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

What is an order of an element of a partition"?

I'm reading a paper, in which the set of all 3^3 mappings from {0,1,2} to itself (for instance {001,020,110,121,122}, {002,010,112,011}, {0,1,2}, ...) is partitioned, after which is written two ...
2
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1answer
97 views

Why is the nuclear norm called so?

A simple question. Why is the sum of the singular values of a matrix called its nuclear norm? What is the origin of, and motivation for, this term? Apparently the term nucleus is sometimes used to ...
2
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1answer
46 views

What is meaning of dyadic compactness?

What is meaning of dyadic compact space? Is it as the same as Cantor cube $D^\kappa$?
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83 views
+150

Linear w.r.t. any measure

Let $X$ be a Banach space endowed with a Borel $\sigma$-algebra. How do we call a real-valued Borel function $f$ that satisfies for any Borel probability measure $\mu$ the following formula $$ ...
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3answers
157 views

Where could I learn basic math terminology?

I am an english learner and I would like to learn the etymology of Mathematics. I would like to know the most common phrases in Algebra, and Geometry as well. I want to know at a level of UK's A+. ...
2
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1answer
2k views

What is the definition of a geometric progression?

If the first term in our geometric progression (GP) is $k$, and the common ratio is 0, then our sequence is $\{k, 0, 0, 0, 0,\ldots\}$. Is there anything wrong with this statement? So, is $\{0, 0, ...
2
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2answers
597 views

What is the general term for a shape that is topologically equivalent to a sphere?

You have a chunk of ideal rubber and can stretch and shape it any way you want, but you are not allowed to puncture it. The chunk of rubber will always be a ____. shapes described by the term: ball, ...
17
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1answer
775 views

Is there such a thing as a mathematical thesaurus?

I want this for two reasons: When writing proofs, I am constantly in need of synonyms of basic words like thus, there exists, for all, such as, contains, etc. A lot of mathematical concepts have ...
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0answers
30 views

How to call a “non-strict” monoidal category?

A monoidal category is a category $\mathsf{C}$ equipped with a bifunctor $\otimes : \mathsf{C} \times \mathsf{C} \to \mathsf{C}$, a unit object, an associator, and right and left unitors satisfying a ...
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10answers
10k views

Why does “convex function” mean “concave *up*”?

A function $f : \mathbb{R} \to \mathbb{R}$ is convex (or "concave up") provided that for all $x,y \in \mathbb{R}$ and $t \in [0,1]$, $$f(tx + (1-t)y) \le tf(x) + (1-t)f(y).$$ Equivalently, a line ...
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2answers
51 views

What is a filled rectangle called, if anything?

In geometry, the set of points within a circle is called a disk (open disk if it excludes the boundary, closed disk if it includes it). Is there a similar notion for squares or rectangles? "A filled ...
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1answer
34 views

What's the name given to the ratio $P^2/A$ for a closed figure in the Euclidean plane?

Let $\mathscr{F}$ be the set of all plane, closed Euclidean figures having positive perimeter, and let $\sim$ be the similarity relation on $\mathscr{F}$. Then, for any equivalence class ...
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2answers
385 views

Are pairwise mutually exclusive events the same as mutually exclusive events?

Larson (1982) defining the probability axioms talks about "mutually exclusive" events, while Poirier (1995) about "$A_1, A_2, \ldots$ as a sequence of pairwise mutually exclusive events events in the ...
8
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1answer
77 views

A function that crosses each horizontal line only finitely many times

Consider a real function $f(x)$ (not necessarily continuous) defined on a finite interval. Given a constant $C$, divide the interval to sub-intervals such that, in every sub-interval, either ...
3
votes
3answers
289 views

Why are “irrational numbers” not named “nonrational numbers”?

Possible that I'm misunderstanding the concept of irrational numbers, but seems like the term nonrational would be much more clear. Why is "irrational" more clear than "nonrational"? UPDATE: Just to ...
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3answers
31 views

Name for region of plane bounded by two rays?

Is there a name for e.g. the locus $$\pi/6 \leq \arg z \leq \pi/3$$ on an Argand diagram? (Perhaps something analogous to a half-plane?)
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0answers
18 views

Limit Terminology

From the $\epsilon-\delta$ definition of a limit, we can see that any limit can be broken up into two "one-sided limits". These "one-sided" limits are simple cases that arise as a consequence of the ...
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4answers
2k views

What is the name of the vertical bar in $(x^2+1)\vert_{x = 4}$ or $\left.\left(\frac{x^3}{3}+x+c\right) \right\vert_0^4$?

I've always wanted to know what the name of the vertical bar in these examples was: $f(x)=(x^2+1)\vert_{x = 4}$ (I know this means evaluate $x$ at $4$) $\int_0^4 (x^2+1) \,dx = ...
2
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1answer
91 views

If a tesseract is to a cube what a cube is to a square, what is to a sphere as a sphere is to a circle? What about rectangle, ring, triangle?

I'm trying to come up with sensible names for a programming library I'm putting together. One minor part of this library is the generation of shapes of varying dimensions. Basically I'm just trying ...
2
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1answer
54 views

Is there an adjective for rings whose every non-zero prime ideal is maximal?

(All my rings are commutative and unital.) Question. Is there an adjective for rings whose every non-zero prime ideal is maximal? Remarks: Every PID has this property; more generally, every ...
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2answers
398 views

Terminology Question: Precompose vs Compose?

I was wondering if there was a standard convention on what 'precompose' means compared to 'compose', as I am often confused between the two when all sorts of text casually use both terminologies. For ...
2
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1answer
33 views

What's the order of a semigroup?

For a group the order, of an element is the smallest positive integer m such that a^m = e. But what's the order of an element of a semigroup? Or there isn't anything like that?
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0answers
15 views

Term for “Remainder in the Whole”

If I have a proper fraction I want to know what the name is for the amount remaining in the whole. So given $\frac1 3$ I want the name of the term $\frac 2 3$.
2
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0answers
32 views

3D shaped matrices - how would multiplication work? [duplicate]

I've been thinking about vectors and matrices lately, and I got a little curious. Why don't we have cubic shaped matrices? After all, vectors are 1-dimensional matrices, so it follows that there ought ...
2
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1answer
29 views

Terminology for $[0,\infty)^n$

It dawned on me a couple of weeks ago that I had no idea what terminology was used for the sets $[0,\infty)^n\subseteq \mathbb{R}^n$ in general. In one dimension, it's just the half line; in two ...
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0answers
20 views

Number transformation

Does somebody know what would be the proper name of this number transformation: ...
3
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1answer
925 views

What does height of an algebraic equation mean?

I want to solve this question but I don't understand what "height" of an algebraic equation is: Find the number of solutions of the set of all algebraic equations of height 2.
0
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1answer
34 views

Word Form of an Expression [on hold]

What is the word form of the expression? $$\sum \frac{1}{n^s}$$ That is exactly the way the expression appears in a paper which I am trying to read. It is $$\sum_{n=1}^\infty \frac{1}{n^s}$$
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0answers
7 views

Exterior algebra subspace of all grade-n wedge products of a vector

Let $V$ be a finite-dimensional vector space, and let $\Lambda(V)$ be its exterior algebra. Then if $S_k = \text{span}(k_1,k_2,...,k_n)$ and $\hat k = k_1 \wedge k_2 \wedge ... \wedge k_n$, there is ...
1
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0answers
15 views

Confusion regarding terminology in Pressley's E.D.G

Here are two definitions taken from page $77$ of Pressley's Elementary Differential Geometry - $2$nd edition. Definition $4.2.1$ A surface patch $\sigma: U \to \Bbb R^3$ is called ...
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0answers
11 views

Number of letters moved by a product of permutations

Let p and q be permutations in the symmetric group on n letters. p and q need not have the same cycle structure. Now compute q * inv(p) -- for inv(p) the inverse of p -- and count the number of ...
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0answers
20 views

(Partial/total/well-) order vs ordering

Order or ordering – what is the difference? Is either correct? Is one British and one American English? Not exactly a maths question but probably still the best place to ask.
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1answer
154 views

Name of the class of graphs obtained by deleting $\mathcal{Q}_d$ from $\mathcal{Q}_n$

Let $\mathcal{Q}_n$ denote the $n$-cube graph. I would like to know if there is a name for the class of graphs obtained by deleting a ${\bf single}$ arbitrary copy of $\mathcal{Q}_d$ from ...
2
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2answers
61 views

How are image and pre-image different from range and domain respectively?

How are image and pre-image different from range and domain respectively, in Layman's terms (as simple as possible)? Are they basically just keywords that often indicate more nuanced subsets of the ...
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0answers
9 views

Terminology for a collection of paths

A path in graph theory is a "sequence of edges which connect a sequence of vertices" (from the Wiki page) Let $p_i$ denote a path between two vertices. Define $P = (p_1,\ldots,p_m)$ as a collection ...
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1answer
56 views

A group specified by Generators and Relations.

I'm confused with some terms in several definitions. Is an alphabet of a free group the same thing as a generator set of any group? If it is right, then by a given alphabet (set of generators) can be ...
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0answers
21 views

Can we use the terms 'class of sets' and 'family of sets' interchangeably?

I read in pg-4, Introduction to Topology and Modern Analysis by Simmons that class refers to a set of sets while family refers to a set of classes. I formulated an example for the same - if points are ...
1
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1answer
27 views

When to use the plural form of “equation”?

For example, is the following a single equation or two equations? $$ \frac{x-1}{2} = \frac{y-2}{-4} = \frac{z+3}{1}.$$ A textbook I'm looking at refers to the above as a single equation. But I ...
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0answers
14 views

Opposite terminology of relaxation

Removing a condition is a relaxation of a statement. What is the opposite? (i.e. adding a condition to a statement)
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1answer
24 views

Show that in a binary tree, if B is the number of branch points (including the root) and L is the number of leaves, then one has the relation L = 1+B

We have been discussing trees lately, but have yet to even touch on the topic of a binary tree. I understand what a leaf is, but we didn't have one for the term "branch points" Without being 100% sure ...
3
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2answers
55 views

Is there a general term for $A\oplus B = \{a \oplus b | a\in A, b\in B\} $?

Is there a general term that specifies that if an operator $\oplus$ is applied to two sets, it's actually applied to all possible pairs of elements of the two sets? Or is that always the case and ...
2
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1answer
28 views

What is the difference between closed-form expression and analytic expression?

What is the difference between closed-form expression and analytic expression? I often see them get referenced in settings where (in my opinion) they are essentially interchangeable. What is a ...
1
vote
1answer
18 views

Is Graph with multiple-inputs and multiple-outputs called MIMO?

MIMO (systems with multiple-inputs and multiple-outputs) is a term in engineering areas and applied mathematics such as process-control and wireless communication. Suppose you have a directed graph ...
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vote
2answers
59 views

Is there a symbol for always less than (or just always?)

For e.g, the quotient of $\frac{1}{n}$, $q$, where $n \gt 1$, $q$ will always be less than $1$. $$\frac qn\le n$$ etc. I can't really write $\frac {q}{n} < n$, because whilst true, it doesn't ...
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1answer
25 views

What are higher dimension analogues of loops called?

A path $f:I\to X$ with the same starting and ending point $f(0)=f(1)=x_0\in X$ is called a loop. What is the higher dimensional analogue of a loop $f: I^n\to X$ called?
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0answers
16 views

Reference request: monotone and strongly monotone with respect to derivatives

Recall, let $H$ be a real Hilbert space. A mapping $F:H \rightarrow H$ is said to be monotone if $$ \langle F(u)-F(v), u-v\rangle\geq 0, \quad \forall u,v\in H; $$ strongly monotone if there exists ...
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0answers
24 views

How to call a partition of $X$ which consists of all singleton subsets of $X$? [duplicate]

In other words, if $X$ is a set, then how do we call $Y=\{\{x\}:x\in X\}$? $\{X\}$ is already named the trivial partition, so that cannot be it. Complete partition and total partition did not yield ...
4
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2answers
159 views

A formal name for “smallest” and “largest” partition

Consider a set $A=\{1,2,3,4,5\}$, is there any terminology for the following partitions of $A$ ? (1) $A=\{ \{1\},\{2\},\{3\},\{4\},\{5\} \}$ (2) $A=\{\{1,2,3,4,5\}\}$.
9
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1answer
191 views

Name for determinant identity

Let $A$ be an $N\times N$ square matrix. There exists a determinant identity $$\operatorname{det}\left(I+A\right)=1+\sum_m A_{mm}+\frac1{2!}\sum_{m,n}\left| \begin{array}{cc} A_{mm} & A_{mn} \\ ...
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3answers
50 views

Name for a “layered” type of partial order?

I have a partial order $\prec$ over a (finite) set $S$ satisfying the following property: There exists a function $f:S\rightarrow \mathbb N$ such that $x\prec y \Leftrightarrow 0<f(x)< ...