

learn more… | top users | synonyms (2)

3
votes
1answer
99 views

What does algebra $A \rtimes G$ stand for?

Let $k$ be an algebraically closed field, $A$ a finite dimensional (unital associative) $k$-algebra of finite dimension, and $G$ a torus over $k$ acting on $A$. What does $k$-algebra $A \rtimes G$ ...
0
votes
0answers
30 views

Terminology of 'impossible' and 'indeterminate' results

In logic (whether boolean logic or real-valued logic), what are the proper terminology for impossible and indeterminate values? I define impossible as the outcome of a statement that cannot exist for ...
1
vote
1answer
19 views

On non-modular lattices and orto-modularity

I would like to have a definition for non-modular lattices which clearly sets them appart from their modular counterparts, thereby focusing on their main distinctive feature. Besides, I would be very ...
0
votes
0answers
34 views

Is there a name for this property (on sequences)

Suppose we have a sequence $(x_n)_{n=1}^\infty\subseteq X$ with $(X,d)$ a metric space, and we have the following property: $$\exists x\in X\forall\epsilon>0[|B_\epsilon(x)\cap ...
1
vote
1answer
35 views

“Englightening” Definition of Simple Lie Group

I'm currently looking for an "englightening" definition of a simple Lie group, for someone who understands the terms Lie group/algebra already. The Wikipedia definition is quite heavy In group ...
0
votes
1answer
35 views

Terminology conventions in optimization

I am writing a paper on optimization and was wondering if it is acceptable to say, for example, "There are many local minimums" or should it be phrased to say "There are many local minima"? Are ...
1
vote
3answers
51 views

How to summarize the sigma signs

I really don't know how to summarize the sigma signs in the best way, I know how to calculate with them, but to summarize them to just one sigma sign is quite new for me and I don't quite understand ...
0
votes
2answers
44 views

What is the mathematical symbol/representation for the remainder operation?

Is there an equivalent in mathematical language to the modulo (or mod) function in computing?
1
vote
0answers
42 views

What is the name for the coefficient of $x^0$ in polynomial equations?

It is probably an embarrassingly simple question, but here is the background: I find myself struggling to verbalize the conceptual, generic name for the terms in simple polynomial equations that are ...
1
vote
1answer
38 views

Is there a short name for series which satisfy the hypothesis of the alternating series test?

The alternating series test says that an alternating series whose terms are monotonically decreasing in absolute value and which approach zero in the limit converges. Of course this is not an ...
1
vote
0answers
40 views

What's the name of this extremely common but extremely pathological continuous function?

Okay, so let's define a random function $F$, such that the value of $F(x)$ is uniformly distributed on $[-1,1]$, and such that for any $x$ and $y$ with $x \ne y$, $F(x)$ and $F(y)$ are independent. ...
2
votes
0answers
28 views

What is the name of this transformation's property?

I have a transformation $P$ with the following property: $P^n = \mathbb{I}$ (the identity) for some specific $n>1$, and all $P^m \neq 1$ for $m \neq n$. What is the name of the property of $P$? ...
2
votes
1answer
88 views

Is there something similar to $\mathbb{R}^2$ for elliptic curve point representation?

Let $E$ be an elliptic curve over a finite field $\mathbb{F}_p$ and denote with $E(\mathbb{F}_p)$ its set of points over $\mathbb{F}_p$. Consider a coordinate system in $\mathbb{R}^2$. Every point is ...
0
votes
0answers
12 views

Which parameter should be considered as “scale” parameter for Gamma distribution?

I originally posted this question on crossvalidated. In case it would be considered too "nerdy" or useless there, I also posted it here with the hope to get more replies. From Wikipedia and ...
0
votes
1answer
9 views

Equation with sums of functions, justification for considering only individual functions

I'm not sure how to title this question, so please edit the title if you know better. I have an equation involving sums of functions: $$ ...
3
votes
1answer
23 views

Meaning of adding rows matrix

English is not my mother tongue and I'm studying Algebra using a book in English. This sentence came up to me in an exercise "every row of matrix $A$ adds to zero". What does that mean, in concrete? ...
0
votes
1answer
61 views

difference between “let” and “for all”

What is the difference between "let" and "for all"? Consider the following example For all natural numbers n, if n is even, then n squared is even. Let n be a natural number. If n is even, ...
5
votes
1answer
29 views

Name for the module corresponding to a square matrix

I recently learned that for each $n \times n$ matrix $A$ with entries in some field $F$, there is a corresponding $F[x]$-module $M_A$. Namely, $M_A$ is the set $F^n$ with vector addition defined as ...
0
votes
1answer
39 views

Is it called the 'multiplication table' for any type of group, or only for multiplicative ones?

Suppose you had an additive group. Would the table showing its elements still be called the 'multiplication table'? If not, what is the general name given to the table showing the elements of a group ...
4
votes
2answers
167 views

Definitions of “linearity” across branches of mathematics or levels of math education

Linearity is a ubiquitous concept in mathematics; however, each branch of mathematics appears to have its own definition of what a linear map (function, functional, functor, transformation, form, ...
2
votes
0answers
55 views

Name for the universal normed space associated to a seminormed space

If $(V,p)$ is a seminormed space, then $(V/N,\overline{p})$ is a normed space, where $N=\{x \in V : p(x)=0\}$ and $\overline{p}(x \bmod N) = p(x)$. My question is as follows: Is there a common name ...
1
vote
0answers
28 views

What is the name of partition without pairwise disjoint property?

Wiki definition of partition: Equivalently, a family of sets P is a partition of X if and only if all of the following conditions hold:[2] P does not contain the empty set. The union of ...
9
votes
0answers
70 views

The term “elliptic”

There are many things which are called “elliptic” in various branches of mathematics: Elliptic curves Elliptic functions Elliptic geometry Elliptic hyperboloid Elliptic integral Elliptic modulus ...
3
votes
1answer
55 views

why there are no parabolic (on a paraboloid) non-euclidean geometry?

I have seen in many contexts that Euclidean geometry is called also "parabolic geometry". As in many things in mathematics (conics, differential equations, algebraic equations) the terms: ...
1
vote
2answers
26 views

What's the correct terminology for these two types of percentages?

You can represent a value reducing by 20% as either: -0.2 or 0.8 Likewise, if a value increases by 20%, you can represent this change as either: +0.2 or 1.2 Your equations clearly need to be aware ...
0
votes
0answers
16 views

What's the technical term for a function which delivers only few unique values?

How is the technical term for a function which has only few unique values ? Say y(x) has a range of real numbers and g(x) has a range of {5,10,15}. The range of g(x) is really small. Does there ...
0
votes
1answer
29 views

Can a subset ever be considered as a member/element of its superset under certain conditions?

For example: Let $\mathrm{S}$ be a 2x2 square matrix. Each element in $\mathrm{S}$, denoted by the term $\mathrm{sector_{\alpha \beta}}$, is itself a set of non-numerical objects (a custom software ...
4
votes
0answers
44 views

A name for elements of a group generating the same cyclic subgroup

Elements with similar properties usually deserve a name in many contexts, say primitive elements in finite fields, integers modulo a number $n$, generators of a free groups etc. Does there exist a ...
2
votes
2answers
27 views

Denoting a “set” versus denoting a “family” (and perhaps a class as well)

Let's work with open intervals of the real line, $\mathbb{R}^1$. That is, let us deal with objects of the form $(a,b), a,b\in \mathbb{R}$ $\{(a,b): a < b, a,b\in \mathbb{R}\}$ I believe represents ...
0
votes
0answers
17 views

What's a name of this quantity: $\max_i \big\lvert {\| x_i \|_2}^2 - 1 \big\rvert$?

What's a name of this quantity: $\max_i \big\lvert {\| x_i \|_2}^2 - 1 \big\rvert$? I defined this quantity to measure how the given set of real vectors is far from a set of normalized ones. Perhaps ...
-1
votes
1answer
63 views

Relationship between cartesian product and cross product?

Is there any relation between cartesian product and cross product? Or is it just the same symbol?
1
vote
2answers
42 views

What is a mathematical term for a non-rectangular matrix/array?

In computer science, we can have a list of lists, and the sublists can have different lengths. In math, is there a concept for such non-rectangular "matrix"? If I am correct, array and matrix are ...
0
votes
1answer
9 views

Convention for generators of monoids - is $ \left\{x^n \right\} _{n\geq 0}$ freely generated by $x$?

I'm trying to understand whether the multiplicative monoid $ \left\{x^n \right\} _{n\geq 0}$ freely generated by $x$ or $1,x$. So for monoids, are "zeroth powers" included in generating sets or not?
2
votes
1answer
209 views

Distinction between “if any” and “if every”. [duplicate]

Today in my math class I presented a counter example to the theorem: "if any infinite sequence in X has an adherent point in X, then X is compact." Let $X=(-1,2)$. Choose $\{X_{n}\}= \frac{1}{n} = ...
2
votes
0answers
45 views

Name of the class of maps between posets such that $f(x)\le f(y)\implies x\le y$

Is there a name for such functions $f:\mathfrak{A}\rightarrow\mathfrak{B}$ from a poset $\mathfrak{A}$ to a poset $\mathfrak{B}$ that $$f(x)\le f(y)\implies x\le y$$ (for every $x,y\in\mathfrak{A}$)?
1
vote
2answers
40 views

Standard terminology for the “quotient of a quotient”

Let $n$ and $m$ be integers. One can write $$ n = mq_0 + r_0 $$ where $0\leq r_0 < m$; the $q_0$ term in the right-hand side is the "quotient". One could then write $$ q_0 = mq_1 + r_1 $$ where ...
0
votes
2answers
31 views

What is the proper adjective/adverb for a power function?

I have a function where space grows as a power of time: $x= at^2$. In my report, I've been using the adjective 'exponential' or adverb 'exponentially' to describe the expansion with time. However, ...
3
votes
1answer
92 views

What is the branch of mathematics called that deals with proofs?

What is the branch of mathematics which deals with how mathematical proofs are constructed? I am looking to learn more about cryptography and category theory, but I am missing some of the mental ...
3
votes
0answers
37 views

The motivation for quivers?

I would like to know about the reasons (I mean, methodological reasons, not just a penchant for innovation in terminology) for Pierre Gabriel to make use of quivers. Is it fair to say he wanted to ...
2
votes
0answers
47 views

Analytic vs algebraic proof

I've ran into phrases like "this is a purely analytical/algebraic proof[...]" in a few books I've read, and I quite never got the full grasp of what the difference between one or the other might be. ...
0
votes
0answers
19 views

Is there a name for a total order with a zero element?

Is there a name for a total order equipped with a zero/bottom element? (And not necessarily a unit/top element.)
1
vote
1answer
30 views

Is there a name or symbol for the set of all subsets of all elements of some set of sets?

Given a set of sets $A$, we construct $A'=\{a\subseteq\bigcup A\mid a'\in A,a\subseteq a'\}$. For $A=\{X\}$ we get $A'=2^{X}$, for $A=\{\{1,2\},\{2,3\}\}$ we get ...
1
vote
2answers
43 views

Is there a name or symbol for this set relation?

Given two sets $A,B$ we say $A\leq B$ if for each $a\in A$ there is some $b\in B$ with $a\subseteq b$. So for instance $\mathbb{2^N<2^Z<2^Q<2^R}$, ...
0
votes
1answer
24 views

Taking derivatives of constants and variables

When implicitly differentiate a function, for example, $f(x)=(G)(x)$, where G is a constant, is it possible to differentiate it such that we can treat G as a variable? From my understanding it is ...
4
votes
2answers
138 views

Word to describe a slice of multi-dimensional space

Ported from English Language & Usage I'm in the market for a mathematical (or otherwise) term to describe a slice of a hypercube. Tensor is out of the running as that's the name of the object I ...
1
vote
1answer
15 views

Word describing a slice of multi-dimensional space

I'm in the market for a mathematical (or otherwise) term to describe a slice of a hypercube. Tensor is out of the running as that's the name of the object I am slicing. The second I could use a hand ...
3
votes
1answer
60 views

The analogy between two Rudin-Keisler orders

Given a set $X$, an ultrafilter $U$ on $X$, and a function $f\colon X\to Y$, we can push forward $U$ along $f$ to obtain an ultrafilter $f_*U$ on $Y$, defined by $C\in f_*U$ if and only if ...
3
votes
1answer
38 views

What is a split $\mathbb{K}$-algebra?

After some considerations the article I'm reading concludes: "...hence H is a simple split $\mathbb{K}$-algebra". I can't find this definition anywhere: what does "split" mean?
1
vote
0answers
29 views

An informal account of Godement resolution??

while reading on the Godement resolution regarding stalks of a sheaf and the relation to the whole of the sheaf itself, https://en.wikipedia.org/wiki/Godement_resolution I found this statement: It ...
0
votes
0answers
18 views

“Clockwiseality” and Chirality

This question was asked over on ELU http://english.stackexchange.com/q/287021/129806. It seems most people agree that "chirality" is the correct word to use, however I am not so sure. I feel this ...