Questions tagged [terminology]

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

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$ax$ is arithmetic; $a^x$ is geometric; $\frac{a}{x}$ is harmonic; what's $x^a$?

I know the following terminology: $ax$ is arithmetic; $a^x$ is geometric; $\frac{a}{x}$ is harmonic. What is $x^a$ called? Is there an equivalent name for progressions of the form $t_x=x^a$, where $...
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“Permutation of a set” vs “permutation of a Rubik's cube”: are these uses of “permutation” equivalent?

So my book defines a permutation as follows : "By a permutation of a set A we mean a bijective function from A to A, that is, a one-to-one correspondence between A and itself." This is ...
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Proper term for “hyperstable” algorithm>

Say an iterative approximation algorithm is "hyperstable" if roundoff error at one step simply doesn't matter, because it automatically gets corrected in succeeding steps. For example, we ...
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What is the name for number systems beyond hexadecimal? [on hold]

I know the name of the first couple base n number systems. But what comes after that? Or do they simply not have a name anymore (other than "base n")? binary (base 2) ternary (base 3) ...
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What's the name of this set theory property? $(A \subseteq B) \land (B \subseteq C) \implies (A \subseteq C)$

What's the name of this property in set theory that states that $$(A \subseteq B) \land (B \subseteq C) \implies (A \subseteq C)?$$
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What is *energy* in the context of linear algebra?

I have heard and read the term energy in the context of LA a few times now. e.g: The algorithm is based on the geometrical observations that the word embeddings (across all representations such ...
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54 views

List of Historic Latin Mathematical Terms?

I am wanting to read some original mathematics literature in Latin (specifically Newton's De Analysi). However, I was wondering if there was a list of specifically mathematical terminology that I ...
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26 views

Why emphasizing only random sample?

We know that random sample is a special case of random vector. Most of the textbooks and online resources defines most of the terminology such as likelihood only on random sample rather than random ...
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53 views

Name of a property in Graph Theory

A multigraph is a graph which allows for more than one edge between a pair of nodes in a graph. What would be the name of a graph which allows for more than one type of node. For example, buyers and ...
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Terminology of Rectangle

I saw from the book of topology & multivariable calculus mentioning that $$Q = [a_1,b_1]\times\cdots\times[a_n,b_n]$$ is a rectangle. How to illustrate it? I mean, what does it actually meant ...
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Terminology: “dimension” vs “coordinate”

"Dimension" often means the minimum number of coordinates needed to specify a point in coordinate space. In this context, a "coordinate" is a number or name referring to an axis. So we might say that $...
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What is the appropriate title of a false statement/proposition?

What is the appropriate term to use for titling a mathematical statement which will be proven false? Note that I'm focusing on the context of labeling and organizing results within a paper or similiar,...
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Name of Subset of Domain Mapping to Specific Subset of Image

Suppose I have a function $f: X \to Y$, and I choose some subset $Y' \subset Y$. Is there a name for the set $X'$ such that for some element $e$, $e \in X'$ if and only if $f(e) \in Y'$? For example, ...
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definition of an infinite descending chain

Given a set with a partial order $\leq$, can we say that the following is an infinite descending chain? $a\geq\cdots a_{-2}\geq a_{-1}\geq a_{0}\geq a_1\geq a_{2}\cdots$ I am confused because I have ...
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30 views

Terminology regarding random sample

This question is solely about terminology. Consider the following definition regarding random sample from All of Statistics by Larry Wasserman If $X_1,\cdots ,X_n$ are independent and each has ...
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Why do we say that a one-parameter subgroup “is” a homomorphism?

The definition of a one-parameter subgroup of a topological group $G$ is given as a particular group homomorphism $\phi: \Bbb{R} \rightarrow G$. I'm not sure I understand the terminology. Why do we ...
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26 views

Is there a name for the exponent of a local representation of a holomorphic function?

Let $A\subset\mathbb{C}$ and let $f:A\to\mathbb C$ be holomorphic. Then for a fixed $z_0\in A$, by a conformal change of coordinates we can write $f$ in the form (locally) $$f(z_0)+z^n$$ Is there a ...
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31 views

Random sample in probability and statistics

Is the word random sample has different definitions in probability and statistics? In probability random sample is a vector of IID random variables. I am confused with the same word in statistics. ...
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Why was 'ordinate' adopted to signify y-coordinate? [closed]

The OED doesn't expound what semantic notions underlie y-coordinate and the Latin etymon. Etymology: < classical Latin ōrdinātus orderly, regular, regulated, (in geometry) in alignment, ...
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How did 'abscissa' semantically shift to signify x-coordinate?

Etymonline avouches that abscissa originally signified 'cut off', but what's 'cut off' about an x-coordinate? X-coordinates are merely numbers, not lines. What semantic notions underlie x-coordinate ...
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54 views

What is the proper name for compositions like (f∘g)(x)

Addition, subtraction, multiplication, and division of functions, $(f+g)(x)$, $(f-g)(x)$, $(f×g)(x)$, $(f÷g)(x)$, are fairly common. Is there an established name for such operations on functions using ...
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Degree and Order of a polynomial

I used the term "order" in place of "degree" to define a polynomial. Are the terms "degree" and "order" of a polynomial the same in algebra?
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Describe/define the area of a scalar field that can be reached by local search

Lets assume I have a scalar field (which is a space, which describes a density. For my publication I want to properly define a certain area in this scalar field. The idea is this: Lets start with any ...
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Geodesics: “Transporting tangent vectors in parallel” vs. “Preserving the tangent vector under parallel transport”

Wikipedia states: "[...] More generally, in the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it." Does ...
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Number system terminology

I've made a schematic of the number systems, and I noticed it's not very systematic. Do the categories labelled with a question mark below have a name? Specifically, imaginary integers, noninteger (...
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Generic name of a function with multiple inputs (vectorial domain) and scalar output

A vector-valued function is: ... a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued ...
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Meaning of and Types of Vector Spaces [closed]

Would it be correct to say that a vector space is any set that is consistent with the list of 8 axioms? The 8 axioms being associativity, commutativity, identity element, etc... In physics we are ...
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Is there a term for a class of conjugacy by elements of a subgroup?

The conjugacy class of an element $a$ of a group $G$ is defined to be the set of elements $gag^{-1}$ for all $g \in G$. I have an application where I only want to consider conjugation by elements of a ...
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Is every $1$-dimensional vector space a field?

We say that every field $F$ "is" a $1$-D vector space over itself. By this we mean that if we consider the elements of $F$ as both vectors and scalars, then we get a vector space by using the addition ...
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Is there a name for a set function such that at least one element can be removed without penalty?

Given a set $S$, consider a function mapping its subsets to the reals, $f:\mathcal P(S)\rightarrow \mathbb R$. Assume that for every $T\subseteq S$, there exists an element $i\in T$ such that $f(T\...
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Function, Mapping and Relation [duplicate]

I believe I understand what a function and relation are, but what is a mapping? At first I thought the term was synonyms with relation, but after looking it up, I’m thinking it could be more or less ...
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Is there a name for this subgroup property?

Suppose that I have a subgroup $H \le G$ such that for any $h \in H$, $[h]_G \cap H = [h]_H$. Is there a name for this property? Here, $[h]_G$ means the $G$-conjugacy class of $h$ and $[h]_H$ is the $...
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Name of a dynamical system that extremizes an “action”?

In physics, the equations of motion of a physical system can be derived by minimizing/maximizing an "action", i.e. a functional of the path of the system: $$J(x)= \int_a^bL(t,x(t),x'(t))dt$$ where $...
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Family of $r$-subsets, all pair-wise intersecting in $s$ elements

Let $X$ be some $n$-element set and $\,\mathcal I\subseteq\mathcal P(X)$ a family of subsets with the following properties: all $I\in\mathcal I$ are of size $r$ any two $I,J\in\mathcal I$ intersect ...
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Name of property: $a \circ (a \circ b) = b$

How do you describe an operation like this? $$ a \circ (a \circ b) = b $$ For example, XOR is like this: $$ a \oplus a \oplus b = b $$
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49 views

Minimal property of a graph.

A graph $G$ is said to be minimal if it loses property $P$ after deletion of an arbitrary edge. I am considering a graph $G$ with edges $e_1,e_2,\ldots,e_n$ with property $P$. It loses its property ...
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Is there such thing as a “3-dimensional surface?”

The reason I'm asking this question: I work at the National Museum of Mathematics and, amidst my sundry duties (which generally have nothing to do with the exhibits), I do have the authority to alter ...
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What is the meaning of “Word Problem” in free algebras [closed]

I am looking for a clear definition of Word Problem in free Lie algebras. May you please describe that?
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does pointwise convergence mean that the support is shrinking?

A simple example Let $f_n = n \cdot \mathbb{1}_{[0, 1/n)}$ the function converges pointwise to 0. Can I also say that the support of f is shrinking or is it best to just keep the phrasing: the ...
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A generalization of the concept of finiteness

For concreteness' sake, let the underlying set theory be ZFC. A set $x$ will be called connex (I've adapted the terminology from here) iff for every $y, z \in x$ either $y \subseteq z$ or $z \...
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Mathematical name for related matrix similarity

Let $A \sim B$ such that $A = PBP^{-1}$ and $C \sim D$ such that $C = PDP^{-1}$ with the same $P$ matrix. Is there a name for the relation between $A$ and $C$? Thank you.
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What does countably many signify?

Consider the following definition of discrete Random Variable from the book titled All of Statistics: A Concise Course in Statistical Inference X is discrete if it takes countably many values ...
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How is this a Pell-like equation?

EDIT: Here is the text of the original problem: A drawer contains red socks and black socks. When two socks are drawn at random, the probability that both are red is $\frac12$. (a) How small can ...
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Algebra on modules vs vector spaces

What is the difference between definition of an algebra on $V$ when $V$ is a $K$-module ($K$ is field) and when $V$ is a vector space? Let us consider Leibniz algebras: A Leibniz algebra over $K$ ...
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A particular filter on a Heyting algebra

Let $(H, \le)$ be a Heyting algebra and $x \in H$. Consider the subset: $$F_x = \{ y \in H \mid ((x \to y) \to x) \le x \}$$ It is easy to prove that $F_x$ is a filter. Moreover, $F_x$ is proper if ...
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Term for data range [-1..1]

I'm working on a software project where a lot of data has been scaled to range [-1..1]. But other data sets are scaled to the range [0..1]. In some cases it is useful to convert from one range to the ...
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Name for a special kind of split graph?

A split graph is a graph $G$ containing a clique $X$ and an independent set $Y$ such that $X\cup Y=V(G)$. Has any name been given to graphs with the stronger property of containing a clique $X$ and an ...
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Is “ensemble” a standard term in probability theory?

The book "information theory, inference, and learning algorithms" uses a definition to formalize probability: An ensemble $X$ is a triple $(x,\mathcal A_X,\mathcal P_X)$ where the outcome $x$ is ...
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Generalization of vertex smoothing for higher valence

Another question asks about the terminology of graph smoothing, which removes a vertex of valence 2 and connecting the two vertices it is connected to with an edge. All the sources I've seen (on the ...
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Matrix inserted into identity. Does this matrix have a special name/notation?

I have $n$ positive integers and let $R\subseteq \{1,\dots, n\}$ so that $|R|=r$. I also have a $r \times r$ matrix called $T$. I define a matrix that arises from the $n \times n$ identity matrix by ...