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

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1answer
11 views

Name for the maximum size of $f^{-1}(w)$

Let $X$ and $Y$ be sets, and $f:X\to Y$ be a function. Is there a name for the following quantity? $$\sup_{y\in Y}\ \big|f^{-1}(y)\big|$$ I was thinking the "maximal valence of $f$".
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2answers
38 views

Is there any complex value for $x$ where $|x| < 0$?

What I'm really asking is if I get to a point in a calculation where I have $|x| = -4$, do I say There is no solution for $x$ or do I say There is no solution for $x ∈ ℝ$
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0answers
19 views

Equation with L2-distance of two single values

I am studying the equation which includes the L2-distance term $||a_n - b_n||_2$ (taken from http://caffe.berkeleyvision.org/doxygen/classcaffe_1_1ContrastiveLossLayer.html). Here, $a$ and $b$ are ...
2
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1answer
52 views

Discrete Mathematics Wording Difference Between “Show” and “Prove” [duplicate]

I just took a midterm for a Discrete Mathematics class. On couple of questions, it says "Show why this is true". For example, a sample question might have said "Show that five consecutive numbers is ...
0
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1answer
25 views

Particular name for the diagonal matrix with only one non-zero components

I need to deal with such matrices who are diagonal and with only one non-zero component. But, how should I call them? e.g, $$A=\begin{bmatrix}1& 0 &0 \\ 0 & 0& 0\\ 0 & 0& 0 ...
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2answers
77 views

Terminology: how to call this relation (inequality/inequation)?

dear native speakers, how would you call the relation like this? $$\ln(\sqrt{5})<\ln(5^2)$$ Is it inequality or inequation? Motivation for this question: In Czech we have different words for a ...
0
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1answer
17 views

Are Cartesian coordinates considered to be curvilinear coordinates?

In the wikipedia page on curvilinear coordinates it is said: "Well-known examples of curvilinear coordinate systems in three-dimensional Euclidean space (R^3) are Cartesian, cylindrical and spherical ...
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11answers
14k views

In simple English, what does it mean to be transcendental?

From Wikipedia A transcendental number is a real or complex number that is not algebraic A transcendental function is an analytic function that does not satisfy a polynomial equation However these ...
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1answer
52 views

Is foliation the right word?

Let say $C$ is a Jordan curve (rectifiable, closed with not self-intersections). Is there a term for the family $\{tC\mid t\in\mathbb R\}$? Is "foliation" the right word?
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1answer
40 views

Does this fact about concurrent lines have a name?

Let $ABC$ be a triangle. Pick $P$, $Q$, $R$ on sides $BC$, $CA$, $AB$, respectively, and then points $S$, $T$, $U$ on the sides $QR$, $RP$, $PQ$ of triangle $PQR$, respectively. Consider the ...
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1answer
52 views

$\cos(\theta) = \cos(-\theta)$ which means that the cosine function is (blank)?

I understand why $\cos(\theta) = \cos(-\theta)$ but I don't know what the specific property this question is asking for is - PreCalc homework. Likewise, another question is: $\sin(-\theta) = ...
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0answers
48 views

Terminology: What is the tuple $(x, x)$ called?

I need to write a few functions in PowerShell which operate on sequences, but I want to use accepted mathematical terminology if possible. I will be using the following terminology ($S$ and $T$ are ...
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4answers
94 views

Scientific name of square root of negative number [closed]

How do you call a number in the form: $\sqrt{-4}$ ? A non real number?
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1answer
26 views

Group morphism or group homomorphism?

I apologize for my question that might sound stupid, but i noticed that my lecturer in abstract algebra course uses always "group morphism" instead of "group homomorphism". In the books i see it ...
0
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1answer
28 views

What is the name for numbers using a comma for a decimal separator versus a dot

I am curious to know if there is a specific name for numbers that use a comma for a decimal separator and a dot for a thousands separator as opposed to numbers that are the reverse. For example: ...
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6answers
8k views

Why does the Cauchy-Schwarz Inequality even have a name?

When I came across the Cauchy-Schwarz inequality the other day, I found it really weird that this was its own thing, and it had lines upon lines of proof. I've always thought the geometric definition ...
0
votes
1answer
39 views

Is product topology of $X\times X$ is $X^2$?

I was wondering if we can write $X\times X$ (Product topology) as $X^2$. Or we can say that $X^2$ is with the product topology means that $X^2=X\times X$.
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1answer
27 views

What is the name of this function on group-ring modules?

Let $G$ be a finite group. Let $M$ be a $\Bbb{Z}G$-module. What is the name of the map $M\to M$ given by: $$ m \mapsto \sum_{g\in G} g m\, , $$ possibly divided by $|G|$? What is it used for? A ...
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3answers
889 views

What does “closed under …” mean?

What exactly is meant by "closed under fill in the blank"? Thanks.
21
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5answers
1k views

Why do we say function “parameterized by” vs just function of (x,y,z,…)?

I'm studying statistics, and in a lot of textbooks, the regression formulas always refers to the functions themselves as f(x) parameterized by a,b,c or something. And they are often written $f(x; ...
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1answer
52 views

Difference between flow and solution of ODE

I am reading Wikipedia's entry on Flow and it is not clear the distinction between solution of an ODE and the flow of an ODE. In particular it is clearly written $φ(x_0,t) = x(t)$, then what is the ...
0
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1answer
33 views

What's the technical term for “place-value”?

When talking about positional notation, is there a technical term for "place-value" (as in, "the place-value of the 9 in 792 is 10), or is that it? Somehow, "place-value" sounds informal, but I don't ...
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0answers
21 views

How to define a non Triangle Free Graph

Consider a Regular Connected Graph $G= \bigcup\limits_{i=1}^{m} U_i$ where- $U_i$ is a sub-graph of $r$ vertices $\forall i$.(i.e. $G$ is a $r$ regular graph) $\forall i$, $U_i$, is not a ...
2
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2answers
72 views

References to these functions relating to binary trees and binary digit counting?

Consider a perfect binary tree with $2^N-1$ elements. Two different numbering methods pop up constantly. For example, for $N=3$: I have worked out the mapping between these (for $ 1 \le k, i \lt ...
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0answers
26 views

Is the wording “parametric integral” standard in English?

For a measured space $(\Omega, \mathcal A, \mu)$, a set $T$ and a map $$f : T \times \Omega \to \mathbb R^n$$ we say in French that $$F(t) = \int_\Omega f(t,\omega) \ d\mu(\omega)$$ is a parametric ...
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0answers
55 views

What is the additive analogue of the word “factor”?

When we have a bunch of numbers multiplied together like $$b=a_1\,a_2\,a_3\,a_4,$$ we say that each $a_i$ is a factor of $b$. What is the additive analogue of this terminology? That is, if ...
2
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0answers
28 views

What does it mean to regress out current features?

First of all, I'd like to say that this is the intro to a homework problem. Please do not post any answers, I am only looking for clarification on some terminology in the setup. I am trying to ...
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1answer
32 views

Topology with No Disjoint Open Sets

The nested interval topology on $(0,1)$ is the collection of open intervals $\{(0, 1- \frac{1}{n}) \mid n \in \mathbb{N}, n \geq 2\}$. This topology has the property that no two open sets are disjoint ...
6
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1answer
53 views

How do you call the relation between these 2 variables?

Let's say I have an X number and I want to increment it by 50%, I would get $X*A=Y$ Then in order to multiply Y and get X again I would need to do $Y*Z=X$ How do you call the relation between A ...
2
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1answer
44 views

What is $x$ in a polynomial?

I know this sounds like an easy question. But I've never been told this. Suppose we have a polynomial... $$3x^2 + 5x - 9$$ I know $3$, $5$ and $-9$ are coefficients. I also know $2$ (form $3x^2$), ...
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1answer
36 views

Is there a mathematical name for the point where $n/x=x$

Were the graph of the asymptotic function $n/x$ rotated counterclockwise about the origin $45^O$, its derivation point would be 0 at $\sqrt{n}$ rotated similarly about the y axis where $n/x=x$. The ...
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1answer
22 views

basic understanding of hereditary property in matroid

I'm trying to prove something is a matroid and to do that I must understand what a matroid is. I don't get the hereditary property. A matroid is an ordered pair $(S, I)$. I is a non-empty family ...
0
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1answer
54 views

Term for 'x' in 'dx'

When writing derivatives in Leibniz notation, the derivative of $y$ with respect to $x$ can be written as $\frac{dy}{dx}$. What is the mathematical term for the '$x$' in '$dx$', in the context of ...
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2answers
25 views

Can someone make clear the concept of a “restricted metric”

I never understood this concept of restricted metric. Consider the following theorem. http://www.math.psu.edu/wysocki/M403/Notes403_4.pdf I don't quite understand this concept since under usual ...
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2answers
21 views

What is the relationship between boundedness and finiteness?

Given a set $A$ in a metric space $(M,d)$ can someone clarify example just what is the relationship between a set being bounded and a set being finite? Does finite $\Rightarrow$ bounded or/and ...
1
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2answers
51 views

Name of line of slope 1 through the origin

Is there a name for the line that goes through the origin and has a slope of $1$? I would call those with $0$ and infinite slope the $x-$ and $y$-axes, and it seems like the slope $1$ case is basic ...
2
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0answers
49 views

Does the following type of integral have a name?

Define $I_{k,b}$ for $k \geq 1$ an integer to be $$\displaystyle I_k = \int_0^\infty \frac{x^{\frac{1}{k} - 1}}{(1 + bx + x^2)^{1/k}}dx, $$ where $b^2 - 4 < 0$. For $k = b = 1$, this is ...
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0answers
39 views

Is there standard terminology for any or all of these concepts designed to help with thinking about Riemann integrability?

When trying to determine whether a function $f$ is Riemann integrable or not, we're typically in the following situation: Write $U_f(P)$ and $L_f(P)$ for the corresponding "upper Riemann sum" and ...
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1answer
83 views

What do the (+) and (-) symbols after variables mean?

This paper describing an Unscented Kalman Filter implementation uses notation that I am unfamiliar with nor can find on eg https://en.wikipedia.org/wiki/List_of_mathematical_symbols Xu et al (2008) ...
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2answers
61 views

Original usage of 'Bénabou cosmos'

A (Bénabou) cosmos is a bicomplete closed symmetric monoidal category (see, for example, the $n$Lab). However, I can't find the paper where Bénabou first uses this term - googling turns up nothing. ...
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0answers
39 views

Is there a name for this graph-theoretic concept?

Let $G$ and $H$ be graphs with vertex sets $V$ and $W$, and $f\colon V \to W$ a function. We say that $f$ preserves $k$-neighborhoods if all points that are at distance $k$ from each other in $G$ are ...
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1answer
25 views

Pluralisation when describing multiple objects simultaenously

An example is: Let $f_i : X \rightarrow Y, f_i(x) = y_i,\text{ for all } i$ be a function. or Let $f_i : X \rightarrow Y, f_i(x) = y_i,\text{ for all } i$ be functions. To me the first case seems ...
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3answers
103 views

Are the assertions “$2 + 2$ equals $4$” and “$2 +2$ is $4$” identical

Are the assertions "$2 + 2$ equals $4$" and "$2 +2$ is $4$" identical? Or is this a linguistic, psychological or murky philosophical thing rather than a mathematical thing
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1answer
41 views

What is the mathematical term for an operation that is self reversing? [duplicate]

What is the mathematical term for an operation that is self reversing? For example: Multiplying by -1 1/x In general: f(f(x)) = x
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2answers
21 views

Smoothness of discrete data

I'm having a hard time putting my question into words, so I made a few pictures. Look at this plot: Clearly, everyone will agree that these data points are following some nice smooth and continuous ...
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3answers
58 views

Is $U = \lbrace (1),(2),(1,2),(2,1) \rbrace$ a permutation? or a permutation of a power set?

Question If for a set $S= \lbrace 1 , 2 \rbrace$ the set $T = \lbrace (1,2),(2,1) \rbrace$ is refered to as a permutation, then how would an alternative set $U = \lbrace (1),(2),(1,2),(2,1) \rbrace$ ...
1
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1answer
34 views

Something similar to the dual map

The dual map is defined as follows: $$f^*(\varphi) = \varphi \circ f$$ I came across something similar: $$f_*(\varphi) = f \circ \varphi$$ Is there some name for the second map?
2
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2answers
41 views

Definition of uniformly cauchy

In this post, the definition of uniformly Cauchy is defined as: Uniformly cauchy sequences A sequence of functions $f_n$ is said to be uniformly cauchy if $$\forall \varepsilon > 0 \ \exists ...
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1answer
71 views

What is the name of this diagram occurring in topology?

I found this on the topology page of Wolfram Mathworld. What is the name of this kind of diagram and what does it mean?
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0answers
42 views

How do you call a non-empty intersection of two sets, where none of the sets is a subset of the other?

Consider two sets $A$, $B$ with the following properties: $A \cap B\not = \emptyset$ $A \not \subseteq B$ $A \not \supseteq B$ Describing the relation of $A$ and $B$, the terms "disjoint", ...