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

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17 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 ...
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2answers
129 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 ...
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0answers
45 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 $B$ ...
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1answer
79 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 ( ...
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0answers
14 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 $\phi$ ...
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2answers
34 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 ...
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3answers
231 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. ...
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0answers
47 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 ...
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2answers
51 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 ...
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1answer
33 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 ...
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0answers
35 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 ...
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0answers
17 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. ...
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0answers
28 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
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1answer
36 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 ...
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1answer
62 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
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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 ...
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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?
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0answers
33 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
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0answers
83 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 ...
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0answers
37 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, ...
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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 ...
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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 ...
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3answers
266 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?
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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
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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 ...
3
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0answers
88 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: ...
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2answers
71 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 ...
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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 ...
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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 ...
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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 ...
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2answers
126 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: ...
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1answer
41 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 ...
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1answer
57 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?
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5answers
618 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 ...
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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! ...
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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 ...
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0answers
55 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 ...
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1answer
30 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 ...
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1answer
38 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. ...
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1answer
97 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
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1answer
121 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 ...
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0answers
35 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?
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1answer
29 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 ...
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0answers
34 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 ...
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3answers
134 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 ...
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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 ...
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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 ...
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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 ...
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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?
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1answer
79 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 ...