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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3answers
139 views

Help with notation for tuples

How would I represent a set of tuples $(a_1,a_2,a_3,...)$, where each element $a_i$ is a positive integer in the interval $1\leq a_i \leq A_i$ The only thing I can think of is defining the set of ...
3
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1answer
67 views

Understanding fourier notation $F(\partial_x)$

Can somebody please help me understand some of the notion in the equations below, taken from a published paper on image de-blurring. I have an energy $E(H)$ defined over an image $H$, a point-spread ...
0
votes
1answer
33 views

How do differentiate between function arguments and multiplication?

Say I have the following: $$ H\left(\frac x{x_o}\right) $$ How do I see that it is the $H$ function at $x/x_0$ and not the quantifty $H_n$ premultiplied by $x/x_0$? In Mathematica, I would have ...
2
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1answer
103 views

What does $\Omega^\bullet(M)$ mean?

What does $\Omega^\bullet(M)$ mean? I know that $\Omega^k(M)$ is the set of all differential k-forms. Thanks in advance!
3
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1answer
481 views

what does it mean for a matrix to be greater than another?

I am reading these notes on viscosity solutions, here is a theorem: Let us assume $u\in C^2$ is a classical solution of $F(x,u,Du,D^2u)=0$, $x\in \Omega$ then $u$ is a viscosity solution whenever ...
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3answers
884 views

Is there any standard notation for specifying dimension of a matrix after the matrix symbol?

I want to explicitly specify dimension of matrices in some expressions, something like $$\boldsymbol{A}_{m \times n} \boldsymbol{B}_{n \times m} = \boldsymbol{C}_{m \times m} \, .$$ Is there any ...
2
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1answer
85 views

Notation Clarification of Koch Curve

I am having trouble making sense of the notation used to describe the Koch Curve in the book Getting Aquanted with Fractals. The link will take you to a preview of the book which describes the ...
2
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2answers
357 views

What is the standard notation for a set of equivalence classes?

What is the standard notation for a set of equivalence relations? Specifically, I have a pair of objects, call them $x$ and $y$ and I denote the ordered pair as $\left(x,y\right)$. I have a set of ...
0
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1answer
28 views

Single variable true or false statements

If I have a true or false statement S, depending on a varible x, is there some standard function or opperation in formal logic, that takes the statement S and the variable x, and outputs $1$ if ...
3
votes
1answer
43 views

Notating each element of a vector which already has a subscript

If I had a vector $\mathbf{x}$, I would denote element $i$ as $x_i$. However, if my vector already has a subscript, for example $\mathbf{x}_j$ or $\mathbf{x}_{10}$, how should I show element $i$? I ...
3
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2answers
132 views

Meaning of $\log$

If you write $\log{x}$ rather than ${\log_a{x}}$ for some base $a$, does it have a particular meaning? Sometimes I see people leave off the base by mistake when posting questions and it seems from the ...
2
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1answer
56 views

Help with Notation

Let $S_{1},S_{2},S_{3},....$ be a sequence of mathematical statements, each of which is dependent on the same variable, such that, at any given moment exactly one and only one of the statements can be ...
3
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2answers
491 views

Less than all positive numbers, greater than all negative numbers, and not zero; what is $\ast$?

A part two, you could say, of my previous question. I was watching a Numberphile video about the favorite number of some mathematicians, and at one point, the creator of ViHart said the following - ...
2
votes
1answer
478 views

$j^2 = 1$, but $j \neq \pm 1$; what is $j$?

I was watching a Numberphile video about the favorite number of some mathematicians, and at one point, the creator of MinutePhysics said the following - Similar to the way that $i$ is $\sqrt{-1}$, ...
3
votes
2answers
112 views

Question about the radical of the Jacobson radical.

I am confused about the notation $\operatorname{rad}^2 A$. It can be considered as $\operatorname{rad}(\operatorname{rad}(A))$ or as $(\operatorname{rad}(A))^2$. Are ...
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3answers
399 views

Should parentheses be used in sums of the form $\sum_{i=1}^k A_i+B_i+C_i$?

Is it possible to write $\sum_{i=1}^k y_i\log p_i +(n_i-y_i)\log(1-p_i)+\log \binom{n_i}{y_i}$ as one mathematician said it is correct but another said that one should write $\sum_{i=1}^k\left ( ...
2
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0answers
659 views

What do angle brackets ($\langle\rangle$ ) mean in mathematics/statistics (autocorrelations)?

Okay, so the logarithmic return on a stock is given by: $$r_τ (t) = \ln P(t+τ) - \ln P(t),$$ where τ is the interval of time. I have no problem calculating that. My question comes to the following ...
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1answer
55 views

Iwaniec Kowalski Notation

On page 532 of the book analytic number theory by Iwaniec and Kowalski, the following notation is used: $C^{~\infty}$ and $\tau(n,\chi)$. Could anyone tell me what these represent? (the former is ...
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1answer
89 views

What's this matrix called?

In an inner product space, $v_1,\dotsc,v_n$ are linear independent iff the matrix $A_{ij} := \langle x_i | x_j \rangle$ is invertible. What's the name of this matrix??
2
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4answers
79 views

Meaning on the sign << [duplicate]

What does the sign '<<' mean, for example angle X << 1? This was in a brilliant.org problem. I won't post the full problem since that would make me a cheat but the first line of the ...
2
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1answer
114 views

What's wrong with this proof of unique factorization?

I've never seen this proof of the unique factorization theorem (aka the fundamental theorem of arithmetic). This doesn't mean much, since my reading in number theory is scant. I like the proof, ...
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0answers
44 views

What are $\sigma$ and $\tau$ in $n = 2^{\sigma(n)}\,\tau(n)$ called?

Every non-zero integer $n$ can be factored uniquely as $2^s t$, where $s$ is a non-negative integer, and $t$ is an odd integer. In other words, there exist functions $\sigma:\mathbb{Z}\backslash ...
2
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2answers
35 views

Nesting of different Asymptotic operators

Is it possible to nest big-oh notation with omega-notation? I came across this here, while doing calculations on an exercise: $$ f(x) \in O(\Omega(\log x)) $$ I'm really unsure on how to properly ...
3
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2answers
256 views

In set theory, what does the symbol $\mathfrak b$ mean?

In set theory, what does the symbol $\mathfrak b$ mean? Could somebody tell me something basic about $\mathfrak b$? In particulat, I want to know the relation between $\mathfrak b$ and $\mathfrak c$. ...
2
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2answers
153 views

What does $a^b$ mean?

Notation $a^b$ seems to be ubiquitous in mathematics and I think that most of us take it for granted. But, at least to me, it seems that it means totally different things depending on the context. ...
3
votes
1answer
111 views

Notation: What is the scope of a sum?

I would interpret $\sum_{i=1}^2 x_i + y$ as $x_1 + x_2 + y$, but I would interpret $\sum_{i=1}^2 x_i + y_i$ as $x_1 + y_1 + x_2 + y_2$. I realize this is a little inconsistent. Should the latter be ...
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1answer
84 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: ...
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1answer
96 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
273 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: ...
4
votes
2answers
184 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
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1answer
39 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 $\lambda_g(x)?$ ...
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2answers
54 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
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1answer
42 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
347 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
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3answers
133 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
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3answers
157 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
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1answer
70 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
83 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
82 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
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2answers
110 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
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3answers
75 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
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1answer
37 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
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3answers
44 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 $a+b$ ...
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2answers
67 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
98 views

What does the notation mean?

Given a measure space $(\Omega,\mathcal{F},\upsilon)$ and a $p>0$. What does the following mean? $$ \|f\|_p=(\upsilon|f|^p)^{1/p}$$
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0answers
96 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
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3answers
97 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 $X_i$ ...
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2answers
1k 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 ...
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1answer
416 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: ...
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2answers
121 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 ...