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

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2
votes
3answers
67 views

What is linear, numerically and geometrically speaking?

For as simple as it is, I never fully grasped what mathematicians and physicists mean with linear . Intuitively anything that looks like a straight line is interpreted as linear, like something in ...
0
votes
0answers
15 views

How to write the condition for Image of a function?

If $\Omega_l$ is $\Omega$ with $|x|<l$ and if $\Omega_S$ is the image of $z$ under mapping how we will write the condition for it. Am I right if I write $\Omega_S$ is $\Omega$ with $|S|<l$ or ...
0
votes
1answer
86 views

What does $\mathbb{Z}_2$ mean?

Wich number space is ment by: $\mathbb{Z}_2$ (I know that $\mathbb{Z}$ stands for Integer)
0
votes
2answers
52 views

Word for “openness”/“closedness” of an interval

What word properly completes the phrase the radius of convergence does not depend on the $\text{______}$ of the interval to mean that it doesn't matter whether $(a, b)$, $[a, b)$, $(a, b]$, or ...
2
votes
2answers
340 views

Is there a name for $\frac{n!}{m!}$?

Is there a name or short way of writing of $\frac{n!}{m!}$? I've searched and the closest I could find was binomial coefficient. Is there any other way?
3
votes
1answer
1k views

How do we pronounce this symbol?

I would like to know how to pronounce in english this symbol $\nabla \phi$ It is something phi ... ? thank you
1
vote
1answer
26 views

“The operation is normal iff it's both monotone and continuous” — which math area studies operation?

I just read Enderton's "Elements of Set Theory" to have a basic understanding of sets (btw it's a great book). One line of it says: "the operation is normal iff it's both monotone and continuous." ...
0
votes
0answers
22 views

“Differential variations”?

This passage in an old book on trigonometry calls these relations among parts of a spherical triangle "differential variations". The "parts" are three sides and the three angles; when the sides are ...
1
vote
2answers
60 views

Name for categories in which isomorphic implies equal?

A quick terminology question: Is there any particular name for a category in which each object is uniquely determined by its isomorphism class?
3
votes
1answer
47 views

Rel: the category of relations

$\text{Rel}$ is the standard name for the category of sets and relations. Confusingly in "Abstract and concrete categories" (ACC), page 22, $\text{Rel}$ is defined as a category whose objects are ...
14
votes
2answers
635 views

Why is analysis called “analysis”?

Just as the topic says, how did the name "analysis" come to denote the specific mathematical branch dealing with limits and stuff? The term "analysis" seems very generic compared to the words for the ...
1
vote
2answers
32 views

What does a probability being i.i.d means?

I know that a sequence of random variables is i.i.d means that they have the same mutually independent probability distribution. I was reading in a paper where the authors said that "the probability ...
1
vote
2answers
39 views

How to find if the sum of periodic function is periodic?

Basically, I am suppose to check if $f(x)=f(x+T)$. however my function is a bit complex: $x(t)=10\cos(20000\pi t)+0.5\cos(24000\pi t)+0.5\cos(16000\pi t)$ How shall I check if this function is ...
2
votes
3answers
30 views

Is sum of a series correct terminology?

What is the correct terminology when referring to the sum of a sequence? I see people and websites use "sum of the series...", but shouldn't we say the value of the series? (Sum of a sequence and ...
1
vote
1answer
85 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
votes
0answers
40 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
votes
3answers
89 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
votes
1answer
28 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 $U$. ...
1
vote
0answers
19 views

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
votes
1answer
89 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 $f(x)=k+x$ ...
0
votes
0answers
35 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 ...
0
votes
1answer
90 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
votes
0answers
18 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
votes
1answer
36 views

$\mathcal N (A):=\mathcal P(A)-\varnothing$ notation

Define $\mathcal N$ $\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ Does $\mathcal N$ has a special name and standard notation?
1
vote
1answer
47 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
vote
2answers
23 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
votes
1answer
40 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
vote
1answer
29 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
votes
2answers
126 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
votes
1answer
31 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 ...
1
vote
2answers
21 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
votes
2answers
50 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 ...
0
votes
0answers
43 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 ...
0
votes
0answers
58 views

The symbol $\mathcal P(\alpha)$ where $\alpha$ is a cardinal

$X$ is a set. There's a term: ‌$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$ the power set $\mathcal P(2^{|X|})$ in an article. What does it mean? It seems $2^{|X|}$ is the power ...
4
votes
4answers
100 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
votes
0answers
43 views

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

By Definition, a series $\sum_{n=1}^\infty a_n$ converges if it's sequence of partial sums $S_n = \sum_{k=1}^n a_k$ converges. My question is, is the converse true? If $\sum_{n=1}^\infty a_n$ ...
3
votes
1answer
82 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
votes
0answers
82 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
votes
1answer
90 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
votes
1answer
31 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 ...
1
vote
0answers
128 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
vote
3answers
79 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
131 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
votes
2answers
68 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
vote
2answers
47 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 $d-1$, $(1<d<=n+1)$. ...
1
vote
0answers
18 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 ...
1
vote
0answers
30 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
vote
1answer
48 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
vote
1answer
30 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
votes
6answers
254 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" ...