# 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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### 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,...
1answer
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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, ...
1answer
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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 ...
1answer
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### 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 ...
0answers
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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 ...
1answer
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### 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 ...
1answer
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### 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. ...
0answers
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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 ...
2answers
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### 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 ...
2answers
52 views

### 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?
1answer
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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 ...
1answer
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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 (...
2answers
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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 ...
1answer
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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 ...
0answers
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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 ...
2answers
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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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### 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.
2answers
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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 ...
1answer
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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 ...
1answer
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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 ...
1answer
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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 ...