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. ...
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
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 ...
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 ...
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| $
7
votes
3answers
594 views

Latin phrase for “accepting without proof”

Is there a Latin phrase that would be used when accepting some statement without providing the proof of such a statement? For example, say you are working on an elementary number theory proof, and ...
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 $n$ ...
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?
2
votes
2answers
267 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 $\tau$?
3
votes
2answers
268 views

What is the name of the function $f(k) = \text{max}(k,0)$ on $\mathbb Z$? [duplicate]

Let $k\in \mathbb Z$; is there a name for the function $f(k)$ below? $$ f(k) = \text{max}(k, 0) $$
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 ...
-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
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
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 ...
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
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 $B$ ...
1
vote
3answers
945 views

What's the opposite of damping?

A colleague asked me this question and I had no clue. When a function (for instance, a sine wave) is multiplied by a decaying exponential, we call the phenomenon damping. What would it be ...
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 $\phi$ ...
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. ...
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
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
2answers
66 views

Using sequential definition of functional limits, show that $\lim_{x \rightarrow 0} 1/x$ does not exist

Using sequential definition of functional limits, show that $\lim_{x \rightarrow 0} 1/x$ does not exist I have two questions regarding this. Firstly, say we have a function that 'converges' to ...
0
votes
0answers
73 views

Has this property for algebraic structures got a name?

Given a binary operation $*:M\times M\rightarrow M$. I define the extension of $*$ to the subset of $M$ in the usual way (with $A,B \subseteq M$) $a*A:=\{a\}*A$and $A*a:=A*\{a\}$, ...
10
votes
6answers
6k views

Is there any difference between mapping and function?

I wonder if there is any difference between mapping and a function. Somebody told me that the only difference is that mapping can be from any set to any set, but function must be from $\mathbb R$ to ...
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 ...
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. ...
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 ...
10
votes
6answers
484 views

Difference in terminology between Let and Assume?

I was writing an solution to a problem in a textbook about how to factor a quadratic equation. I was told that my use of assume was incorrect and it should have used let; however, my teacher ...