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
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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
votes
2answers
399 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
440 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
104 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
265 views

Summation and brackets

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 ( ...
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0answers
548 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
50 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 ...
1
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1answer
74 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
76 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
votes
1answer
106 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, ...
1
vote
0answers
39 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
votes
2answers
242 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 $\mathfrak c$. ...
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2answers
136 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
86 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
73 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
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1answer
74 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 ...
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3answers
264 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
170 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
38 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 ...
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1answer
41 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
309 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 ...
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3answers
80 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
139 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
63 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: ...
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3answers
82 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
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2answers
78 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
91 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
votes
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
64 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
90 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
73 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
91 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
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2answers
756 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
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1answer
305 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
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2answers
105 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 ...
3
votes
0answers
75 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
94 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
118 views

Notation $f^{-1}$ for the inverse vs. notation $f^n$ for $n$-fold application

We often use to denote invertible function of $f$, as $f^{-1}$. In applied mathematics, This is the general rule. But very rigorous concepts of mathematics, like axiomatic number systems, it is just a ...
0
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1answer
185 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
79 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
101 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. ...
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1answer
47 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.
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2answers
2k 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
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1answer
64 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
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1answer
82 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 ...
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1answer
54 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 ...