# Tagged Questions

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.

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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: ...
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 ...
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: ...
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 ...
1answer
44 views

### What Does this Subscript Mean?

I've found some weird notation on Wikipedia like this: $a_m$. What does it mean?
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 ...
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 $\lambda_g(x)?$ ...
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 ...
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? ...
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 ...
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 ...
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 ...
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: ...
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? ...
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 ...
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 ...
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 ...
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 ...
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 $a+b$ ...
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. ...
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? $$\|f\|_p=(\upsilon|f|^p)^{1/p}$$
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 ...
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 $X_i$ ...
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 ...
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: ...
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 ...
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, ...
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 ...
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 ...
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 ...
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. ...
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.
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.
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.
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 ...
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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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.
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 ...
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 ...
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