Tagged Questions
16
votes
9answers
2k views
How to represent the floor function using mathematical notation?
I'm curious as to how the floor function can be defined using mathematical notation.
What I mean by this, is, instead of a word-based explanation (i.e. "The closest integer that is not greater than ...
2
votes
1answer
39 views
how to write the process of decomposition of a graph into shortest closed sub graphs
If I want to decompose a graph in to possible shortest closed cycles (as shown in right side).
then how can i describe this process with mathematical notations.
to understand please refer below ...
0
votes
1answer
45 views
Mathematical notation of graph subdivision
If anyone can define a directed graph subdivision with mathematical notation, please post a response.
My second question is: Irrespective from the planar embedded graph or not, is this
definition ...
3
votes
2answers
63 views
two notation: semi-metric and pesudometric
There are two notations: semi-metric and pesudometric make me unclear. Are they the same thing, or they are different?
Thanks ahead.
3
votes
0answers
51 views
Define composition of small cyles and making a big graph
I am having following sub graphs and wish to compose all and make a
one bigger graph (say G). After that, I want to select the closed path
where it is passing along the outer vertices of that ...
1
vote
2answers
73 views
What is the meaning of the expression $\liminf f_n$?
I am a little confused as to what $\liminf f_n$ means for a sequence $f_n$ of functions converging to $f$. I can not locate a definition anywhere.
2
votes
1answer
56 views
“[T]ransversely isotropic and mirror-symmetric (space group:$D_{\infty h}$)”, its orbifold notation?
I am trying to understand this frieze pattern $D_{\infty h}$ aka its orbifold notation. This describes spider's silk. The authors call it a space group, some sort of generalization from orbifolds.
...
1
vote
3answers
135 views
Is ∞ considered defined?
$\infty$ (Infinity) is not a number, but infinity is considered to be defined, right?
There are expressions in mathematics such as: $\frac x0,0^0, \frac\infty\infty,$ which are not defined because ...
2
votes
2answers
59 views
A simple notation question on grad and Lp norm
What does this notation
$||\nabla u|| _p$ mean? I would like an exact definition.
Also I have seen $|\nabla u|_1$. Does this mean the $\sum_i|\partial_i u|$?
0
votes
0answers
42 views
What is $Pic(S)^G?$
Let $S$ be a projective surface and $\text{Pic}(S)$ its Picard group, $G$ is some group (in fact, it consists of automorpisms of $\mathbb P^2$). I came across a notation "$\text{Pic}(S)^G$". Could you ...
2
votes
0answers
65 views
Where can I find a description of math language symbols?
I am reading math articles. I meet math symbols.
For example $\exists$ or $\forall$.
For example for "For any a exist e that" can be rewriten as: $\forall a \exists e$
Where can I find full ...
0
votes
2answers
66 views
Exponentation vs Power
What definition of $a^b$ operation is the most popular and standartized: Exponentation or Power?
Is any difference between them?
5
votes
4answers
262 views
What is the correct definition of the absolute value of $x$, $|x|$?
What is the correct definition of the absolute value of $x$, $|x|$?
Option A
$$
|x|=
\begin{cases}
-x&\text{if } x < 0\\
0& \text{if } x=0\\
x&\text{if } x>0
\end{cases}
$$
Option ...
6
votes
1answer
126 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- ...
10
votes
3answers
357 views
What is the purpose of the $\mp$ symbol in mathematical usage?
Occasionally I see the $\mp$ symbol, but I don't really know what it is for, except in conjunction with the $\pm$ symbol thus: $a \pm b \mp c$ which (I believe) means $a+b-c$ or $a-b+c$ (please ...
0
votes
4answers
752 views
What does it mean when a function is finite?
When someone says a real valued function $f(x)$ on $\mathbb{R}$ is finite, does it mean that $|f(x)| \leq M$ for all $x \in \mathbb{R}$ with some $M$ independent of $x$?
6
votes
1answer
302 views
What do these arrows mean? (Froda's Thm)
I was reading "A Course in Probability Theory" by Kai Lai Chung, and in the book he was discussing discontinuity of monotonic functions, and after doing some searching online to learn more about the ...
1
vote
1answer
143 views
What is the nature of the definition symbol?
A question about definitions and also notation, illustrated with a trivial example:
Let $a,b,c\in\mathbb{N}$ and
$$a:=2,$$
and
$$b:=1$$
I postulate the the following formula holds
...
3
votes
1answer
108 views
What do mathematicians call the Two's Complement on 8-bits group?
It is isomorphic to $\mathbb{Z}_{2^8},$ only difference is the symbols usually identifying the elements of the set are from $\{-128, \ldots, 127 \}$ and not $\{0, \ldots, 256\}.$
What is an elegant ...
2
votes
2answers
415 views
$\{0,1\}^n$ and $[0,1]^n$ notations
Can someone please help me clarify the notations/definitions below:
Does $\{0,1\}^n$ mean a $n$-length vector consisting of $0$s and/or $1$s?
Does $[0,1]^n$ ($(0,1)^n$) mean a $n$-length vector ...
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
2answers
179 views
What is the product of the empty set?
Give:
$fn(S)=\prod_{x\in S}x$
what is:
$fn(\emptyset)$
I can see reason that it would be defined as 1 or 0.
Note: I thought about restricting the domain of $S$ but that would make the problem ...
3
votes
2answers
329 views
How to write “let” in symbolic logic
How do I write let in symbolic logic? For example, if I am in the middle of a proof and there is a variable which I can assign to an arbitrary value, what would I write? My best guess is:
$$ x := a ...
3
votes
1answer
103 views
Clarification on Dirac notation
I am new to the Dirac notation, so would appreciate some clarification.
Suppose $\Psi=\psi_1+\psi_2$ where $\Psi$ is normalized and $H$ is a linear operator such that $H\psi_1=E_1\psi_1$ and ...
7
votes
3answers
511 views
What is the operation $\boxtimes$?
Reading papers about $p$-adic analysis and Galois representations, I have found objects like this $D \boxtimes \mathbb{Q}_p$. So my question is what is $\boxtimes$ and how do we read it ?
4
votes
1answer
248 views
What is this R-like symbol power 2?
I found this in a computer medical research text.
What is the meaning of this R-like letter? S, in this context is an iso-intensity surface.
[edit]
Since context is not sufficient, I think it is ...
2
votes
3answers
182 views
“Defined as” versus “Equivalent to”
This is a lazy question, but very often textbooks use the "$\equiv$" (equivalent to) sign and the "$:=$" (defined as) sign in the same places from book to book. I suppose equivalence to a previously ...
5
votes
4answers
334 views
What differences are between $\mathbb{E}^n$ and $\mathbb{R}^n$
What differences are between the two notations $\mathbb{E}^n$ and $\mathbb{R}^n$?
Do they represent/define the same space set with the same structure(s)?
Thanks and regards!
1
vote
0answers
183 views
Why are there two different Leibniz notations?
Why do we have dy/dx with the regular d, and 'del y/del x' with the 'funny' d? I can easily find definitions for each expresion, but the definitions appear to be logically equivalent. However, they ...
9
votes
2answers
363 views
Formalizing Those Readings of Leibniz Notation that Don't Appeal to Infinitesimals/Differentials
[disclaimer: I've studied a lot of logic but never been good at analysis, so that's the angle I'm coming from below]
in my attempt to find a precise version of the 'definitions' usually given when ...
