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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Conventions for distinguishing the two senses of an ultrafilter on X

Are there any well-established conventions to distinguish the two senses of being an ultrafilter on a set $X$ (when $X$ happens to be equipped with an ordering)? This ambiguity is confusing at first; ...
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What is the correct term for an unnormalized mean of a function?

I want to report statistics for a region of interest $[x_0, x_1)$ of a function $f(x)$. As a concrete example, consider $f$ to be the spectrum seen by a radiation detector, such that $x$ has units of ...
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39 views

How is it called percent with base one?

When we are referring to something that is a percentage (base 100). We talk in these terms: There is 30 percent of water It has 15 percent of fats But, when we are just representing these values in ...
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Does the operation $(A\times B) \cup (B\times A)$ have its own name?

I use such an operation a lot in a computer program I write and I was wondering if it has its own mathematical name. That's all. I was looking for "commutative cartesian product" and for ...
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38 views

What is the categorical-theoretical generalization of order-embeddings and downsets?

NB: even though this question's longish setup gives the impression that it is about the theory of ordered sets, in fact it is really more general than that. The setup here serves only as the ...
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Name for the result of characterizing isomorphism of linear mapping between vector spaces?

Let $V, W$ be two finite dimensional vector spaces and $E = \{e_1,\dots,e_n\}$ the basis of $V$. I do know that $T:V \to W$ is an isomorphism if and only if the image $T[E]$ is a basis for $W$. But is ...
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93 views

How is this integral operation called? $\langle f(x),\phi(x)\rangle = \int_{-\infty}^{\infty}f(x)\phi(x)dx $

Please, can someone tell what is the name of this operation in the context of Fourier analysis? $$ \langle f,\phi \rangle := \int_{-\infty}^{\infty}f(x)\phi(x) \,{\rm d}x $$ And what is the meaning ...
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Name for topology defined by order

Consider a topology on $\mathbb{R}$ that includes the following sets: $\varnothing, \mathbb{R}, (a,\infty), [a,\infty)$ for any $a\in \mathbb{R}$. Does it have a name? Postscript. There is right/...
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50 views

Is being directly negatively proportional same as being inversely proportional?

If I have the proportionality $$x\propto-y$$ It suggests that x increases with $-y$ and since there's a negative symbol present it would mean that the lower the value of $y$ the higher the value of $x$...
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55 views

Terminology on "Compact Subset"

Let's say that $U\subset X=\mathbb{R}^n$ is open. If someone says that $K$ is a compact subset of $U$, what exactly does this mean? Does it mean that $K$ has compact relative closure in $U$ ($\bar{K}\...
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38 views

Is there a name for the fixed-length sequence $[a_0, a_1, \cdots, a_k]$, where $a_i = \frac{2^i}{2^{k+1}-1}$?

I am wondering if there is a known name for the following sequence or if it belongs to a known family. It looks to me like there is one but I cannot remember. It's a fixed-length sequence of the type: ...
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38 views

How do you call call the operation that takes all possible sums of two elements from two vectors?

Take two vectors $a\equiv (a_1,...a_n)$ and $b\equiv (b_1,...,b_m)$. Is there any name and symbol for denoting the vector that lists all possible sums of one element of $a$ and one element of $b$? ...
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Referencing something: Proposition, Lemma, Corollary, etc.?

I have question on how to refer to some mathematical results in order to highlight their hierarchical order. (i) I have a major result which is formulated like: "Assume Assumptions 1 holds. Then ...
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Terminology of "rescaling" a matrix

Is there a name for the mathematical operation that consists in multiplying a matrix $A$ by a diagonal matrix $D$ and its inverse as follows: $D^{-1} A D$. Is the term "rescaling" ...
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Regression curve that can only go down, never up

I have a regression curve that I use to model road condition over time. $$y=21-e^{a x}$$ In this scenario, the way a road's condition works is: the condition can only ever go down (deteriorate); a ...
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Name of Division property in Congruence Equations [duplicate]

Find all solutions for $x$ in the congruence equation $30x\equiv40(\text{mod } 50), 0\leq x\leq 50$ 30 does not have a modular inverse since $\text{gcd}(30,50)=10>1$. However, we can employ a &...
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Why do we not name $-a+bi$ in relation to $a+bi$?

Given a complex number $a+bi$, it has a complex conjugate $a-bi$. The product of this complex number with its complex conjugate gives $(a+bi)(a-bi)=a^2+b^2$. One might imagine flipping the sign of the ...
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Is there a name for graphs that appear as Hasse diagrams of finite lattices?

Hasse diagrams are mathematical diagrams used to represent finite partially ordered sets, and may be seen as a kind of graph. Apparently, there are some relations between particular kinds of lattices ...
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What exactly is a "vector" in math (in terms of vector spaces)?

I am browsing through / reviewing terminology from a more philosophical standpoint, and landed on the term vector. There are Euclidean vectors which is "a geometric object that has magnitude (or ...
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Is a mathematical group also a mathematical "space"? [duplicate]

A mathematical space is defined as: A set (sometimes called a universe) with some added structure. Well, a mathematical group is: A set defined with a combining operation and some additional ...
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53 views

What kind of graph coloring is this?

Assume a very simple graph with 3 points: V0—V1—V2 The following represent all the different possible colorings using 3 colors. I’ve labelled all of the types of colorings that are isomorphic (is that ...
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What is the generic name for an $N$-sided polygon whose sides are $a$, $b$, $a$, $b$ and so on? [closed]

Obviously, the number of sides has to be even. If $N = 4$, you have a parallelogram. I guess Regular truncated polygon might be close for $N > 4$, but that only refers to polygons where all the ...
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A group product

If $G$ and $H$ are two groups, and $\triangleright$ and $\triangleleft$ are a left action and a right action of $H$ on $G$ by group automorphisms such that $$h\triangleright(g\triangleleft h')=(h\...
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"Dependent and independent variables" in first order logic?

In calculus, students are taught the notion of "dependent and independent variables" of a function. (I am not talking about "independent" random variables in probability theory.) ...
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39 views

What's a sequential part of an n-tuple called?

Say I have an ordered tuple $T = (x_1,x_2,x_3,x_4)$. I want to create new tuples that are only valid if they satisfy the following properties: The first element of the tuple must be $x_1$. The ...
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Why $f(x) = x^2$ has variable derivative but its tangent has constant slope?

I'm taking Brilliant.org's calculus course, and I'm on the section called The Derivative. My (mis)understanding: A tangent line is a linear function that grazes a point, $a$, on the graph of a ...
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Established conventions for distinguishing the consequence relations of FOL

Are there any established conventions for distinguishing the consequence relations of first-order logic? I'm thinking both in terms of what to call them (e.g. global vs local) and what notation to use....
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Regarding some symbols in set theory.

I came across this interesting statement that defines the aleph numbers: $$\aleph_{n+1} = \bigcap \{ x \in \operatorname{On} : | \aleph_n | \lt |x| \}$$ However, I do not understand a couple of ...
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Why is a free group action called free?

A group action is called free if every element other than the identity in the group has no fixed points. What does "free" mean? Not able to connect the name to the math definition, I am ...
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The precise meaning of the term 'antiderivative'

I have been helping a friend prepare a calculus curriculum for a high school course, and I've encountered some apparent ambiguity concerning the precise meaning of the term 'antiderivative'. It arose ...
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Terminology "bounded away"

Let $f:[a, b] \rightarrow \mathbb{R}$ be a function. We say that $f$ is bounded away from $1$, if there exists $\epsilon > 0$ such that either $f(x) \geq 1 + \epsilon$ or $f(x) \leq 1 - \epsilon$ ...
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Does Dividing by Zero Return All Numbers?

My understanding assumption is that division inverses multiplication. That may be incorrect or incomplete. I will copy the inversion from WolframMathworld $$a * b = c$$$$a = c \div b$$ Why is the ...
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Why a 'collection' of sets and not a 'set' of sets in sigma-algebra

All the sources I've checked speak of 'a collection', say $\mathcal{F}$, of sets from some set $X$, and then go on to write things like: If $F\in\mathcal{F}$ then $F^c\in F$, and so on. Is it just ...
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What is the terminology used for equations that don't have the same tensor rank (order) on the LH and RH sides of the equation?

For example, in physics, if the dimensions of the term on the LHS of an equality do not match the dimensions of the RHS we say the equality is not dimensionally consistent. So, what do we say for ...
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Term for a set of vectors with equal magnitudes?

Is there a mathematical term for a set of vectors which all have the same magnitude? For my motivation in asking this: I realize that "vectors of equal magnitude" isn't too hard to say. But ...
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83 views

Name this polynomial $\sum_{k=0}^n x^k$

What is the name for the monic polynomial of order $n$ where all $n+1$ terms have coefficient of $1$? i.e. $\displaystyle \sum_{k=0}^n x^k$. Is it something like elementary monic polynomial? For some ...
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How to describe integers calculated from sparse addition and subtraction of integral powers of a certain radix

I'm practicing implementing the elliptic-curve cryptography in my spare time. The first curve I choose to implement is the P-256 curve (also known as secp256r1 in the SEC#2 standard). The modulus of ...
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Understanding a statement about palindromic numbers

I have the following statement: "Palindromes starting with $n$ such that the sum of the digits of the product of the factorial of $n$ and reverse of $n$ is equal to the center digit." And I ...
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What is the difference between saying that $X$ is topological space and $(X,T)$ is topological space?

In some theorems I see in our lecture notes, sometimes it mentions that $X$ is a topological space. But isn't $X$ is just a set, and there must be some topology $T$ with $X$ to have a topological ...
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What's the name of this graph?

I saw this special graph is used in graph theory for a counterexample of several statements. But I don't remember the name of this graph. Could you help me? Thanks.
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Specific term (adjective) to describe a function which is not monotonic?

Is there a specific adjective to describe a function which is not monotonic? I found this question whose title sounds promising, but which asks about something other than the terminology. In case the ...
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Definition in Math or Axiom in First-Order Logic

I have been thinking about what definition is in math. For instance, we may define the power set as follows: for a set $x$, the power set of $x$, denoted by $\mathcal{P}\left(x\right)$, satisfies the ...
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Does this property of two binary operations have a name?

I am wondering whether the following property of two binary operations $\diamond$ and $\star$ has a name. I haven't seen it listed in overviews of properties of binary operations, and I wouldn't know ...
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Notational differences b/w Iterated functions & exponentiation.

https://en.wikipedia.org/wiki/Exponentiation#Iterated_functions https://en.wikipedia.org/wiki/Function_composition#Functional_powers https://calculus.subwiki.org/wiki/Higher_derivative Why does ...
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Coefficients in homology

The singular homology of a space $X$ is defined to be the homology of the chain complex $${\displaystyle \ldots {\stackrel {}{\longrightarrow }}\mathbb Z[Sing_2(X)]{\stackrel {}{\longrightarrow }}\...
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Are there words for topological spaces without "special" points?

What I mean when I say "without 'special' points" is something along the lines of "such that for any pair of points, there is a (disjoint?) pair of respective (connected?) neighborhoods ...
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71 views

What is a "positive statement" in mathematical proof?

I'm going through How to Prove It: A Structured Approach by Daniel J. Velleman and some terms that I frequently see are "positive statement" and "negative statement". I'm not sure ...
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20 views

Word that denotes number of numbers by which a number can be divided without a remainder

Is there a word that denotes the number of numbers by which a number can be divided without a remainder? That is, for 12 it is 4 (because 12 can be divided by 2, 3, 4, 6), and for 14 it is 2 (because ...
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201 views

Is there a name for this property of functions on groups?

Let $G$ be a group and $F:G^n \to G$ with the following property: If $x_1,…,x_n,h \in G$, then $F(hx_1,…,hx_n)=hF(x_1,…,x_n)$. Is there a name for this type of function property? It is something I’ve ...
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Seeking terminology for highly decimalised numbers and their decimalised aspect

Is there a particular term or turn of phrase to describe a highly decimalised number (e.g., 3771388.6900399177) as opposed to a number that is decimalised to only a few decimal places? Also, is there ...

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