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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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Is there a term for calculating a logarithm where the base, exponent, and power are integers and counting the digits of the power?

Is there a term for the process of calculating a logarithm where the base, exponent, and power are integers, counting the digits of the power, and then converting the results to the particular base? ...
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1answer
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What is a “n-valued function”?

Has $n$ parameters? i.e. 0-valued function: $f(\emptyset)=2$ 1-valued function: $f(x)=x$ 2-valued function: $f(x,y)=x+y$ 3-valued function: $f(x,y,z)=x+y+z$ Not sure
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Metaphors for the entropy of a question

What would be appropriate metaphors to call the entropy of a question? I was thinking along the lines of "information value," but this would clearly be inappropriate, because it is the answers that ...
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Orbit of a Permutation

On page 66 of these notes is proposition 4.26: Every permutation can be written (in essentially one way) as a product of disjoint cycles. The proof begins as follows: Let $\sigma \in S_n$, and ...
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1answer
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What do you call a matrix with these properties?

What do you call a matrix, when multiplied from left and right by vectors $x$ and $v$, then it produces the same result as multiplying it from left and right with $v$ and $x$ respectively. Basically: $...
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Why is 2's complement called as it is? [closed]

We know that 1's complement of a number 001 in binary is 110 in binary. Further, 2's complement of a number is 1's complement of the number, plus 1 added to it.
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Is there a term for the opposite of an interpolation?

The question is specifically about linear Interpolation, which is usually defined to be a function $$ f : V \times V \times \mathbb{R} \rightarrow V \\ f(v_0,v_1,\alpha) = v_0 + (v_1-v_0) \cdot \alpha ...
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standard definition and notation for a truncated permutation

I am seeking the standard notations or the standard way to define a truncated uniform random permutation. Let $M$ be an $n \times n$ matrix where each row and each column contain a single 1 and all ...
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1answer
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Name of the following integral identity

I remember the following integral identity but not sure of the name. I tried to search all the names I remember (like beta integrals, gamma integrals, etc.) but couldn't find for the one given below. ...
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1answer
46 views

What does it mean to generate a random variable?

I am learning about the generation of random numbers, however, many references instead talk about how to generate random variables. Many references will write something like "Suppose we want to ...
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1answer
47 views

Can a sequence be neither decreasing nor increasing?

Given the definition of a increasing sequence: "A sequence $(a_n)_{n\in\mathbb{N}}$ is increasing if for all $n\in \mathbb{N}$, $a_n\le a_{n+1}$." My question is: by this definition isn't the ...
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1answer
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Terminology Filtered probability space

What is the difference between a "filtered probability space" and a "Stochastic base"? I see both terms used but it is not clear to be me if there is a difference. Maybe one is complete but the ...
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Inventor of Topological groups

I had difficulty in finding the person who introduced the term "topological groups". I just want to know who introduced the term topological groups.
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1answer
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Is there a better name for a “spherical annulus”?

For example, the set $\{x\in\mathbb{R}^d: 1\leq|x|\leq2\}$. For $d=2$, I'd call this an annulus. What do we call it in higher dimensions?
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How do you call the operation carried out to set an equation equal to “y”? [closed]

For an assignment I need to set the equation of an ellipse equal to "y". What is the name of this process?
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What is and what isn't a “closed form solution” [duplicate]

I had a friendly discussion with someone about closed form solutions. They contended that the backpropagation algorithm used in calculating the gradients of deep neural networks can't be called a ...
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1answer
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Simpler terminology for determinant and other matrix terms [closed]

Wondering what words you could use to describe the following Matrix properties. Determinant Eigenvalues and Eigenvectors Identity Trace Adjugate Cofactor Conjugate transpose The prefix eigen- is ...
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Is there a special name for a normal subgroup which defines a split extension?

If $G$ is a group and $N$ is its normal subgroup then $G$ is the extension of $G/N$ by $N$. The elements of $G/N$ are the equivalence classes of $G$ of the equivalence relation $g\equiv h$ defined as "...
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1answer
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What exactly is the phase of a complex number? [closed]

I've heard the term "phase" several times (e.g. in the context of waves), not just in the context of complex numbers (which are often mentioned e.g. in the context of quantum computing), but, in this ...
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2answers
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What is a local group isomorphism?

What does it mean for 2 groups to be locally isomorphic? E.g. $SO(4)$ is locally isomorphic to $ SO(3)\times SO(3)$ -why not globally?
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9answers
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Why do we say ‘pairwise disjoint’, rather than ‘disjoint’?

I don’t see the ambiguity that ‘pairwise’ resolves. Surely if $A$, $B$ and $C$ are disjoint sets then they are pairwise disjoint and vice versa? Or am I being dim?
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8answers
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Why do we call complex numbers “numbers” but we don’t consider 2-vectors numbers?

We refer to complex numbers as numbers. However we refer to vectors as arrays of numbers. There doesn’t seem to be anything that makes one more numeric than the other. Is this just a quirk of history ...
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1answer
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Is it appropriate to consider a hole in the graph a zero?

Let there be a function $$f(x) = \frac{x^2}{e^x-1}$$ which has a hole at $x=0$. It also approaches $f(x) = 0$ at this point. Would it be appropriate to call this hole a "zero" or not?
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If $E$ is a vector space, is there an established terminology for functions $f:E\times E\to\mathbb R$ whose values $f(x,y)$ only depend on $y-x$?

Let $E$ be a $\mathbb R$-vector space and $f:E\times E\to\mathbb R$ with $$f(x,y):=g(y-x)\;\;\;\text{for all }x,y\in E.$$ Is there an established terminology for such a function $f$? (I'm aware of ...
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Span of an equation

I use this term to denote a set of numbers of the form $\sum z_n x^n$, where $x$ is the solution of some polynomial $x^a=\sum z_ix^i$ for $i=0$ to $a-1$. $a$, $i$, and the $z_j$ are all in $\mathbb{Z}...
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What is the name of this convex figure?

The figure is given by $x^4+y^4\leq\frac1{2^4}$ https://www.wolframalpha.com/input/?i=x%5E4+%2B+y%5E4+%3C1%2F16. In general is there a name for the figure $x^{2t}+y^{2t}\leq\frac1{2^{2t}}$ or ...
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2answers
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What does minorize mean?

Let $f$ be closed and convex. Then the conjugate of $f$ is $f^*(y) = \sup_{x}(y^Tx - f(x))$. If $y \in \text{dom}(f^*)$, then the affine function $h(x) = y^Tx - f^*(y)$ minorizes $f$. What ...
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Opposite of common factor

If I have the following expression: $$ (\alpha-1)x^{\alpha-2}(1-x)^{\beta-1} -(\beta-1)x^{\alpha-1}(1-x)^{\beta-2} $$ And I simplify it as follows: $$ ((\alpha-1)(1-x)-(\beta-1)x) \quad (x^{\alpha-...
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4answers
37 views

What does it mean when $u$ and $v$ are functions of a single variable?

I am currently trying to learn how to do integration by parts again (haven't done it for years) and am stuck on the very first line of the lecture. The lecturer says that we should "recall the product ...
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1answer
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How is the term “sequence” defined? [closed]

In CodeChef (an online programming contest) I encountered a problem where they used the term "sequence of $N$ integers" and give the examples "3, 2, 4" and "3, 1, 3". How can these be sequences? Am ...
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Do we use “subdomain” terminology in order to specify that $Y$ is subset of domain $X$?

I have very simple question. For simplicity, let's take into consideration a function $f(x)$ defined over domain $X$. I consider some set $Y$, that is $Y\subset X$. Can I say that "$Y$ is subdomain ...
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Matrix with non-one terms on the diagonal

I'm wondering what you call a square matrix that's a diagonal matrix, but isn't the identity matrix? Orthogonal Matrix definition: $$A^T A = I$$ What about an "Almost Orthogonal Matrix": $$A^T A =...
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What is the name of rule: $a^2\cdot b^2 = (ab)^2$ and how to justify it mathematically?

It is easy to illustrate the rule, for instance $ 10^2 \cdot 5^2 = 50^2 = 2500 $ The question is, what is the name of this rule: $a^2\cdot b^2 = (ab)^2$ and how to justify it mathematically?
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A positive integer “modulo a sequence”.

Motivation: The (principal) value of $$m\pmod{n}$$ for some positive integers $m> n$, might well be viewed as the value $$m-\sum_{i=1}^{M_{m,n}}n,\tag{$\Sigma$}$$ for some $M_{m,n}\in \Bbb N$ ...
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2answers
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“Etymology” of symbols for injections and surjections

Excuse me if this sounds silly. Does anybody know why injections and surjections are sometimes denoted symbolically as $f:V\hookrightarrow W$ and $g:V\twoheadrightarrow W$? How do the arrows $\...
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Almost clopen sets and Baire property?

A set $A$ is said to have the Baire property if it differs from an open set by a meagre set, that is, if there exists an open set $G$ such that $A\Delta G$ is meager (where $\Delta$ denotes the ...
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What does “super-integrable” mean?

What does "super-integrable" mean? Example from here (p. 2): …the Coulomb problem is super-integrable. Namely, it is not just rotation invariant, but as well admits further integrals given by ...
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General terminology for probability/statistics.

As an armchair academic, I am trying to teach myself some college level mathematics . Currently I am reading an introductory book into probability and statistics. However, I am a bit confused by the ...
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What is the word for a matrix which has all zeroes in its last column?

In other words, every equation in the system of equations represented by the matrix equals zero. I know for a fact there's a specific name for this type of matrix, but I can't remember it. Any guesses?...
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1answer
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Correct terminology for optimization problem

An optimization problem aims to minimize the sum of a variable u over a time-series. It is made of three variables that are in a linear relationship. Two binary variables $$x_1, x_2, \dots x_n$$ and ...
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Different usage between “Riemann” and “Riemannian” in terminology

I found it a problem when searching references for Riemannnian Geometry, as I wrongly typed as Riemann Geometry just like Riemann Surface. So are there any criteria to decide if we should use ...
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Math Lessons with Two Parts and a Combination

This is fairly open ended, so I understand if people consider this to be off-topic. I'm interested in creating math lessons where two groups each learn how to use a different simple math skill, and ...
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3answers
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a problem in justifying ONLY IF truth table

EDITED:I saw the link above but it does't answer my question.I have a clear understanding of "P ONLY IF Q", I know that it equals "IF P THEN Q" .. but I see that there is a difference in the case ...
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Is there a name for this kind of subcategory of an abelian category?

I have encountered a full subcategory $\mathcal D$ of an abelian category $\mathcal C$ which satisfies the following property: If $$0 \to M' \to M \to M'' \to 0$$ is a short exact sequence in $\...
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What is the term for the smallest number that two numbers can both divide into evenly?

For example, for the numbers $2$ and $3$ it would be $6$, which is the smallest number that's evenly divisible by both $2$ and $3$. More examples: for $10$ and $40$ it would be $40$. For $7$ and $11$ ...
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Connectivity of planar embedding of graph

I would like to know some terminology regarding graph theory. In order to be specific, consider the following example. Consider an arbitrarily large 2D square lattice. This can obviously be embedded ...
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Player A wins a game 50% of the time, player B wins 80% of the time. Player B is ___% better than player A

There are two players A and B. They each play a game against a third player C. Player A has a 50% chance of winning, whereas player B has an 80% chance of winning. I want to use a sentence to say how ...
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tautology vs axiom vs premise

I am trying to sharpen the line among the definitions of tautology, axiom and premise. What I have understood so far is this: Tautology: A statement that is proven to be true without relying on any ...
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Is there a name for a square matrix with constant diagonal and off-diagonal elements?

I am interested in real symmetric matrices of the form: $$\mathbf{M} = \begin{bmatrix} a & t & t & \cdots & t \\ t & a & t & \cdots & t \\ t & t & a & \...
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Terminology for dependent random variables

Let $A(\omega)$ be a random variable with a uniform distribution over $[-1, 1]$. Let $B(x, \omega)$ be a random process that is a function of physical space $x$. It is defined in terms of $A$ such ...