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

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1answer
96 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 ...
0
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0answers
55 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
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3answers
96 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
32 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 $U$. ...
2
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1answer
46 views

Name of 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
100 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
40 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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2answers
3k 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 ...
0
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0answers
23 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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2answers
79 views

$\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ notation

Define $\mathcal N$ $\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ Does $\mathcal N$ has a special name and standard notation?
1
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1answer
105 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 ...
1
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2answers
24 views

Quick Question on Pre-image Terminology

Sorry for the daft question, but, is the following a correct thing to say? "The preimage of a function f is a function iff for any element b in the range, there exists exactly one a in the domain ...
0
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1answer
42 views

Pi is the circumference over the radius?

Pi is the circumference over the radius and the radius half of the circle so what is a full circle? I know it starts with "D" and I tried a 100 words but I don't know it. Please help, I'm just a 5th ...
1
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1answer
162 views

Arbitrary's Meaning

I am not a native English speaker nor have I studied Physics in English before. I came across this word "Arbitrary" when I read a Mathematics for Physics book. I don't understand what it means. Here ...
3
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2answers
141 views

existence = well-defined?

When something (like a limit) is said to "exist" is this perfectly equivalent to "is well-defined"? And, is "well-defined" more-or-less equivalent to, "computers could use this definition and there ...
0
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1answer
35 views

Is there a general name for matrices which only have zeros on their main diagonal?

A diagonal matrix is one where every component not on the main diagonal is zero. E.g. $$ \begin{array}{cc} 12 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & -2 \end{array} $$ Is there a term ...
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2answers
24 views

What is the term for a group of graphs?

I know the term for a group of trees is a "forest", but what is the term for a group of graphs? The difference between a graph and a tree is that a tree can have no cycles, and usually has a node ...
2
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2answers
161 views

“Slow” and “fast” rates of convergence

I have recently read about convergence and divergence. However, I am having trouble understanding how something can converge/diverge "slowly" or "fast". If you sum up two series (that converge to the ...
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0answers
65 views

what is a degenerate function?

Consider the functin $f(x, y)$, e.g: \begin{align*} f(x, y) &= (x+y)^2 \\ f(x, y) &= (x+y^2)^2 \\ f(x, y) &= (35 \sin x+y^2)^2 \\ \end{align*} Dennis Auroux called this kind of ...
4
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4answers
112 views

Is $0 $ radians an acute angle?

I know that an angle less than $\frac {\pi}{2} $ radians is called acute, but under this definition, is an angle that is $0$ radians also considered acute?
0
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1answer
86 views

If a series converges does its sequence of partial sums converge?

By Definition, a series $\displaystyle \sum_{n=1}^\infty a_n$ converges if it's sequence of partial sums $\displaystyle S_n = \sum_{k=1}^n a_k$ converges. My question is, is the converse true? If ...
3
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1answer
85 views

Seeking proper terminology

Consider $\qquad a = b^2 \pmod c$. Are there special "names" for $a$ and/or $b$? I mean something like '$b$ is a modular root of $a$' or similar.
4
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0answers
104 views

“diverges to $1$”

$\newcommand{\logit}{\operatorname{logit}}$ A series may "diverge to $\infty$" or "diverge to $-\infty$"; a product may "diverge to $\infty$" or "diverge to $0$". postscript in response to comments: ...
3
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1answer
106 views

Is every “almost” isomorphism an isomorphism?

Let $f:A \mapsto B$, $g:B \mapsto A$ and $h:B \mapsto B$ be such that $g \circ f=\operatorname{id}_A$ and $f \circ g \circ h=\operatorname{id}_B=h \circ f \circ g$. Can we conclude ...
0
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1answer
40 views

Is this a discrete time Lyapunov function?

I have an algorithm to optimize a process. It is a discrete time algorithm. Every iteration of this algorithm changes the state of the process. I found a function, say $f(s)$, where $s$ is the state ...
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0answers
134 views

“Dual cardinality” in the graphs $(V_\alpha,\in_\alpha)$

04-25-2014 Enriched with more details Let define the graphs $(V_\alpha,\in_\alpha)$ in $ZFC$ $V_\alpha$ can be finite too $\in_\alpha \subseteq V_\alpha \times V_\alpha$ and ...
1
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3answers
85 views

What is a co-dimension?

I'm looking for a simple explanation (without complex formula) what a co-dimension is. When does objects have a co-dimension of 0 and when > 0? Context: A Critical Comparison of the 4-Intersection ...
4
votes
4answers
167 views

“Logically equivalent formulae express the same _______.” <- What word do logicians use for the blank?

Meaning denotes the truth conditions of a sentence: what would have to be the case for the interpreted formula to be true. Nevertheless, without an interpretation, two logically equivalent formulae ...
0
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2answers
77 views

Is there a name for models whose every element is named by (one or more) variable-free terms?

Let $T$ denote a first-order theory. Is there a name for those models $M$ of $T$ such that for all $x \in M$, there is a variable-free term in the language of $T$ whose interpretation under $M$ is ...
1
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2answers
77 views

Physical significance of knot vector in B-spline.

A B-spline blending curve formulation is: $P(u)=\sum_{k=0}^np_k B_{k,d}(u)$ Given $n+1$ control points, B-spline blending functions are polynomials of degree $d-1$, $(1<d<=n+1)$. ...
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0answers
19 views

Concept of knots in B-splines [duplicate]

Given $n+1$ control points, B-spline blending functions are polynomials of degree $d-1$, $(1<d\leq n+1)$. This much is easy to comprehend. Now comes the part I am not able to make any sense ...
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0answers
33 views

What would be the mathematical name for a function like the following?

x is an independent variable, p is a proportionality constant, and k is a critical value for x. Let's say: f(x)=p (a proportionality constant), where x >= k, a critical value. f(x)=0 where x ...
1
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1answer
60 views

One-sided Derivative Question

Let's say we define $$D_{+}f(x):=\lim_{h\to 0^+}\frac{f(x+2h)-f(x+h)}{h}$$ to be the "right-handed" derivative. This way the function does not have to exist (or equal what it 'should') at the point ...
1
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1answer
33 views

What is the name of this measure property?

if we have a function $f \in L^p$ sucht that $||f||_p =1$ and $m$ being a finite measure. Define a new measure $\mu$ by $$\mu(A):=\int_A |f(x)|^p dm(x).$$ Then $\forall \epsilon > 0 \ \ ...
2
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6answers
627 views

Algebra: What does “is defined for” mean?

In algebra what does: "Is defined for" mean? I have a question posted: $\sqrt{a+b}$ is defined for $-b \leq a$. The question posed is: Is this true... My question: WHAT DOES "Is Defined For" ...
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2answers
56 views

Difference between the definition of monoid action and group action?

The question is essentially in the title. From what I read in the wikipedia article about monoids it seems to me that we can define a monoid action in the exact same way we define a group action. Is ...
0
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1answer
122 views

What's maximal clique?

I'm unable to understand what maximal clique is. I mean how a clique can't be extended by a node and remain a clique? If I add a node and then I connect this node to every other nodes in the clique, ...
3
votes
0answers
27 views

Is there a name for this partial order between metrics?

Suppose we have a set $X$ and two metrics $d_1,d_2$ on it (which may or may not attain $\infty$). Assume furthermore that $d_1,d_2$ have the same metric components (where a metric comoponent is a ...
3
votes
1answer
96 views

Is there a name for the trivial probability distribution P(X=x) = 1 for a unique x?

Is there a name for the trivial probability distribution given by $P(X=x) = 1$ for a unique $x$ and $P(X=y) = 0$ for all $y \ne x$? I know it is very trivial, but since it is the distribution that ...
0
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1answer
13 views

What is the different between generating expression and infinite expansion?

What is the different between generating expression and infinite expansion? I can't figure it on my own
3
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1answer
155 views

Is a homomorphism expected to be a (structure-preserving) map?

Is a homomorphism a special type of morphism, namely a structure-preserving map? For a morphism (of a category), it is clear that we can't always expect that a morphism is necessarily a ...
4
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0answers
43 views

Subsets of cyclic group with distinct pairwise differences

Given a number $m\in\mathbb N$, let $\mathbb Z_m=\{0,1,\dots,m-1\}$ denote the ring of integers modulo $m$ (although we won't need multiplication, so any cyclic group of order $m$ will do). Given a ...
0
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1answer
29 views

Semantic question about chirality

Is it enough to generally say that an object is (or is not) chiral in some space/some number of dimensions according to some convention, or is some sort of structure or description of how it is chiral ...
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2answers
265 views

Is there any distinction between these products: scalar, dot, inner?

I hope you will forgive a math question that comes up in physics contexts where language is loose. This question migrated from Physics SE. I'm finding that I sometimes don't know what kind of product ...
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0answers
44 views

Is there a traditional name for the “eigenspace” function?

Let $A$ denote a field, $X$ denote an $A$-vector spaces, and suppose $\varphi : X \rightarrow X$ is a linear transformation. Is there a traditional name for the corresponding "eigenspace" function? By ...
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0answers
45 views

The term $rank$ in methematics

Reading wikipedia's disambiguation page about the "rank" word I see many concept of rank of many different matematical object. I only know about the rank of a graded poset and the rank of a set that ...
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2answers
81 views

Confusion related to definitions involving free groups

From Wikipedia ...the free group $F_{S}$ over a given set $S$ consists of all expressions (a.k.a. words, or terms) that can be built from members of $S$, considering two expressions different ...
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0answers
18 views

Terminology: Contraction *of* normed spaces? *Between* normed spaces? *On* normed spaces?

I have a terminological question. Suppose $X$ and $Y$ are normed spaces, and let $f$ be a contraction $X \to Y$. Which of the following expressions is correct? $f$ is a contraction of normed spaces. ...
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2answers
130 views

What subject in mathematics investigates the type of problems that constitute the LSAT “logic games” (example given)?

For my own curiosity, I read part of an LSAT study guide yesterday. The "logic games" section comprised questions like, An advertising executive must schedule the advertising during a particular ...
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1answer
33 views

Limiting probability of Markov chain(Terminology)

If I am asked to find the limiting probability of a Markov chain, what does this pertain to? $\lim \limits_{n \to \infty} P^n$? Where $P$ is the stepping matrix and $n$ is the number of steps. "What ...