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)

1
vote
0answers
30 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 ...
0
votes
0answers
14 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
27 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
35 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
54 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
41 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
32 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
27 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
59 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
36 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
24 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
265 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?
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
73 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: ...
5
votes
2answers
69 views

What is a finitary proof?

I started reading "mathematical logic", by J.R.Shoenfield, but I cannot quite understand a sentence in the very first chapter: Proofs which deal with concrete objects in a constructive manner are ...
0
votes
1answer
46 views

how would you define the term “elementary” in the context of categories and sets?

I was just reading P.T. Johnstone's introduction to his book "Topos Theory", where he uses the term "elementary" many times to classify the nature of theorems and definitions, examples below. I ...
0
votes
1answer
25 views

What does this mean?

What does the following sentence mean? The $n^{th}$ power of the sum ${a_1}+{a_2}+\dots {a_k}$ is the sum of all terms of the form $$\frac{n!}{i_1!i_2!\dots i_k!}{a_1}^{i_1}{a_2}^{i_2}\dots ...
1
vote
0answers
33 views

Types of definitions

My question is about terminology. Consider the following two types of definitions of a circle: A circle is the collection of all points at the same distance from a given point. A circle is the ...
0
votes
2answers
123 views

Why do we use the term “equivalent” with Operators but “equal” with Functions?

Why do we speak in terms of "equality" when we deal with functions but "equivalence" when dealing with operators? To elaborate: Two functions, f and g are equal to each other (denoted: f=g) if: ...
1
vote
1answer
39 views

terminology for “a number with at least two distinct prime factors”

Is there an established terminology for "a number with at least two distinct prime factors"? These are the composite numbers 6 (2x3), 10 (2x5), 12 (2x2x3), 14 (2x7), 15 (3x5), ..., but not 4 (2x2), 8 ...
2
votes
1answer
54 views

What do you call a set whose subsets all have unique sums?

An example would be $\{1, 3, 7\}$, which has subsets with sums $1, 3, 7, 4, 10, 8, 11$. What is this called?
6
votes
5answers
614 views

What's the name of this algebraic property?

I'm looking for a name of a property of which I have a few examples: $(1) \quad\color{green}{\text{even number}}+\color{red}{\text{odd number}}=\color{red}{\text{odd number}}$ $(2) \quad ...
0
votes
2answers
59 views

Very simple notation question

What notation is it called when a number is represented as a series of additions, for example: 124 = 100 + 20 + 4 This is a very simple question obviously but I don't remember what it's called! ...
2
votes
1answer
42 views

Terminology on pullbacks

I'm quite confused with the use of pullbacks, and in particular I wonder which terminology I shall use in the following examples. Let $X$ and $Y$ be arbitrary sets. Suppose that $f,g:X\to Y$ and I ...
2
votes
0answers
52 views

What do you call the following operations on a symmetric matrix?

Suppose we have a symmetric matrix of the following form, where the diagonal is always zero: \begin{array}{cccc} 0 & 1 & 1 & 0\\ 1 & 0 & 1 & 1\\ 1 & 1 & 0 & 0\\ 0 ...
0
votes
1answer
29 views

Terminology: Alternatives for zero crossing

Is it correct to name the red and blue points hinge points, as an alternative to zero crossing? Or are their better terms to describe these points? Update I have several functions like these. I ...
1
vote
1answer
32 views

Is the colimit of finite tensor products a tensor product?

Let $(R_\lambda)_{\lambda\in\Lambda}$ be a family of $A$-algebras. Atiyah & MacDonald defines the "tensor product" of the family as the direct limit of the tensor product of finite subfamilies. ...
4
votes
1answer
66 views

What is the name of the matrix that is created by a vector times its transpose.

I am looking for the name of the matrix created by the following operation: $Z = z*z^T$ I know it should create a symmetric matrix with an element $Z_{ij} = z_{i}z_{j}$
3
votes
1answer
110 views

What does “calculus” mean?

"calculus" and "formal system" From http://en.wikipedia.org/wiki/Propositional_calculus#Terminology a calculus is a formal system that consists of a set of syntactic expressions ...
1
vote
0answers
33 views

Why are compact and noncompact manifolds without boundary called closed manifolds and open manifolds, respectively?

Why not just call them compact and noncompact manifolds? Isn't the general assumption that manifolds have empty boundary unless stated otherwise?
0
votes
1answer
27 views

An English question for a logical term

Consider a tuple of logical expressions: $(P_1, \ldots, P_n)$ such that $P_i\Rightarrow P_{i+1}$ for every $i=1,\ldots,n-1$. An English question: Should I call it implications tuple or tuple of ...
0
votes
0answers
27 views

Meaning of abstractness and concreteness

Do abstractness and concreteness mean for formal systems and their models respectively? Do they relate to how big the theory is? For example, the theory of rings is richer than the theory of ...
1
vote
3answers
133 views

The Name for $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$ and $\mathbb{O}$ Exclusively Algebras?

The Wikipedia page for Normed Division Algebras has been redirected to Normed Algebras and the explanation given is that $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$ and $\mathbb{O}$ algebras are not the ...
2
votes
1answer
46 views

When does intersection of measure 0 implies interior-disjointness?

If there are two "nice" shapes in $R^2$, such as circles or polygons, whose intersection has area 0, then they must be interior-disjoint, as their intersection can only contain pieces of their ...
0
votes
1answer
47 views

Why we use ANY in the definition of a maximal element?

I am confused about the following definition: "a maximal element of a subset S of some partially ordered set is an element of S that is not smaller than any other element in S." I do not understand ...
0
votes
0answers
23 views

Canonical term for $\overline X / X$ where $X$ is a normed space.

Let $X$ be a normed vector space. Let $\overline X$ denote its completion. Is there a canonical name for the quotient space $\overline X / X$? Some authors seem to use "torsion" as a name, but I ...
1
vote
0answers
49 views

Why is it called a primitive root?

I am looking for a paper or reference that explains why primitive roots are called primitive roots. I know what they are but was wondering if there was a reason?
3
votes
1answer
76 views

What is a 'disjunct' of a union called?

Say I have a set $C = A \cup B$ and I want to refer to $A$ in natural language. Had the expression been a Boolean formula with a disjunction, then I would call $A$ the first disjunct. Is there a ...
1
vote
0answers
35 views

Different names for “function”

Quoting a book, "functions can also be named: Mappings, Transformations, Operators, Arrows or Morphisms" I have the idea that these different names are used depending on different contexts. But I ...
2
votes
0answers
64 views

Please identify this equation: $\nabla^2 \mathbf F -k^2 \mathbf F = \mathbf A$

Is this equation $$ \nabla^2 \mathbf F -k^2 \mathbf F = \mathbf A $$ somehow named? F and A are vector fields. I guess inhomogeneous sign reversed Helmholtz equation isn't appropriate ...
1
vote
1answer
29 views

Definition of a geodesic ball?

I think it goes along the lines of: a ball made of a series of flat sides. Also is a geodesic ball and geodesic dome the same thing?
5
votes
0answers
34 views

Name for Number of Ancestors/Descendants of Vertex in Directed Acyclic Graph

Let $G = (V, E)$ be a directed acyclic graph. For each vertex $v \in V$, define the ancestors of $v$ to be the set of vertices $u \in V$ such that there exists a directed path from $u$ to $v$. ...
1
vote
2answers
66 views

How to call two subsets that can be deformed into each other?

Given a topological space $X$, is there a canonical name for the equivalence relation generated by the following relation on the subsets of $X$? $A \sim B :\Leftrightarrow \exists \text{ continuous } ...
0
votes
0answers
23 views

What is the edge called that converts a tree to a directed acyclic graph?

Neither Wikipedia nor mathworld gave the answer: What is the name of the edge (or multiple edges) without which a DAG would be a tree? Or maybe instead: What is the name of the subgraph such that ...
1
vote
1answer
36 views

A simple, yet non-superficial explanation of what “paramodulation” means in the context of automated theorem proving?

Modern automated theorem provers seem to be paramodulation-based. I only have a superficial understanding of what this means: we derive a proposition whose truth is implied from the truth of [two?] ...
0
votes
0answers
38 views

What do we call those functions that can be obtained from term operations by partial evaluation?

Let $T$ denote an algebraic theory and suppose $X$ is a $T$-algebra. Then a term operation of $X$ is a function $f : X^n \rightarrow X$ that is definable by an expression in the language of $T$. ...
37
votes
17answers
4k views

What exactly is a number?

We've just been learning about complex numbers in class, and I don't really see why they're called numbers. Originally, a number used to be a means of counting (natural numbers). Then we extend ...
2
votes
1answer
53 views

How to call a tree with a single branch?

How do you call a tree with only one branch (in other words, where every vertex has maximum one direct successor)?