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

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2
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2answers
26 views

Name for complex number with nonzero imaginary component

Complex numbers include all real numbers. Is there a name for the subset of complex numbers which does not include any real numbers (i.e. where the imaginary component is nonzero)?
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2answers
41 views

Name of the notation where number is expressed as a sum

I have the following general form of a number: Does this notation have a name? Here is the example of using the form:
6
votes
1answer
66 views

Why are second order linear PDEs classified as either elliptic, hyperbolic or parabolic?

Is there a geometric interpretation of second order linear partial differential equations which explains why they are classified as either elliptic, hyperbolic or parabolic, or is this just a naming ...
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0answers
15 views

Difference between modular equation and congruence equation

Is there any difference between a modular equation and a congruence equation, or are both the same thing?
0
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1answer
17 views

What is different between in a set and on a set?

I saw that in is sometimes used and so is on. For example, Let $f$ and $f_k$, $k=1, 2, \cdots$, be measurable and finite a.e. in $E$. If $f_k\to{}f$ a.e. on $E$ and $|E|\lt+\infty$, then $\{f_k\}$...
2
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1answer
25 views

what is the terminology of this form of equation $x^2 +1/x^2 + \sqrt{x}$

what is the terminology of this form of equation. It has only one variable, but with rational exponents, it can be positive, negative or fraction such as below: $ax^2 +b/x^2 + c\sqrt{x} =0 $ I ...
1
vote
1answer
40 views

What is it asking when it says define and then gives a function and some conditions?

For example, the question: Define $f$ on $[3,4]$ by $f(x)=x+5$. Using the definition of the Riemann integral, show that $f$ is integrable on $[3,4]$. or Let $E=\{x \in \mathbb{R} : x \ge 1\}$. Define ...
3
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0answers
27 views

What to call a term-in-context whose context contains exactly the variables occurring in the term?

In type theory, a term-in-context $\Gamma \vdash t : \tau $ is only well-formed when $\Gamma$ contains all the variables occurring in $t:\tau$. Is there a name for when it contains exactly the ...
0
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1answer
41 views

Math-english for non-natives: What does “supported in” mean?

As a non-native English speaker, I am struggling with the following sentence: "Fix a function $f:\mathbb{R}\to\mathbb{C}$ such that $f$ is supported in the unit Ball." Does this mean $\...
4
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0answers
58 views

Does this operation have a name?

For a field $F$, define the binary operation $\parallel :(F\mathbb{P}^1 \times F\mathbb{P}^1 \setminus\{(0,0)\}) \to F\mathbb{P}^1$ by $$a \parallel b = \frac{1}{\frac{1}{a} + \frac{1}{b}}.$$ This ...
1
vote
1answer
82 views

How do you pronounce $\preceq$?

I've been reading about partial orders and partially ordered sets and have come across sentences like "Suppose that $\preceq$ is a partial order on $X$" and "If $x\preceq y$ and $y \preceq z$ then $x \...
0
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1answer
59 views

Does a cylinder with equal height and diameter have a special name?

I'm working on z-calibration part for my 3d-printer and I'm wondering if this has a special name? cylinder({r: 5, h: 10}) Basically a cylinder that has a height ...
0
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2answers
30 views

Is there a name for generalized ellipsoids?

In two dimensions, we have the following series of generalizations: circle $\rightarrow$ ellipse $\rightarrow$ smooth, convex, closed curve $\rightarrow$ smooth, simple, closed curve And in three ...
0
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0answers
9 views

Meaning of the term “dense relative to..”

In understand the meaning of the mathematical term dense. In the lecturers solutions I came across a sentence which said "...dense relative to .." Does this just mean to say "..it is dense in.."?
5
votes
2answers
63 views

In layman's terms what is the difference between a model and a distribution?

The answers (definitions) defined on Wikipedia are arguably a bit cryptic to those unfamiliar with higher mathematics/statistics. I am a high school student very interested in this field as a hobby ...
1
vote
1answer
9 views

What does it mean for the difference $V(\overline{x}_L -dx) -V(\overline{x}_L)$ to be of the second order in $dx$

What does it mean for the difference $V(\overline{x}_L -dx) -V(\overline{x}_L)$ to be of the second order in $dx$, where $dx$ is some tiny increment of $x$? What we know about $V$: $V(z) = U(z) - c\...
2
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2answers
85 views

About the Words “recursion” and “recursive”

According to Wikipedia, Recursion is the process of repeating items in a self-similar way. On the other hand, the word "recursive" is an adjective and is often used as a synonym of "computable" when ...
4
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0answers
43 views

Is there a name for those concrete categories in which every subset / quotient set inherits the structure of an object in at most one way?

The following situation seems to occur a lot in abstract algebra: We have a category $\mathbf{C}$, concrete over $\mathbf{Set}$, that satisfies: For every object $Y$ of $\mathbf{C}$ and every set $...
2
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1answer
32 views

Regarding those $\mathbb{Z}$-modules whose every finite subset generates a finite submodule.

Let $X$ denote a $\mathbb{Z}$-module (aka an abelian group). Then $X$ may or may not satisfy: $(*)$ for all finite sets $F \subseteq X$, the module generated by $F$ is finite. This properly ...
0
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0answers
19 views

Topology; difference between open subsets of $X$ containing $x$ and open neightborhood od $x$?

I see my lecture notes and some texts alternate between the two. What is the difference in saying that "an open subset of $X$ containing $x \in X$" and an "open neighborhood of $x \in X$"?
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0answers
14 views

What is cut space of directed graph (digraph)?

A cut is partition of vertices into two disjoint subsets. Digraph is a directed graph. Cut space is defined for an undirected graph as by Wikipedia where the definition for an undirected graph, ...
0
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0answers
58 views

Is it acceptable to refer to “the $\ell_2$-norm ball of radius $r$”?

Assume $r > 0$. Is it standard to use the expression "the $\ell_2$-norm ball of radius $r$" to refer to the set \begin{equation} B = \{ x \in \mathbb R^n \mid \| x \|_2 \leq r \}. \end{equation} ...
0
votes
1answer
27 views

In Graph to tree: name of operation where edges removed and vertex/edge additions?

The graph has tree paths IN-1-OUT, IN-2-OUT and IN-3&4-OUT between IN and OUT in the left. I want to make each path to a branch like the right. What is the name of this operation or the name ...
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0answers
62 views

What is the name of the group $\mathbb Z_2\times \mathbb Z_2\times \mathbb Z_2$?

I know, that $\mathbb Z_2\times \mathbb Z_2$ is the Klein four-group. Is there a nice name for $\mathbb Z_2\times \mathbb Z_2\times \mathbb Z_2$ too?
1
vote
1answer
13 views

What are those weighed graphs called?

Let $G = (V, E)$ be a directed graph, and define the weight function $f : V \sqcup E \to \mathbb{R}^+$ as follows: sum of weights of vertices is 1, if a vertex has edges coming out of it, their ...
0
votes
1answer
73 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 ...
0
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0answers
44 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 ...
0
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0answers
20 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 ...
0
votes
3answers
33 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?)
4
votes
2answers
68 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?
2
votes
2answers
61 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 ...
2
votes
1answer
57 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 ...
0
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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
38 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
votes
1answer
30 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: ...
0
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1answer
41 views

Word Form of an Expression [closed]

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
9 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
16 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
22 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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0answers
10 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 ...
0
votes
1answer
58 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
22 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 ...
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1answer
33 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 would'...
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0answers
19 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)
0
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1answer
30 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 ...
2
votes
1answer
31 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 ...
3
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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 ...
2
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2answers
72 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 ...