Tagged Questions
0
votes
1answer
22 views
How could I define this $\mathrm{nw}(X)$ by using only one sentence?
A family $\mathcal N$ of subsets of a topological space $X$ is a network for $X$ if for every point $x\in X$ and any neighbourhood $U$ of $x$ there exists an $M \in \mathcal N$ such that $x\in M ...
0
votes
0answers
12 views
definition of raw variable
i would like to clarify definition of raw variable,for instance,let us see following article
http://www.psych.umn.edu/faculty/waller/classes/FA2010/Readings/rodgers.pdf
where it is written that
The ...
3
votes
3answers
80 views
What does boson-type realization mean?
I have seen several different contexts the expression "boson-type realization", for instance in the study of algebras growth and realization of affine algebras.
To be or not be a boson-type ...
0
votes
1answer
48 views
What is the difference between isomorphism and homeomorphism?
I have some questions understanding isomorphism. Wikipedia said that
isomorphism is bijective homeomorphism
I kown that $F$ is a homeomorphism if $F$ and $F^{-1}$ are continuous. So my question ...
3
votes
2answers
39 views
Hartshorne Lemma(II 6.1)
Hi I am wondering what Hartshorne means by "an open affine subset on which $f$ is regular". This is part of the first sentence in the proof of lemma 6.1 in chapter two of the book "Algebraic Geometry ...
2
votes
0answers
98 views
Is there any compelling reason why $0$ *shouldn't* be a natural number? [duplicate]
This seems to be (from what I've heard from various math people of various statures) a heated debate. One of my previous professors proclaimed very strongly that $0$ is not a natural number. Another ...
1
vote
2answers
33 views
Help to understand the ring of polynomials terminology in $n$ indeterminates
In the Hungerford's book, page 150, the author defines a ring of polynomials in "n" indeterminates in the following manner:
After the author defines the operations in this ring with a theorem:
...
2
votes
2answers
69 views
Why the terms “unit” and “irreducible”?
I'm trying to understand why in a ring we choose the names unit to an invertible element and irreducible element in this definition
Maybe historical reasons?
For example, I suppose the second ...
0
votes
2answers
65 views
Definition of metastability
I was reading Terence Tao's blog post on analogies between soft and hard analysis when I saw that the soft analysis statement "$x_n$ is convergent" corresponds to the hard analysis statement "$x_n$ is ...
5
votes
2answers
84 views
Does this qualify as a statement?
Is this a statement?
All positive integers with negative squares are prime.
What do we need to qualify as such?
1
vote
1answer
95 views
Definition of correspondence
A one-to-one correspondence is an alternative name for a bijection between two sets, but to what does the term 'correspondence' alone refer? As far as I can see, it seems to be another term for ...
2
votes
2answers
39 views
Name of the order with irreflexivity, antisymmetry and transitivity?
I have an order otherwise poset aka partial order but it is irreflexive so relationships such as 1R1 and 2R2 are impossible. What is the name of this order?
4
votes
1answer
91 views
Allegories in easy words?
1) What is, in easy words, the definiton of an allegory?
2) And when are allegories useful?
What does it have to do with the category theory and categories?
With the definiton of category, ...
3
votes
0answers
71 views
Infinite set ordered like a “infinite tree”
Obviously I don't need to say that I'm still a newbie, so I'll try to explain my question with some pics too.
I have a infinite set $T$ I have a visual idea of how this set is ordered, but I don't ...
2
votes
1answer
71 views
Is there a common name for the property $f(\lambda x+(1-\lambda)y)\leq f(x)+f(y)$?
For $X$ a vector space and $f:X\to\mathbb{R}$, I'm considering the property
$$f(\lambda x+(1-\lambda)y)\leq f(x)+f(y) \qquad\forall x,y\in X, \;\forall\lambda\in[0,1].$$
So it's like convexity ...
1
vote
3answers
53 views
Precise differences in meaning of Power Series, Taylor Series
Being an physicist/artist, not a real mathematician, I often toss around the terms "Taylor Series" and "Power Series" without any concern. Are these terms be considered interchangeable by ...
2
votes
1answer
45 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, ...
0
votes
2answers
83 views
Is an unit-cube polyhedron? What about other platonic solids?
Definitions
According to my linear programming course and screenshot here (Finnish), a polyhedron is such that it can be constrained by a finite amount of inequalities such that $$P=\{\bar x\in ...
2
votes
2answers
92 views
Associativity with one operation or two (or more) operations
It seems to me there are different 'types' of associative law that are all said to simply have the property of associativity.
For example this term is applied if we are only considering one operator ...
5
votes
5answers
242 views
What exactly is “approximation”?
There are a lot of great "approximations" that exist in the mathematical field:$$\dfrac{22}{7} \approx \pi$$
$$e \approx \left(1 + \dfrac{1}{n}\right)^n$$But the fact that I have yet to know what ...
3
votes
1answer
72 views
Are distinctions in definitions of “finite” material in, eg, topology or measure theory?
There are several definitions of "finite", like Dedekind's and Tarski's (Thanks to A.K. for point out the latter - first time I've heard of it): From the Wikipedia entry on Finite Set:
(Richard ...
1
vote
1answer
42 views
Use of the term “normal section” in a theorem of Maria Lucido.
Prop. 3 in this paper (p.135) states
Let $G$ be a solvable group with $\text{diam}\Gamma(G)=4$. Then either $l_F(G)\leq 3$ or $l_F(G)=4$ and $G$ has a normal section isomorphic to $H$.
($H$ is ...
12
votes
2answers
2k views
What happens if we remove the requirement that $\langle R, + \rangle$ is abelian from the definition of a ring?
Ever since I learned the definition of a ring, I've wondered why the additive group is required to be abelian. What happens if we allow $\langle R, + \rangle$ to be nonabelian as well as $\langle R, ...
1
vote
1answer
104 views
What is the difference between a function and a map? [duplicate]
Possible Duplicate:
Is there any difference between mapping and function?
I am an aspiring mathematician who just started out. What is the difference between a function and a map? Or are ...
1
vote
1answer
283 views
Why are vector spaces sometimes called linear spaces?
I have never come across the term 'linear space' as a synonym for 'vector space' and it seems from the book I am using (Linear Algebra by Kostrikin and Manin) that the term linear space is more ...
1
vote
2answers
42 views
what does it mean to say a space is norm separable?
I came across in my textbook the term: norm separable. I looked in the textbook and online and could not find a definition.
0
votes
0answers
106 views
What is the correct definition for an imaginary number?
The following is taken from Wikipedia's definition.
An imaginary number is a number whose square is less than or equal to
zero.
But I also heard that
An imaginary number is a number whose ...
2
votes
1answer
72 views
What is the meaning of $K/F$ is a cyclic extension?
I have it that $K/F$ is a (finite) field extension, what is the definition
of when $K/F$ is called cyclic ?
I heard it while I studied Galois theory and it was defined as
$K/F$ is called cyclic ...
0
votes
1answer
43 views
Legal actions on a PDA and terminology
I am unsure about the following so I would like to verify if my statements
are true:
We can remove at most a single character ($Z\in\Gamma$) from the
PDA (top ?) of the stack with one step of the ...
2
votes
2answers
80 views
What is a non-degenerate module?
I know what a non-degenerate bi-linear form is, but what does it mean for say a left $R$-module $M$ to be non-degenerate? (Here $R$ is a ring without unit$)
I came across a module being called ...
6
votes
1answer
127 views
When do modifiers denote sub or super? Pseudo-, quasi-, ultra-, strong-, well-, pre-, c0- …
One only needs to search MMA.SE, math journals, wikipedia, or god-forbid, n-cat lab, for keywords listed in the title, which can be extended with: uniform-, regular-, complete-, local-, partial-, non- ...
1
vote
1answer
97 views
What is the meaning of the term “inductively P map”?
In this page is the definition of an inductively open map. But in this pdf is the definition of a inductively P map, where P is a property of maps.
But there is a difference in the definitions. In ...
3
votes
2answers
230 views
What exactly is a manifold?
Wikipedia's "Simple English" entry describes a 2D map of the Earth as a manifold of the planet Earth.
Does this mean that in mathematics a manifold is essentially a representation of something that ...
2
votes
1answer
70 views
What is the name of the group linear functions on a finite field?
More precisely what is the name for the group
$$\{ X\mapsto \alpha^2X+\beta : \alpha,\beta \in GF(q), \alpha \neq 0\}$$
I've always called it the special affine group, but I see that can mean ...
18
votes
3answers
1k views
difference between class, set , family and collection
In school I have always seen sets. But I was watching a video the other day about functors and they started talking about any set being a collection but not vice-versa and I also heard people talking ...
2
votes
1answer
236 views
What does “quotient-ring” mean?
I am reading a paper about rings (http://malaschonok.narod.ru/publ/ma01.ps, page 3). In this paper the term "quotient-ring" appeared.
What is a quotient-ring?
(Note: The text in the original ...
3
votes
0answers
58 views
Isotropic subspaces [duplicate]
Possible Duplicate:
Etymology of the word “isotropic”
Let $V$ be a vector space and we have a symmetric, non-degenerate bilinear form with signature $(n,n)$ on it. A subspace ...
1
vote
2answers
74 views
Quibble with terminology
Proposition 5.15 on page 63 in Atiyah-Macdonald goes as follows:
Let $A \subset B$ be integral domains, $A$ integrally closed, and let $x \in B$ be integral over an ideal $ \mathfrak a$ of $A$. Then ...
0
votes
1answer
90 views
Meaning of the term single letter formula
It is common in information theory to look for single letter formulas or to dismiss a result as suboptimal if no single letter formulas are available.
Could someone clarify the meaning of what is a ...
2
votes
2answers
214 views
What are the carried numbers called in an Addition problem
What is the 1 that is carried called?
These are all Latin, would this make sense?
The Latin word for "carry" is "porto", would it be called Porto?
Just guessing here
Example:
...
6
votes
2answers
135 views
Usage of the word “formal(ly)”
This is weird. To me, in mathematical contexts, "formally" means something like "rigorously", i.e. the opposite of informally/heuristically.
And yet, I very often read papers very the word seems to ...
-1
votes
0answers
62 views
How to name a relation between posets?
I am writing a research article and want to introduce a definition like this:
Definition XXX $f$ is a pair consisting of a family $\operatorname{form}(f)$ of posets indexed by the some index set and ...
1
vote
0answers
44 views
Definition of fragility
What does it mean for a solution to a system of differential equations to be fragile?
A context for the term can be found here:
This is taken from here in Mathematical Methods for Mechanics: A ...
5
votes
1answer
174 views
What set operation is this?
Given two sets $ A = \{\{1\} , \{2 , 6\} \}$ and $ B = \{\{2\} , \{3\} , \{4 , 5\} \}$, what set operation can produce $$ C = \{ \{ 1 , 2 \} , \{ 1 , 3 \} , \{ 1 , 4 , 5 \} , \{ 2 , 6 , 2 \} , \{ 2 , ...
0
votes
1answer
50 views
Math vocab: operator on $S$ and into $S =$?
Is there a special name for a binary operation on the set $S$ that is also into $S$, that is unambiguous with other uses. I.e. if it's "operator on $S$", I've heard that in other places meaning the ...
4
votes
3answers
201 views
What's the difference between tuples and sequences?
Both are ordered collections that can have repeated elements. Is there a difference? Are there other terms that are used for similar concepts, and how are these terms different?
1
vote
1answer
116 views
Name of binary relation: if $(x, y)\in R$ then there is no $z$ such that $(y, z)\in R$
Is there a term for a binary relation $R\subset A^2$ on some set $A$ such that if $(x, y)\in R$ then there is no $z$ such that $(y, z)\in R$ ? Are there any examples of it? Are there any related ...
1
vote
3answers
776 views
why do we use 'non-increasing' instead of decreasing?
In english based math language it seems that
non-increasing $\Longleftrightarrow$ less or equal (non-strict decreasing)
decreasing $\Longleftrightarrow$ strict less ( strict decreasing)
...
2
votes
1answer
1k views
Relationships among the terms “slope”, “parameter”, and “coefficient”?
In $y=mx$, is $m$, are there different implications of referring to $m$ as a "slope", a "coefficient", a "parameter"? Or perhaps the "slope coefficient" or "slope parameter"?
For context, I am ...
2
votes
3answers
381 views
Definition of “maximal” and “minimal” [duplicate]
Possible Duplicate:
difference between maximal element and greatest element
When I first encountered the terms maximal and minimal, I confused them with maximum and minimum. Many of my ...
