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

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17 views

Maximal angle between kernel of rows of a matrix

Consider a matrix with 2 columns $$ \begin{pmatrix} a_1 & b_1 \\ a_2 & b_2 \\ a_3 & b_3 \\ \vdots & \vdots \end{pmatrix} . $$ To each row $(a_i \;\;\; b_i)$, one draws the kernel ...
2
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0answers
32 views

Where does the name “toral” come from?

Where does the name "toral" come from in "toral subalgebra"? I know a little (very little) Lie groups theory, so I guess it could be related to a Lie group whose Lie algebra is the toral one. Is ...
7
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1answer
121 views

History of the terms “prime” and “irreducible” in Ring Theory.

In ring theory, a nonzero, nonunit element $p$ of a integral domain is called irreducible if $p=ab$ implies that exactly one of $a$ and $b$ is a unit, and it's called prime if $p\mid ab$ implies that ...
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2answers
48 views

Word for the number being added-to OR subtracted-from another number

I first asked this on english.stackexchange.com, but this site would probably be a better-suited to answer it: In division, we have a dividend and a divisor. According to this page, we also ...
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2answers
41 views

Commutative vs. Symmetric

When we are discussing a binary operation $*:X \times X \to X$, we typically say that $*$ is commutative if $*(x,y) = *(y,x)$ for all $x,y \in X.$ However, when discussing a function $F: X \times X ...
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0answers
16 views

Correct terminology for “normalizing” data (making them add up to 1)

Let's say I have the data points 2, 2, 8, 10 (sum = 22) and convert them to: ...
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1answer
28 views

Mean squared [X] or Mean [X] squared?

If I have two functions, as below, which one is "Mean [X] squared" and which is "Mean squared [X]"? Would I be correct in saying the former is number 1 and the latter is number 2? Thanks in advance ...
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0answers
18 views

Double standards on recognizing expression as functional

The Calculus of Variations starts with a definition of functional Such an expression, the argument of which is a function, is called a functional. Particularly, they say that $J = ...
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1answer
29 views

Directly or inversely proportional

Take two cases- y = -x y = 1/x in both these cases as 'x' increases 'y' decreases, so according to me 'y' should be inversely proportional to 'x' in both. Please correct me if I am wrong but I ...
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1answer
57 views

Using sequential definition of functional limits, show that $\lim_{x \rightarrow 0} 1/x$ does not exist

Using sequential definition of functional limits, show that $\lim_{x \rightarrow 0} 1/x$ does not exist I have two questions regarding this. Firstly, say we have a function that 'converges' to ...
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2answers
37 views

How can I describe the tenths digit with an even number?

How can I describe the following numbers? 0.2 0.4 0.6 0.8 Can I call them "even tenths"? For example: "If the maximum value in the data set is 1, then the ...
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0answers
24 views

What is the name for the operation of swapping the two components of a complex number (rectangular form)?

I wonder if there is a name for the operation of swapping the real and imaginary part of a complex number.
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4answers
48 views

Why is a sphere in an $n $-dimensional space called $(n-1) $-sphere?

Why is a sphere in an $n $-dimensional space called $(n-1) $-sphere? Isn't it natural to call a sphere in 3D a 3-sphere, a sphere in 2D (i.e. a circle) a 2-sphere, etc?
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1answer
27 views

What is the “correct” label for quadrants?

Currently studying trigonometric functions and the book has the quadrants labeled for (+x,+y) is quadrant I, quadrant 2 is (+x,-y), quadrant 3 is (-x,-y), and quadrant 4 is (-x,y). While I ...
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0answers
25 views

Terminology: Delta vs… absolute?

Delta is the change in a value. Using the term "delta" on the one hand, how, on the other hand, would you refer to the base value from which the given delta is derived? Is there a more precise term ...
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2answers
25 views

Name for a set of pairs of elements that equalise two functions?

Is there an established name for this $eql$ function? $$\operatorname{eql}(f, g) = \{\ (x, y)\mid f(x) = g(y)\ \}$$
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3answers
95 views

Colloquialisms in Math Terminology

What are some of your favorite colloquial sounding names for mathematical objects, proofs, and so on? For example, manifolds are often described using an atlas and a neighborhood describes a small ...
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2answers
96 views

Two natural extensions of every algebra. Extension to subsets or functions.

I don't exactly know the technical meaning of extension, but I was thinking that given a set $A$ and an operation $*$ on it we can extend the set $A$ in a very natural way and thus extend any ...
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2answers
19 views

What's the name of the minimum number of transpositions required to build a permutation?

What's the name of the minimum number of transpositions required to build a permutation? I thought it was "rank" but apparently "rank" refers to the lexicographic number.
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0answers
18 views

“Dependence” or “dependencies” of a function on multiple variables.

If we have a function $f(x)$ that depends on a single variable $x$, we can speak of the dependence of $f$ on $x$. What is the plural of 'dependence' when it's used in this sense? Is it a mass noun? ...
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0answers
37 views

Binary operation (english) terminology

Foreword: I have read R.H. Bruck's A Survey of binary systems, where the notion of halfoperation is given. A halfoperation $\ast$ differs from a (binary) operation since $a\ast b$ may not be defined ...
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0answers
22 views

Is there a particular name for the set of all relations?

I know that a relation on a set $S$ is a subset $R \subseteq S \times S$ such that for all $(s,s') \in S \times S$, $(s,s') \in R$ iff $sRs'$, therefore the set $T$ of all relations on $S$ is the set ...
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1answer
44 views

Is there a way in matrix math notation to show the 'flip up-down', and 'flip left-right' of a matrix?

Title says it all - is there an accepted mathematical way in matrix notation to show those operations on a matrix? Thanks.
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1answer
28 views

What does it mean to say that an element 'satisfies' a polynomial?

In the context of finite fields, the definition of a primitive element $\alpha$ is given by: $\alpha$ is primitive if it generates all elements of $F_q - \{0\}$ when raised to powers up to $q-1$. ...
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1answer
28 views

What do we call the disjuncts of the conclusion of an argument?

If we have an argument with a single premise of the form $A \wedge B$, then we can refer to $A$ and $B$ collectively as "premises" of the argument without causing any confusion. However if we have an ...
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3answers
67 views

What is linear, numerically and geometrically speaking?

For as simple as it is, I never fully grasped what mathematicians and physicists mean with linear . Intuitively anything that looks like a straight line is interpreted as linear, like something in ...
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0answers
15 views

How to write the condition for Image of a function?

If $\Omega_l$ is $\Omega$ with $|x|<l$ and if $\Omega_S$ is the image of $z$ under mapping how we will write the condition for it. Am I right if I write $\Omega_S$ is $\Omega$ with $|S|<l$ or ...
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1answer
88 views

What does $\mathbb{Z}_2$ mean?

Wich number space is ment by: $\mathbb{Z}_2$ (I know that $\mathbb{Z}$ stands for Integer)
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2answers
57 views

Word for “openness”/“closedness” of an interval

What word properly completes the phrase the radius of convergence does not depend on the $\text{______}$ of the interval to mean that it doesn't matter whether $(a, b)$, $[a, b)$, $(a, b]$, or ...
2
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2answers
340 views

Is there a name for $\frac{n!}{m!}$?

Is there a name or short way of writing of $\frac{n!}{m!}$? I've searched and the closest I could find was binomial coefficient. Is there any other way?
3
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1answer
1k views

How do we pronounce this symbol?

I would like to know how to pronounce in english this symbol $\nabla \phi$ It is something phi ... ? thank you
1
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1answer
26 views

“The operation is normal iff it's both monotone and continuous” — which math area studies operation?

I just read Enderton's "Elements of Set Theory" to have a basic understanding of sets (btw it's a great book). One line of it says: "the operation is normal iff it's both monotone and continuous." ...
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0answers
22 views

“Differential variations”?

This passage in an old book on trigonometry calls these relations among parts of a spherical triangle "differential variations". The "parts" are three sides and the three angles; when the sides are ...
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2answers
60 views

Name for categories in which isomorphic implies equal?

A quick terminology question: Is there any particular name for a category in which each object is uniquely determined by its isomorphism class?
3
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1answer
48 views

Rel: the category of relations

$\text{Rel}$ is the standard name for the category of sets and relations. Confusingly in "Abstract and concrete categories" (ACC), page 22, $\text{Rel}$ is defined as a category whose objects are ...
14
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2answers
637 views

Why is analysis called “analysis”?

Just as the topic says, how did the name "analysis" come to denote the specific mathematical branch dealing with limits and stuff? The term "analysis" seems very generic compared to the words for the ...
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2answers
34 views

What does a probability being i.i.d means?

I know that a sequence of random variables is i.i.d means that they have the same mutually independent probability distribution. I was reading in a paper where the authors said that "the probability ...
1
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2answers
39 views

How to find if the sum of periodic function is periodic?

Basically, I am suppose to check if $f(x)=f(x+T)$. however my function is a bit complex: $x(t)=10\cos(20000\pi t)+0.5\cos(24000\pi t)+0.5\cos(16000\pi t)$ How shall I check if this function is ...
2
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3answers
30 views

Is sum of a series correct terminology?

What is the correct terminology when referring to the sum of a sequence? I see people and websites use "sum of the series...", but shouldn't we say the value of the series? (Sum of a sequence and ...
1
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1answer
85 views

$V_\omega$, $\mathcal V^{B}_\omega$, $\mathcal V^{*B}_\omega$ and $\mathcal S^{B}_\omega$: alternative superstructures and properties

I was not able to find a beginner introduction to superstructures and the cumulative hierarchy that makes me able to answer to some of my questions about them so I tried to ask here and I apologize ...
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0answers
41 views

Why do we use the terms “non-increasing/non-decreasing/non-negative”?

I am not sure if I have to ask my question here. But I will try and thank you in advance. Why some authors (in books or in papers) use the following terms: Function $f$ is non-increasing; Function ...
7
votes
3answers
89 views

Why do we say $n$ distinct points?

" Let's say we have $n$ distinct points... " , you see this every time you open a geometry textbook. Why not just $n$ points ? If the points are not distinct, they are not exactly $n$ points, are they ...
0
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1answer
28 views

Terminology for “coordinates”

As a non-native speaker, I am not sure about the following terminology for coordinates on manifolds. Given a manifold $M$, we pick up a local coordinates $(U, x^i)$, where $x^i$ are functions on $U$. ...
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0answers
19 views

Theorem about two quadrilaterals with parallel edges

I'm looking for a name for the following theorem: If $abAB$ lie on one line and $cdCD$ lie on another line, and furthermore $ac\Vert AC,ad\Vert AD,bc\Vert BC$, then $bd\Vert BD$. One can ...
3
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1answer
89 views

$f_{n+1}(x)=f_n(x+1)-f_n(x)$ functional equation and “classification of functions”

Doing a quiz I found a question of this kind "given $a_0, a_1, a_2, ...,a_n$ find $a_{n+1}$" In order to find the $f$ such that $f(a_n)=a_{n+1}$ I tryed for a function like $f(x)=k+x$ ...
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0answers
35 views

Are there official names for these functions?

$\newcommand{\sgn}{\operatorname{sgn}}$ Does anyone know if the simple function $$ y(x)=x^2\sgn(x)$$ or alternately $$ y(x)=x|x|$$ has any (official) name in mathematics or engineering? or ...
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1answer
111 views

Is an anti-symmetric and asymmetric relation the same? Are irreflexive and anti reflexive the same?

I don't understand the difference between an anti symmetric and asymmetric relation. From my understanding, it is asymmetric if there is not any element where: if (x,y) (y,x). But what if you have ...
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0answers
18 views

Number of orientations of a graph without a source

An orientation of an (undirected, loopless) graph is an assignment of direction to each edge, turning the graph to a directed graph. A source in a directed graph is a vertex with outdegree equal to ...
0
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1answer
36 views

$\mathcal N (A):=\mathcal P(A)-\varnothing$ notation

Define $\mathcal N$ $\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ Does $\mathcal N$ has a special name and standard notation?
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1answer
47 views

symmetric/antisymmetric

according to both the text and my professor, these properties are not mutually exclusive. i.e. a relation can be both symmetric and antisymmetric. I understand the properties themselves, but I don't ...