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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0answers
34 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 ...
0
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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 $$\sum_{n=1}^\infty \frac{1}{n^s}$$
0
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0answers
8 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
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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 ...
0
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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 ...
1
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1answer
32 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
17 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
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
votes
2answers
71 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 ...
1
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0answers
20 views

Is a finite dimensional vector also a covector?

I am reading something where it seems they have defined a covector/linear functional as a map $F: \mathbb{R}^n \to \mathbb{R}$ where $F$ is a vector For example, $F(x) = \begin{bmatrix} 1 & 2 ...
1
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1answer
34 views

Why marginal probability is called mariginal probability?

I want to know why marginal probability is called marginal probability but not something like single probability? Is the word marginal has some similar or related meaning?
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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 ...
0
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0answers
11 views

Does the Method of Compliments also work for (non-integers)?

I have only ever seen Method of Complements applied to integers, never non-integers (most notably in the field of modern programming) However curiosity got the better of me, and I was wondering if ...
1
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2answers
53 views

Linear Algebra Trivia: Can anyone identify this class of matrix?

Consider a matrix: \begin{pmatrix} 0 & -y & x \\ x & 0 & -y \\ -y & x & 0 \\ \end{pmatrix} where $x,y$ are positive real numbers I wish to identy the most "specific" class ...
0
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0answers
58 views

Why such coordinates are still called “isothermal” in the Lorentz case?

We know that in a two dimensional Riemannian manifold there always is, at least locally, a coordinate system in which $g_{ij} = \lambda^2 \delta_{ij}$ - such coordinates are called isothermal. There ...
0
votes
1answer
162 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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0answers
35 views

How to say increasing or decreasing as one word? Monotoneness?

In Calculus I, I can ask my class to "find the intervals of concavity". Is there a simpler way to say to say "find the intervals of increasing and decreasing"? In other words, "find interval of ...
1
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0answers
12 views

What's uniform block signed permutations?

Let $[n]=\{1,2,\ldots,n\}$ and $P(n)$ the set of all partitions of [n]. A partition of $[n]$ is non-empty disjoint subsets of [n], called blocks, whose union is $[n]$. A block permutation of [n] is ...
1
vote
2answers
60 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 ...
1
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1answer
27 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
26 views

what is a ordinally quadratic function?

A function is ordinal equivalent to another means there exist a (unique) monotonic transformation between wiki definition of ordinal utility. I am a little confused, a function is ordinally quadratic ...
0
votes
1answer
21 views

Elements of the range of a random variable that are transformed into the same element

Let $X$ be a random variable and $Y = g(X)$. Then, the range or support of $Y$ can be written as $R_Y = \{g(x) \mid x \in R_X\}$. My question is whether there is a name (or standard notation) for ...
1
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0answers
30 views

Is there a term in lattice theory for this?

Let $\mathfrak{A}$ be a lattice with join denoted $\cup$, meet denoted $\cap$, and least element $\bot$. Consider a set $S\in\mathscr{P}\mathfrak{A}$ such that the following property holds (for every ...
1
vote
3answers
51 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)< ...
0
votes
0answers
27 views

Does the “truncation function” $\langle a,b\rangle : \mathbb{R} \rightarrow \mathbb{R}$ have an accepted name or notation? [duplicate]

Given real numbers $a$ and $b$ satisfying $a \leq b$, define: $$\langle a,b\rangle (x) = \mathrm{min}(b,\mathrm{max}(a,x)) = \mathrm{max}(a,\mathrm{min}(b,x))$$ (These numbers are equal because $a ...
1
vote
1answer
19 views

Is this a hyperplane or a half-space in $\mathbb{F}_2^n$?

Simple terminological question: the equation $x_1+\dots+x_n = 0$ over $\mathbb{F}_2^n$ is called a subspace. I'm wondering if we could also call it a hyperplane, a half-space or neither? The equality ...
-1
votes
2answers
17 views

Difference between Increasing sequence of functions and Sequence of increasing functions

Suppose we define a sequence of functions $\{f_n \}_{n \in \mathbb{N}}$. I am confused in the following terminologies regarding this sequence of functions - 1) Increasing sequence of functions 2) ...
2
votes
3answers
136 views

Is it acceptable to use “But” in a proof that doesn't use contradiction?

I have recently read a lot of proofs that like to say "But..." right before the punchline. I feel that the word "But..." should be used if what follows is contradictory in some way, as in proofs by ...
0
votes
0answers
12 views

Terminology for a Complex Semicircle

A while back I read about a special type of number system termed (if I remember correctly) as "degrees of sign". The idea was that numbers sat on a series of 0 to 180 degree rays. Positive ways the 0 ...
0
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0answers
30 views

How is “Binomial” defined in Algebraic Geometry?

I am learning ideal arithmetics and I was flabbergasted that $\langle x\rangle$ is binomial ideal, as observed with Macaulay2 here. $x$ is clearly not a polynomial with two terms. Then I read paper ...
1
vote
1answer
19 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 ...
0
votes
1answer
12 views

Terminology: “Unique algebraic combination”

I recently came across the term "unique algebraic combination" and wasn't sure what this meant. For example, for two numbers $a$ and $b$ what are their "unique algebraic combinations"? Would it be ...
0
votes
0answers
17 views

Sum of the product of a cartesian product

I have two disjoint (though I suppose they don't need to be disjoint) sets, $M$ and $N$. I now want to take something like $$\sum_{(i,k) \in M\times N} i\cdot k$$ In english, I want a sum of the ...
0
votes
0answers
10 views

What is the geometric center and what is the other point?

In Euclidean geometry it is simple: In a triangle $\triangle ABC$ there is a single point $H_a$ on $BC$ such that the triangles $\triangle ABH_a$ and $\triangle ACH_a$ have the same area. the ...
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0answers
45 views

Is it “okay practice” to exclude the epicness from the definition of extremal / strong epis?

Basically I wonder, whether I "should" include the property of being epi in the definition of extremal epis / strong epis (/...) (dually for extremal monos etc.). One hand it is terminology-wise a ...
0
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0answers
8 views

Contour lines are synonyms for level curves. What is the “contour” synonym for level surfaces?

Contour lines are synonyms for level curves in 2 dimensional functions. What is the "contour" synonym for level surfaces in 3 dimensional functions?
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0answers
32 views

Is there a concept of distance between number of steps needed to move from one step to another?

Let's say that we have a set of rewrite rules: $$AB \mapsto AC, A \mapsto B, B \mapsto A$$ Given the two strings $ABC$ and $BCC$ we know we can rewrite $$ABC \mapsto ACC \mapsto BCC$$ We can ...
3
votes
0answers
51 views

Is there a name for this principle of logic? From $\exists a P(a), !bQ(b), \forall a(P(a) \rightarrow Q(a)),$ infer $\forall a(Q(a) \rightarrow P(a))$

In set theory, we have the following: Observation 0. Let $X$ denote a set. Let $A$ and $B$ denote subsets of $X$. Then if $A$ has at least one element, $B$ has at most one element, and $A ...
1
vote
1answer
30 views

What is the definition of a single valued function

this is potentially a dumb question but I am a touch confused about some terminology. I'm reading Ahlfor's complex analysis, and I am in a section on integrals of harmonic functions. I may be being ...
2
votes
0answers
16 views

Is there a name for smoothed maximum value function?

I have several arrays that look something like this: Spectrum Plot. Think gaussian curves, but shorter and with lots of noise. I've been comparing values for the sake of peak detection. Through ...
0
votes
1answer
15 views

Generic term for results of applying mathematical transformation to a value

Is there a generic way to refer to the summed values in this equation: I wanna say something like 'the result is the sum of three individual XXX XXX XXX performed on the percentile values', where ...
0
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0answers
25 views

Are scalar/vector fields basically just “multi-valued” functions?

Not really familiar with terminology in higher Mathematics, so I will try to use python to express my ideas instead. From Wikipedia: a scalar field associates a scalar value to every point in a ...