Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.
0
votes
1answer
20 views
Function returning the set of sets which are no superset of each other
Given a set $S$ of sets.
Assume a function $f$ which removes all supersets of any set in $S$.
Example:
$f(\{\{ a\}, \{ a,b\}, \{ a, b,c\}, \{ b,c\},\{ b,c,d\} \}) = \{\{ a\}, \{ b,c\} \}$
Does this ...
3
votes
1answer
33 views
What is the name of graph problem that ask to select some vertices to see every edges.
I want to place light bulbs on some vertices (each bulb will lit up every edges it connected) where all edges lit up.
e.g. suppose I have this simple planar graph,
Sufficient vertices to place ...
9
votes
2answers
124 views
Etymology of the word “normal” (perpendicular)
While the word "normal" is one of the most overloaded mathematical terms, in linear algebra, it is usually associated with the notion of being perpendicular to something, as in "normal vector" or ...
3
votes
0answers
48 views
What is the Induced Representation in Geometric Terms
As is well known, for $G$ a Lie group, and $H$ a subgroup of $G$ such that $G/H$ is homogeneous space (or maybe this is always a homogeneous space?), we have a correspondence between representations ...
0
votes
1answer
46 views
meaning of open sets in topological space
For a topological space $(X,\Omega)$ , $\Omega$ represents open sets of this space. But why are they called open sets and are they the same open sets as normal set theory?
How will naming them closed ...
0
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0answers
12 views
Terminology: Ramification point
What does a ramification point mean in combinatorics? Is it the same as a branching point?
1
vote
1answer
43 views
What does multilinear function mean?
A draft research paper claims that $Q(p)=1-p_1 p_2 p_3 p_4 - p_2 p_3 p_6 p_7-p_1p_2$ is multilinear where $p_i = \mathbb P(e_i)$ and $e_i$ is a basic event of a component to fail.
I have learnt in LP ...
1
vote
1answer
44 views
Correct way of saying that some value depends on another value x only by a function of x
I would like to know what good and valid ways there are to say (in words) that some value f(x), which depends on a variable x, in fact only depends on x "through" some function of x.
Example: For ...
0
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0answers
15 views
Is there a specific name for an integer range that extends from a negative value to a positive value?
I'd like to make a reference in a text to an integer range that extends from a negative number to a positive number. Is there a specific name for this type of range, ie. it includes (continuously, as ...
5
votes
3answers
54 views
What is the term used to describe this
When .5 and .5 combine additionally, you get one. You can say "they add to one".
When the sqr(2)/2 combines with another sqr(2)/2 in pythagoreans theory to get one, you can say they ____.
Fill in ...
0
votes
2answers
57 views
How to read $10^{-5}\,\mathrm m^3$? [closed]
When a number is less than or equal to one, should I read the unit as cubic
meter, and not as cubic meters?
Does the below read as "10 to the negative 5 cubic meter" or
"10 to the negative 5 cubic ...
2
votes
1answer
30 views
Every subset of A is f-saturated
Let $f:A\rightarrow B$ be a function such that $\forall X\subseteq A[ f^{-1}[f[X]]=X]$ (In other words, every subset of $A$ is $f$-saturated). Does the property of the function $f$ have a name ?
I ...
2
votes
2answers
73 views
What is a Ramsey Graph?
What is a ramsey graph and What is its relation to RamseyTheorem?
In Ramsey Theorem:
for a pairs of parameters (r,b) there exists an n such that for every (edge-)coloring of the complete graph on n ...
3
votes
1answer
99 views
Difference between functional and function.
I have come across the term 'functional'. How is a 'functional' different from a 'function'? The exact term I came across was 'statistical functional.'
In terms of the background, can you please ...
1
vote
1answer
63 views
What is the definition of coefficient?
How to define coefficient? And what does it mean when someone says: put the $i$th term to be the coefficient of $x^i$
3
votes
3answers
68 views
What does “lower density” mean in this problem?
If $\mathscr{U}$ is a ultrafilter on $\omega$, then $\mathscr{U}$ contains a subset $A$ of lower density zero.
This is an exercise on page 76 of Problems and Theorems in Classical Set Theory, ...
3
votes
2answers
65 views
Does “indeterminate” mean “divergent”?
Just learning about series and someone tried to tell me that when doing the alternating series test, if the limit is indeterminate, it means it is divergent, and I wanted to know what exactly the ...
1
vote
1answer
82 views
What is the purpose of defining the notion of inflection point?
What is the purpose of defining inflection point?
I know that it is defined to be the point where the second derivative is zero and the second derivative sign changes.
It has to have some purpose ...
0
votes
0answers
26 views
Is there a term for the point/line/curve division of concavity of a surface in three dimensions?
Point of Inflection is the name given to the location at which a two dimensional curve changes from concave up to concave down.
Is there a similarly defined term or concept in three dimensions where ...
2
votes
1answer
51 views
What does this phrase about the weak topology of bounded operators mean?
Can somenone remind me of the meaning of the following statement:
the family of operator valued functions $A(\omega)$ converges to $A(\omega ')$ in the weak topology of bounded operators from ...
2
votes
1answer
37 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 $\{0, 0, ...
0
votes
1answer
29 views
Cost-to-go form of Dynamic Programming algorithm?
My lecture of Mat-2.3148 (Finnish) defines dynamic-programming-algorithm so that$J_N(x_N)=g_N(x_N)$ and $J_k(x_k)=\min_{u_k}\left\{g_k(x_k,u_k)+J_{k+1}(f_k(x_k,u_k))\right\}$ where
the state ...
1
vote
3answers
75 views
What is the term for a graph on $n$ vertices with no edges?
What is the term for a graph comprised of $n$ pairwise disconnected vertices?
I could call these $1$-colorable graphs or something like that, but I would rather use standard terminology if it ...
1
vote
1answer
36 views
Holomorphic extension to a closed half-space
While reading D. Zagier's expository paper on the proof of the prime number theorem given by Newman, I encountered the following terminology problem : let $f$ be a holomorphic function defined in an ...
0
votes
1answer
58 views
What does one mean by NOT directed acyclic? Doesn't it means the same as directed acyclic?
I did this question in a course and it is
Consider our algorithm for computing a topological ordering that is based on depth-first search (i.e., NOT the "straightforward solution"). Suppose we run ...
0
votes
1answer
111 views
what does 'arbitrary' mean?
Can arbitrary union of open intervals be written as countable union of open intervals?
Here, I don't even understand what do they mean by arbitrary.
Help me please.
6
votes
9answers
315 views
Are all integers fractions?
In a college class I was asked this question on a quiz in regards to sets:
All integers are fractions. T/F.
I answered False because if an integer is written in fraction notation it is then ...
0
votes
0answers
56 views
Nomenclature and/or notation for the intersection of a set with its boundary.
Is there standard nomenclature and/or notation for the expression $A \cap \partial A$?
1
vote
0answers
26 views
What is the etymology of the term “reduction” in the context of “reducing problem A to problem B?”
I teach a theory of computation course and each quarter a student asks me about why reductions between problems are called "reductions." I am not fully sure why this is - saying that "problem A ...
3
votes
3answers
106 views
Terminology: elegant proofs [duplicate]
What do mathematicians mean when they say: that's an "elegant proof" of such and such. What are the ingredients of an elegant proof? Maybe you can give examples of elegant proofs of your own.
0
votes
1answer
21 views
Name of a maximum bound
I'm reading this paper, which uses the quantity
$$\max_{x\neq0} \frac{x^T A x}{x^Tx}$$
where $A\in R^{n\times n}$ is nonsingular and $x\in R^n$.
This quantity looks so familiar to me that I'm almost ...
2
votes
1answer
44 views
Could a subspace of a normed linear space be not a linear subspace?
On page 38, Functional Analysis, Pater Lax:
Let $X$ be a normed linear space, $Y$ a subspace of $X$, The closure of $Y$ is a linear subspace of $X$.
But on Wikipedia, linear subspace
A ...
6
votes
0answers
78 views
'Galois Resolvent' and elementary symmetric polynomials in a paper by Noether
In Emmy Noether's 1915 paper "Der Endlichkeitssatz der Invarianten endlicher Gruppen", I saw the notion of a 'Galois resolvent', which I don't quite understand. Google didn't really help me with that, ...
0
votes
1answer
38 views
Optimum exists but not extreme point in Standard Form LP problem?
Standard form problem
$$\min \bar c^T \bar x \text{ so that } A \bar x=\bar b, \bar x\geq \bar 0$$
I am thinking the point II (Finnish) i.e. optimum exists but it is not extreme point, why it ...
7
votes
3answers
103 views
The usage of the term “family” in mathematics
In our lecture notes, the term "family" is used quite persistently and with no definition given. Some examples:
(i) Let V be a vectorspace and $(v_i)_{i \in I}$ a family of vectors... ...
1
vote
1answer
24 views
-$\infty$ cost in unconstrained LP problem?
I am trying to understand this lecture slide (Finnish) and the point in bold. It is a part of an OR condition, this is how I understand it. I cannot understand the optimal cost statement.
Example
...
3
votes
3answers
125 views
What does the phrase “except possibly” mean?
This term was used by my math professor when he was teaching us limits. This term also appears online like this "Let f be a function which is defined on some open interval containing $a$ except ...
0
votes
2answers
80 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 ...
1
vote
1answer
56 views
Does a half-diagonal of a rectangle have a mathematical name?
Your simplest math question of the day---but I really want to know!
Is there a name for the half-diagonal of a rectangle?
3
votes
6answers
250 views
How to express inequality between variables?
I have variables $a, b, c, d \in N^+$, how do I express the condition that all their values must be different? Also, what field of mathematics covers ways of expressing constraints? I couldn't even ...
1
vote
0answers
22 views
Origin of “direct variation”?
A definition from "College Algebra, 4ed." by Beecher, Penna, and Bittinger:
If a situation gives rise to a linear function $f(x) = kx$, or $y = kx$, where $k$ is a positive constant, we say that ...
0
votes
3answers
207 views
What is the meaning of equilibrium solution?
What are the equilibrium solutions for the differential equation $\dfrac{\mathrm{d}y}{\mathrm{d}t} = 0.2\left(y-3\right)\left(y+2\right)$
My Question: What does equilibrium solution mean in this ...
1
vote
1answer
52 views
Complement and Negation: $P(A)=0\rightarrow P(\neg A)=1$?
My earlier question became too long so succintly:
Suppose $P(C)=0.2$. Its complement is 0.8 i.e. $P(C)^C=0.8$ but what does $P(¬C)$ mean? I think I am messing up the term complement and negation?
...
1
vote
3answers
71 views
Where could I learn basic math terminology?
I am an english learner and I would like to learn the etymology of Mathematics. I would like to know the most common phrases in Algebra, and Geometry as well. I want to know at a level of
UK's A+. ...
3
votes
2answers
88 views
How to describe discretization to a novice?
While going through some C++ code about stochastic processes, I came across this concept of discretization repeatedly. I have checked the Wikipedia link but description goes into deeper details too ...
4
votes
2answers
64 views
What should I call a sentence which must (not) be true, but the provability is still unknown?
For example, let $\phi$ be a sentence in $ZF$ and $ZFC\vdash \neg\phi$. Then, $\phi$ must not be provable in $ZF$, but we still don't know whether $ZF\vdash \neg\phi$. What should i call this sentence ...
2
votes
2answers
89 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 ...
0
votes
1answer
34 views
What is a “rotated” basis?
My text (p. 19) introduces the concept of a "rotated" basis without explanation. What properties or characteristics of a basis make it "rotated" with respect to another? What operation on one basis ...
2
votes
2answers
127 views
What graph is this?
For my game I am trying to implement a continues world by interconnecting the nodes like below
I beg your pardon for my bad drawings
I don't know how to explain it but its NOT DENSE GRAPH
It is ...
10
votes
1answer
116 views
What does it mean for a set to have “structure”?
I understand that a set is like a list of things, except that the order doesn't matter and that you can't have any duplicates in a set. For example: $\{3, 1, 4, 2\}$ is the same set as $\{1, 2, 3, ...
