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

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0
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1answer
39 views

What is the name of a certain subset in a poset?

Is there a name for a subset $\{x_i\}$ of a poset $(P,\leq)$ satisfying $x_1 \leq x_2 \geq x_3 \leq \cdots \geq x_{n-1} \leq x_n$? (The subset could be infinite and the inequalities could be strict.) ...
0
votes
1answer
95 views

The correct term for $y$ in $y=f(x)$

Given: $y=f(x)$ than y is: a) range b) domain c c) variable d) co do-main I saw this question on an fb page and I couldn't get the right answer. a,b,d cannot be the answers since these are ...
2
votes
0answers
24 views

Standard deviation and related quantities

By definition, standard deviation is the square root of the variance. There is some common terminology for the quantities $$\mathbb{E}(|X-\mathbb{E}X|^p)^{1/p} $$ for $p \geq 1$? Or, they are just ...
2
votes
1answer
147 views

Difference between classification and characterization [closed]

What is the difference between classification and characterization in reference to mathematical objects ? Some examples will be appreciated.
0
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1answer
49 views

Is there a name for numbers that have 2 as their greatest common divisor?

Is there a name for numbers that have two as their greatest common divisor? Such as 8 and 130.
0
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1answer
46 views

What's the difference between “continued fractions” and “compound fractions”?

What should we call a fraction which includes another fraction in its numerator or denominator, like $${ab\over {c \over d}}$$?
2
votes
1answer
115 views

How many contiguous subsets of size $N$ does an infinite grid have?

Suppose I have an infinite grid. How many sets of grid points are there that contain $N$ contiguous grid points, and include the grid point at the origin? So for example, if $N$ = 2, then there are 4 ...
0
votes
1answer
73 views

What is the name of $a \mapsto b$?

$f: A \to B$ is called a mapping, where $A$ and $B$ are two sets. What is $a \mapsto b$, where $a \in A$ and $b \in B$, called then? Thanks. Note that $a↦b$ is not a function/mapping, since $a$ and ...
0
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4answers
65 views

Why to see that $\overline{B}(x;r)$ is closed if it was just defined?

I'm reading Conway's A Course in Point Set Topology. He defines open and closed balls and then he introduces some examples, one of these examples is this: (c) For any $r>0$, $\overline{B}(x;r)$ ...
1
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1answer
55 views

Is cocycle condition necesarry for coassociativity of coproduct and why is it called “cocycle condition”?

Let $\Delta_0$ and $\Delta$ be coproducts related by \begin{equation} \Delta h = \mathcal F \Delta_0 h \mathcal F^{-1} \end{equation} where $\mathcal F \in H\otimes H$ is Drinfeld twist and $h \in H$ ...
1
vote
0answers
47 views

Name for numbers with a single non-zero digit.

Given a base, is there a name for the numbers (positive or negative) that have only a single non-zero digit? For example: Decimal: 4000, -30, 0.0008 Binary: 1000 Base 5: 300, -0.1 Contrived ...
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2answers
860 views

Why the name “square root”?

Why do we say that $\sqrt{a}$ is a square root of $a$? Is this because $\sqrt{a}$ is a root of the function $f(x)=x^2-a$? Cubic root similarly? Thanks in advance
0
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1answer
23 views

Critical points of a function of absolute value

Say I have the function $f(x) = |x|$ I believe that $x = 0$ is a critical point, although not I'm not positive. As the function is decreasing and increasing each side of $x = 0$ does that alone make ...
0
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1answer
49 views

Why does $ \frac {a}{b}$ of $c$ mean $ \frac {a}{b} \cdot c$ [closed]

When someone writes "$ \frac {a}{b}$ of $c$", why is the preposition "of" interpreted as multiplication of $c$ by $a/b$?
0
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1answer
41 views

What's the difference between a partial function and a relation?

My understanding of a partial function is that it is one which only maps a subset of some set $A$ to another set $B$ (where $B$ could be $A$). On the Wikipedia page, the below image is given as an ...
3
votes
1answer
93 views

The walk of a knife

"A knife is slowly moved parallel to itself over the top of a cake. At each instant the knife is poised so that it could cut a unique slice of the cake. As time goes by the potential slice increases ...
30
votes
6answers
1k views

Why are integrals called integrals?

What is the historical background for this term? I cannot quite see what is integral about an integral, even if we go back to the viewing it as the area under a curve. It seems a strange choice of ...
1
vote
1answer
218 views

two interlocked circles are homeomorphic to two noninterlocked circles

This is what I learned from here the post: two interlocked circles are homeomorphic to two noninterlocked circles, thus they (two interlocked circles and two noninterlocked circles) are homotopic ...
6
votes
1answer
94 views

Terminology in forcing

In the context of forcing one reads the relation $p \leq q$ in a poset $P$ as "$p$ extends $q$". A typical example is the poset $P$ of finite partial functions, where one defines $p \leq q$ when $q ...
1
vote
1answer
36 views

The origin labelled on a graph: $0$ or O?

When one draws a graph, say in the x,y plane, we label the origin with a circular/elliptical symbol. Now is this a $0$ (zero), or is it O (for Origin), or simply just a circle/ellipse? Can it be ...
2
votes
1answer
25 views

Corrective terms for combinations

Take: $12$ people need to be split up into equal teams for a quiz. How many ways can this be done? The answer may initially seem to be $\displaystyle \frac{12!}{6!6!}$. but, since a single grouping ...
1
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0answers
28 views

Has an order with this property a special name?

If $a$ is an element in a preorder then you can eventually go 'a step back' (and repeat this) in the sense of finding an element with $b\leq a$ and not $a\leq b$. Is there a special name for ...
1
vote
1answer
86 views

Is there a difference between “unity” and 1 in applied mathematics?

Is there a difference between "unity" and 1 in applied mathematics? I know mathematicians have "roots of unity" and "partitions of unity", but at least those have become standardized. In ...
1
vote
0answers
90 views

term for a sum of diagonal and skew-symmetric matrix?

Is there a term for a matrix that is a sum of a diagonal and a skew-symmetric matrix? One particular example of this is a 2x2 matrix of the form $$ M = \begin{bmatrix} a & b \\ -b & a ...
1
vote
0answers
355 views

What is the operation inverse to vectorization (vec operator)?

There is a well knows vectorization operation in matrix analysis $\mbox{vec}$: https://en.wikipedia.org/wiki/Vectorization_%28mathematics%29 I've vectorized my matrix equations, did some ...
1
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3answers
59 views

Definition of homogeneous ODE

In my lecture notes, it gives this following definition of a homogeneous ODE: A differential equation is called homogeneous if it can be written in the form $x′=f(\frac{x}{t})$ Then in one of ...
3
votes
2answers
120 views

Can we define the normal set without $G$ being a group?

Let $X$ be a set in $G$ and $G$ be a group. A normal set is a set $X$ for which $gxg⁻¹∈X$ for every $x∈X,g∈G$. It's just like the normality condition for subgroups, except that $X$ doesn't have to be ...
2
votes
0answers
42 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 ...
6
votes
1answer
220 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 ...
1
vote
2answers
78 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 ...
2
votes
2answers
281 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
30 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: ...
0
votes
1answer
34 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 ...
0
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0answers
20 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 = ...
0
votes
1answer
77 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 ...
1
vote
2answers
370 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 ...
1
vote
2answers
43 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 ...
0
votes
0answers
32 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.
1
vote
4answers
69 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?
0
votes
1answer
38 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 ...
1
vote
1answer
173 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 ...
1
vote
2answers
27 views

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

Is there an established name for this $eql$ function? $$\operatorname{eql}(f, g) = \{\ (x, y)\mid f(x) = g(y)\ \}$$
3
votes
3answers
117 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 ...
1
vote
2answers
102 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 ...
2
votes
2answers
25 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.
0
votes
0answers
139 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
55 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 ...
0
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0answers
24 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 ...
3
votes
1answer
85 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.
1
vote
1answer
38 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 $q-1$. ...