Question on the meaning, history, and usage of mathematical symbols and notation. Please remember to mention where (book, paper, webpage, etc.) you encountered any mathematical notation you are asking about.
1
vote
1answer
47 views
Notation for an Array
What is the proper mathematical notation to deal with an array?
Beginning with the declaration, I am used to the following format as a programmer:
...
1
vote
1answer
42 views
Correct Notation for Loop
What is the proper mathematical notation for a loop structure such as the following?
FOR i=1 to 10 BEGIN
{Perform loop task}
END;
I am a programmer, but prefer ...
8
votes
3answers
187 views
Interpretation of “not equal” notation
This will be a short question. Let $x$, $y$, $z$ be three elements from any set. Is the following:
$$x \ne y \ne z \tag{1}$$
Equivalent to:
$$x \ne y, ~ ~ y \ne z, ~ ~ z \ne x \tag{2}$$
Or simply:
...
0
votes
0answers
27 views
Integrate from min to max: Notation
I'd like to integrate over the entire range of a set of values (i.e. from $\min(x_i)$ to $\max(x_i)$). Is there an "elegant" way of expressing this instead of:
$\displaystyle ...
3
votes
1answer
44 views
What Does this Subscript Mean?
I've found some weird notation on Wikipedia like this: $a_m$. What does it mean?
4
votes
2answers
96 views
How to evaluate powers of powers (i.e. $2^3^4$) in absence of parentheses?
If you look at $2^{3^4}$, what is the expected result? Should it be read as $2^{(3^4)}$ or $(2^3)^4$? Normally I would use parentheses to make the meaning clear, but if none are shown, what would you ...
0
votes
1answer
29 views
Some questions regarding the convention used
I've some questions regarding the following problem from Herstein. BTW I'm not looking for its solution:
Do $\lambda_g$ is actually $\lambda_g(x)=xg$ when I write $x\lambda_g$ as $\lambda_g(x)?$
...
1
vote
2answers
48 views
Is it okay to write $n = n(k)$ to say that $n$ is a function of $k$?
In Physics, there is the index of refraction $n$. Sometimes, it will be just a scalar, sometimes it will be a function of the wave number $k$. I often see $n = n(k)$ to denote that $n$ is actually a ...
1
vote
1answer
32 views
What does $\left< dz_j , \frac{\partial}{\partial z_j}\right>$ mean?
Here, in page 2 of Steven Krantz's book Function Theory of Several Complex Variables, what do those angle brackets mean? What kind of product is that between differentials and partial derivatives?
...
3
votes
3answers
162 views
What do these old symbols from set theory mean? (Large E, $\cdot$ and $+$ for sets, and $\ \bar{\!\bar X}\,non\!\geqslant\frak n$)
So, I'm trying to prove the theorems in this paper by Tarski:
On Well-ordered Subsets of any Set, Fundamenta Mathematicae, vol.32 (1939), pp.176-183
but it is from 1939, and I don't recognize a few ...
0
votes
3answers
39 views
How to write $b$ between $a$ and $c$ formally?
How to write $b$ between $a$ and $c$ formally ? I mean it could be
1) $a<b<c$
or
2) $a>b>c$
but I want to leave it in the middle which one it is.
If I use the sandwich theorem for ...
5
votes
3answers
71 views
Limits notation: equals or arrow
Recently I was using the following notation to express the limit in a publication:
$$ \lim_{x \rightarrow \infty} f(x) = 0 $$
The reviewer said this is wrong. Instead it should read:
$$ \lim_{x ...
2
votes
1answer
44 views
Notation question for the set of real numbers
I realize this is probably very specific to the person writing the textbook, but I was wondering if anyone else out there knows the answer.
I encountered this in one of my textbooks: ...
0
votes
3answers
76 views
Where's the boundary between $\mathcal O(10^i)$ and $\mathcal O(10^{i+1})$?
When we(?*) say that some $x$ is of the order of $\mathcal O(10)$, we imply that it is not of order $\mathcal O(1)$ or $\mathcal O(100)$. (Don't we?)
Where are the cutoff points between those orders?
...
3
votes
2answers
66 views
A question on notation for open sets
Yesterday I was presenting a seminar where I started using this notation to make sentences shorter; whenever I wanted to say that $A$ was open in $B$, I would write $A\underset{op}\subset B$, with the ...
0
votes
2answers
43 views
What are these bracketing symbols and what do they mean?
What do the matching "L" shapes (near .5 and 20) mean in this forumla?
The document where I found this formula can be found ...
0
votes
3answers
60 views
Different methods to write an integral
I saw someone write this for showing substitution. Is it correct.
$$\int \frac{2x}{\sqrt{x^2+2}}\, \mathrm{d}x$$
$$\int \frac{\mathrm{d}u}{\sqrt{u}}\, \mathrm{d}\left(2xdx\right)$$
Just wondering ...
3
votes
1answer
31 views
Is it necessary to state that $y_i \leq 1$
In a class test for Linear Programming, my professor deducted some marks because I missed the condition $y_i \leq 1$ in the mixed strategy games solution.
$ y_i $ stands for the probability of any ...
3
votes
3answers
36 views
How to read this expression?
How can I read this expression :
$$\frac{1}{4} \le a \lt b \le 1$$
Means $a,b$ lies between $\displaystyle \frac{1}{4}$ and $1$?
Or is $a$ less the $b$ also less than equal to $1$?
So $a+b$ ...
-1
votes
2answers
39 views
How to display matrices and other mathematical formulae [closed]
This is a very basic question, as I'm not familiar with computer typography and mathematics...
I'm a stackOverflow guy, and I do lots of work with matrices, including answering questions for others. ...
3
votes
2answers
49 views
What does the notation mean?
Given a measure space $(\Omega,\mathcal{F},\upsilon)$ and a $p>0$.
What does the following mean?
$$ \|f\|_p=(\upsilon|f|^p)^{1/p}$$
0
votes
0answers
21 views
Notation for drawing a distribution from a constrained distribution
$X$ is a random real variable drawn from a distribution $F$ on the reals, $X \sim F$.
In a particular model, the density of $F$, $pdf_F$, is estimated using a collection of points $d$ and a free ...
4
votes
3answers
76 views
Notation for $X - \mathbb{E}(X)$?
Let $X$ be a random variable with expectation value $\mathbb{E}(X)=\mu$.
Is there a (reasonably standard) notation to denote the "centered" random variable $X - \mu$?
And, while I'm at it, if $X_i$ ...
1
vote
2answers
65 views
Symbol for the area of a shape
There are mathematical symbols to represent angles ($\angle AB$) and magnitudes ($|AB|$) and what not (ie: not variables, but rather symbol operator thingies).
Is there a symbol to represent the area ...
0
votes
1answer
57 views
What does a dot after a number mean?
So I'm making some calculations for numerical analysis and the output I get in Wolfram or Mathematica for input like:
...
0
votes
2answers
58 views
Notation for “absolute value” in multiplicative group.
In an additive number group (e.g. $(\mathbb{Z},+)$) there is a well known notation for absolute value, namely $|a|$, which coincides with $\max(a,-a)$, for $a \in \mathbb{Z}$.
When the context is a ...
2
votes
0answers
29 views
Mathematical notation for formulas involving trees
I am working on document that requires me to write such things as "$T_1$ is a descendant of $T_0$", or "$N_1$ is an parent of $N_2$". For now, I've been highjacking set notation for use in formulas, ...
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
44 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
67 views
Meaning of $ \sup_{n}f_{n}(x)$
What does $ \sup_{n}f_{n}(x)$ mean? In what sense is one function "bigger" than the other?
Context: If $\{f_{n}\}_1^{\infty}$ is a sequence of measurable functions, then $ \sup_{n}f_{n}(x)$ is a ...
2
votes
1answer
66 views
What is $\tan^3 x$?
I can't find how to calculate $\tan^3 x$. I don't even know how to use it on a calculator and have no idea what it means. If $\tan x$ is the ascending of the angle $x$, is $\tan^3 x$ the ascending^3. ...
1
vote
1answer
38 views
Notation for the coefficient of the $i$th term of formal power series.
What notation is standard for the coefficient of $X^i$ in a formal power series $P$? I was thinking of $X^i \cdot P$, by analogy with the dot product.
1
vote
2answers
137 views
How to Make a Math Symbol in Word
I have a student typing up her thesis. She needs to type external tensor, $\boxtimes$. Is there anyway to get that symbol in Microsoft Word? She doesn't know how to use TeX.
0
votes
1answer
49 views
What do $\mathbb{R}^n$ and $\mathbb{Z}^n$ mean?
If we see the following:
$\mathbb{R}^n, \mathbb{Z}^n$, what do they refer to?
Thanks.
1
vote
1answer
27 views
in type theory does (x:A) imply ((x:A):A)
In the formulation of type theory I'm reading, (x:A) is an expression of type A. This would seem to imply ((x:A):A) and (((x:A):A):A)... Is this a common feature of type theories? Or am I reading too ...
0
votes
0answers
37 views
Einstein notation non-repeating indices
I forget the rule for Einstein notation. If I have something like the gradient:
$$\vec\nabla f = \frac{\partial f}{\partial x_i} = \langle \frac{\partial f}{\partial x}, \frac{\partial f}{\partial ...
1
vote
1answer
44 views
How do I write the integral over all $x$ in $\Bbb R^n$?
If I have $f:\mathbb{R}^n\to\mathbb{R}$ I would write the integral over some region $\mathcal{R}\subset\mathbb{R}^n$ like:
$$
\int_\mathcal{R}f(\mathbb{x})\mathrm{d}\mathbb{x}.
$$
What subscript ...
3
votes
2answers
104 views
$H ≤G$ means $H$ is a subgroup of $G$?
I was reading this page:
http://www.proofwiki.org/wiki/Definition:Subgroup
I never heard that $H ≤G$ means $H$ is a subgroup of $G$. Is this standard notation ?
And if not, what is/are normal ...
4
votes
6answers
336 views
What does the notation $f\colon A\to B$ mean?
I've been doing an online course in discrete mathematics, and the notation $f\colon A\to B$ has come up a few times, and it has not been explained what it means. I tried searching for it on Google, ...
6
votes
1answer
241 views
What are $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$?
Sometimes reading on wikipedia or in this site (and in very different context like topology, arithmetic and logic) I have found these symbols $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$. They are ...
4
votes
1answer
280 views
Why doesn't logic, math, physics etc have a symbol for “example”?
We have symbols for everything but there is no symbol for "example" despite examples being fundamental to achievements.
Why is there no symbol for "example" when there are symbols for everything ...
1
vote
1answer
37 views
Name/Symbol for set of combinations without repetition
Given a set $\mathcal{S}=\{1,2,3\}$, I'm interested in the set of all combinations of two elements without repetition:
$\{(1,2),(1,3),(2,3)\}$
Is there a name and symbol for such a set? Something ...
1
vote
1answer
39 views
Mathematical notation to describe tiling shapes?
I stumbled across the following Wikipedia article which contained information on tiling by regular polygons.
Underneath each image, it contained a sort of sequence of numbers which appears to be ...
0
votes
3answers
88 views
Distance between two points
The distance between the two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ is the quantity
$$\mathrm{distance}(P, Q) = \sqrt{(\Delta x)^2 + (\Delta y)^2}.$$
Is $(P, Q)$ above indicating an open ...
0
votes
1answer
28 views
Birkhoff Lattice theory notation question- probably easy to answer
In Lattice Theory p. 30 3rd edition:
Lemma 3. In any distributive lattice, every polynomial is equivalent to a join of meets, and dually:
$p(x_1,...,x_r)=\lor_{\alpha \in A}\{ \land_{S_\alpha} x_i ...
2
votes
3answers
44 views
A question about $[c_0,c_1,\ldots,c_n]$ notation for continued fractions
I try to understand why by definition
$[c_0,c_1,\ldots,c_n]=[c_0,[c_1,\ldots,c_n]]$ and also
$[c_0,c_1,\ldots,c_n]=[c_0,c_1,\ldots,c_{n-2},[c_{n-1},c_n]]$ .
Those are continued fractions, and ...
1
vote
0answers
51 views
Is $\langle f \rangle $ an “inner product”?
Let $$\langle f(x,y)\rangle = \iint_S f(x,y)\,\mathrm{d}x\,\mathrm{d}y$$
I have seen the above in multiple papers as the definition of $\langle f(x,y)\rangle$. I would normally associate angle ...
-2
votes
4answers
93 views
Derivative of product notation?
Presume $f(x,y)$ is a continuous function. How would I take the derivative of $$\prod_{x=1}^N f(x,y)$$?
Edit: derivative with respect to $x$, that is.
6
votes
2answers
138 views
Is a bra the adjoint of a ket?
The instructor in my quantum computation course sometimes uses the equivalence
$$(\left|a\right>)^\dagger\equiv\left<a\right|$$
I understand that this is true for the typical matrix ...
2
votes
1answer
97 views
Does bra-ket notation work for all inner product spaces?
My quantum computation instructor keeps referring to the vector space in which he is using Dirac's bra-ket notation as an "inner product space", but doesn't it need additional properties to use that ...
