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
74 views

What is the mathamatical term for this programming concept?

In python's itertools, there is a function called permutations. It returns the number of ways to arrange x number of variables into a given space. For example, ...
2
votes
1answer
18 views

How is it called when you apply min / max seperatly to each dimension?

I want to do the following: $$\begin{pmatrix}3\\1\\4\\1\end{pmatrix} = \min( \begin{pmatrix}4\\4\\4\\4\end{pmatrix}, \begin{pmatrix}3\\1\\4\\10000\end{pmatrix}, ...
0
votes
0answers
8 views

A standard terminology for different definitions of complete sublattice

Let $(X,\le)$ be a complete lattice and $A\subseteq X$. I'm trying to find a standard terminology for special types of sublattice. What is $A$ called if $(A,\le_A)$ is a complete lattice. ...
0
votes
1answer
42 views

generators vs basis of an algebra

Are all bases of an algebra generating sets, but all generating sets are not bases? A basis can only use addition and scalar multiplication to generate an algebra, which means it is a generating ...
0
votes
0answers
26 views

What's the name of $\sum_{k = 0}^{n} (-1)^k {n \choose k} (n-k)^w$?

I worked out the following expression as the number of all possible "words" consisting of exactly $w$ letters from an alphabet $L$ of size $\left|L\right| = n \leq w$, and containing each of these $n$ ...
1
vote
1answer
26 views

Terminology for idempotents that commute with every other idempotent

Given a semigroup $S$, is there terminology for those $x \in S$ such that the following hold? $x$ is idempotent Given any idempotent $y \in S$, we have $xy=yx$. Comments. Let $E$ denote the set ...
4
votes
2answers
103 views

Usage of the term “Free”

What is the difference between free groups and free modules/vector/algebras spaces, or in other words what does free mean in algebra? I have seen two uses of the term free: something of ...
0
votes
1answer
91 views

Does “arbitrarily small” mean very close to zero or very negative?

In mathematical writing, does “arbitrarily small” mean very close to zero (like $0.000001$) or very negative (like $-1000000$)? Are there better phrases to distinguish these two cases?
4
votes
1answer
66 views

Is there a name for the property of a function f such that $f(x,y)=f(y,x)$?

As in the title: is there a name for the property of a function such that $f(x,y)=f(y,x)$. I don't know how to be clearer than that. I tried to look for symmetric property on Google, but without any ...
3
votes
1answer
54 views

Why are normal subgroups called “Normal”?

Why are normal subgroups called "Normal"? Who is credited with naming them, and why are they named such?
20
votes
6answers
2k views

Is there a name for the function max(x, 0)?

Is there a name for the function $ \max(x, 0) $? For comparison, the function $ \max(x, -x) $ is known as the absolute value or modulus of x, and has its own notation $ |x| $
1
vote
0answers
42 views

What do you call a matrix where the rows sum to zero and the columns sum to zero?

What do you call a matrix where the rows sum to zero and the columns sum to zero? Or is there no standard name for this type of matrix?
0
votes
0answers
10 views

Phrases for uniform boundedness and uniform convergence

I have some doubts about using prepositions. I. Let $f_a : \mathbb{R} \to \mathbb{R}$, $f : \mathbb{R} \to \mathbb{R}$. Assume that $f_a (x)$ converges uniformly to $ f (x)$, $x \in [0;1]$, as $a ...
0
votes
0answers
34 views

Is a set of some $m \times n$ matrices a relation?

A relation between sets $A_i, i = 1, \dots, n$ is defined as a subset of $\prod_i A_i$. Given $m, n \in \mathbb N$, is a set of (some or all) $m \times n$ matrices over $\mathbb R$ considered a ...
0
votes
1answer
59 views

Is there a name for continuous functions $\Omega \rightarrow \mathbb{R}$ that can be continuously extended to $\overline{\Omega}$?

Given topological spaces $X$ and $Y$ together with a subset $\Omega \subseteq X$, is there a name for those continuous functions $f : \Omega \rightarrow Y$ such that $f$ can be extended to a ...
0
votes
1answer
26 views

Is there a name for sum over one set divided by the cardinality of another set?

What is the summation of one set real numbers divided by the cardinality of another set called? $$A \subset\mathbb R$$ $$\frac{\sum A}{|B|}$$ I will try and be specific to my problem because I lack ...
0
votes
0answers
30 views

Can we call the boundary of a subset of a topological space “partial X”?

Intuitively, one might be tempted to say $\partial S$ (the boundary of $S\subseteq X$ for X a topological space) as "partial X". Is this formally valid?
0
votes
1answer
29 views

Is there a technical term for a 'complementing' number that sums to 1?

I'm looking for a technical name (if one exists) for a number that 'completes' or 'complements' another. The motivation for this is to develop a proper understanding of mathematical language, for ...
0
votes
1answer
57 views

Is there a name for this variant on “continuous function”?

Let $X$ and $Y$ denote topological spaces. Then a function $f : X \rightarrow Y$ is said to be continuous iff for all $U \in \mathcal{P}(Y)$, it holds that if $U$ is open in $Y$, then $f^{-1}(U)$ is ...
1
vote
1answer
24 views

What does it mean for a function to be uniquely determined by another function?

In munkres topology, I went through an exercise which asks me to show that a function is uniquely determined by another function. I wonder, What does this mean? I googled it but No answer! Here is ...
6
votes
3answers
114 views

Is $x^x$ a polynomial, an exponential or both?

If $c$ is a constant, and $x$ is a variable, we'd say that $f(x) = x^c$ is a polynomial function of order $c$. Conversely, the function $f(x) = c^x$ would be called an exponential function. Is there ...
-1
votes
0answers
66 views

What is even meant by the “cardinality of a model?”

Please help me understand even the most basic ideas in model theory: When in model theory we speak of the cardinality of a model, what exactly is meant by that? I assume that when we say that the ...
0
votes
0answers
16 views

How to call a function defined on a set with gaps on arbitrarily small scales.

Let $I$ be an interval and $A\subset I$ such that for any two points $x,x'\in A$ there exists an interval $J$ between $x$ and $x'$ such that $J\cap A=\emptyset$. How does one call this proerty of ...
1
vote
2answers
77 views

Names of 3 input logic gates

I've tried to look this up online, I may have used the wrong terminology. This question is about the names of logic gates with three boolean inputs, and one boolean output. This is a truth table for ...
1
vote
0answers
40 views

Is there a name for the following type of block matrices?

Is there a name for the following type of block matrices? A matrix $A$ is [insert name here] if it can be decomposed into non-zero non-scalar submatrices such that each sub-matrix $B$, with $B$ ...
0
votes
1answer
77 views

How is the curve with equation $1/x^4 + 1/y^4 = 1$ called?

Well what is the graph for $$\frac 1{x^4} + \frac 1{y^4} = 1$$ called? According to $ Wolfram-Alpha$: http://www.wolframalpha.com/input/?i=plot+1%2Fx%5E4%2B1%2Fy%5E4%3D1+and+y%3Dx+and+y%3D-x ( ...
0
votes
0answers
10 views

Nomenclature for the function appearing in Carathéodory's criteria of differentiability

In my previous question Concerning Carathéodory's criteria of differentiability and a proof that differentiable implies continuous I stated the criteria as follows: There exists a function $\phi$ ...
3
votes
1answer
27 views

Is there are term for location plus orientation, without magnitude?

Is there a concise, accepted term for a piece of information that describes location (translation from origin) plus orientation (angular position / attitude), but ignoring magnitude? In a little ...
0
votes
3answers
72 views

Is there an adjective appropriate for describing mathematical terminology that you feel needs to be phased out? [closed]

Let me firstly apologize; this is more of an English language question, so posting it here is perhaps slightly inappropriate. But I couldn't think of a non-mathematical example, so here we are. ...
0
votes
0answers
34 views

Hyperbolic sinc function

Cardinal sine function or sinc function is defined by: \begin{equation} \mathrm{sinc}x=\begin{cases}\frac{\sin x}{x}, & x \neq 0,\\ 1, & x = 0,\end{cases} \end{equation} Is there any ...
4
votes
2answers
50 views

A question on terminology (Group Theory)

Is there a standard adjective to describe a finite group $G$ of composite order which possesses, for each (positive) divisor $d$ of $|G|$, a subgroup of order $d$? I would guess "Lagrangian" but I ...
1
vote
1answer
32 views

What type of Banach spaces $X$ does the sum $x + c$ make sense where $x \in X$ and $c \in \mathbb{R}$?

What are such spaces called where we can add a constant to an element of the Banach space and the addition makes sense somehow? Eg. in $L^2$ this always is sensible. Is there a difference to the name ...
1
vote
0answers
27 views

In regards to metric spaces, does $d^\star$ have an accepted name, or notation? Do any authors use it?

(I write $\omega$ for the set $\{0,1,2,\ldots\}$.) Let $X$ denote a metric space with metric $d$. Define a function $d^{\star} : X^\omega \times X^\omega \rightarrow [0,\infty]^\omega$ by writing ...
-2
votes
0answers
26 views

What should it be called please suggest me.

Given two functions $T1: S\rightarrow U$ and $T2: U\rightarrow V$, who do we read the composition $T2\circ T1$? By "read", I mean in the sense that "$A\subset B$" is read "$A$ subset $B$" or "$x\in ...
0
votes
0answers
13 views

Tree of arity n: How to call a vertex that has only k (k<n) children?

What is the correct adjective for a vertex in an n-ary tree that has only k children (k < n)? I was thinking of something like "unsaturated", but I don't know if that is the correct word for this. ...
1
vote
0answers
26 views

Name of this property: all maps from given class of spaces into $X$ are nullhomotopic?

Let $X$ be a topological space and let $\mathcal{C}$ be some class of topological spaces. Is there a standard name for the following property of $X$? For every space $C\in \mathcal{C}$ all maps $C\to ...
2
votes
1answer
32 views

Unbounded “polygon”

If we take the unit square and push its north-eastern corner to the north-east towards infinity, we end up with the first quarter-plane. We can do the same to other polygons, for example, if we take ...
0
votes
1answer
41 views

Term For Rotating 3d Vectors About a Pivot Point

What is the term for Rotating a 3d Vector about another 3d Vector (Pivot Point)? For example; if I want to move X distance from one point towards another point - the mathematical term for this ...
2
votes
1answer
36 views

Name for percentage as a decimal between 0 and 1 inclusive

Problem I'm unsure if I should be asking this here or on English Language, so sorry if it's not a good fit for a site. I'm looking for a term that describes a number between 0 and 1, inclusive, that ...
1
vote
0answers
31 views

Name of the natural bijection between $[a,b] \subset \mathbb{R}$ and $[c,d] \subset \mathbb{R}$

Given $[a,b],[c,d] \subset \mathbb{R}$, we can take the natural bijection between those intervals $$\phi: [a,b] \to [c,d] \\ x \mapsto (x-a) \frac{d-c}{b-a} + c$$ Does this bijection have any name?
0
votes
0answers
25 views

When is the higher-order theory of a model categorical?

I'm interested in (classical) type theories $L$ with the following property. For $M$ any model of $L$ (in Set), let $T(M)$ be the type theory of $M$, i.e., the strongest extension of $L$ satisfied by ...
2
votes
0answers
56 views

What is this semicircle-like shape called?

I would like to know the name of the shape shown below I know that the shape without the straight part at the bottom between the two quarter circles is called a semicircle. Also this shape vaguely ...
0
votes
0answers
33 views

What does “single set” mean in this context?

I encountered this problem in Munkres topology. Let $X_1 , X_2$ denote a single set in topologies $\tau_1$ and $\tau_2$, respectively; let $Y_1 , Y_2$ denote a single set in the topologies $U_1, ...
0
votes
0answers
22 views

Is there accepted notation and/or terminology for the smallest cover of $S$ with cells from $P$?

Let $X$ denote a set. Then for $S \subseteq X$ and $P$ a partitioning of $X$, define $P \diamond S$ as the smallest cover of $S$ with cells from $P$. Explicitly: $$P \diamond S = \bigcup\{Q \in P ...
0
votes
1answer
38 views

How do you call it when you remove the top n% and the bottom n% of a dataset?

I am currently writing about a dataset of collected handwritings. I want to show some characteristics of the dataset. For example I think it is interesting to show how long it took users to create the ...
3
votes
3answers
262 views

Name of the point whose coordinates are the mean of the coordinates of a list of points.

Let $ X = \{ (x_i,y_i) \, | \, i \in I\}$ be a set of points (where $I$ is a finite index set). Does the point $x_0 = \frac{1}{|I|} \sum_{i \in I} (x_i,y_i) $ have any name?
1
vote
0answers
22 views

Tautologies with quanitfiers added

What is the class of formulas that are propositional tautologies with quantifiers added called? For example, something like: $$ \exists x((x=0) \vee \neg (x=0)) \qquad\text{or}\qquad \forall x \exists ...
0
votes
1answer
21 views

Terminology: “entries” of a tuple

Is there a conventional term for the "entries" of a tuple? Possible candidates that come to mind are "entry," "term," and "element," but I don't know if one is more common than the others.
2
votes
1answer
71 views

Do those 'groups' have a name?

Is there a name for 'groups' that only have a neutral element on the right and an inverse for each element on the right ? If there is, does that name also hold for a neutral elt on the right and an ...
2
votes
0answers
25 views

Have any authors suggested mathematics-wide prefixes for “missing a quotient” and/or “missing an identity”?

The prefixes in the following terms both mean: "missing the obvious quotient by the obvious equivalence relation." seminorm pseudometric Similarly, the prefixes in the following terms both mean: ...