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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5
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6answers
121 views

$(\mathbf{u}^T\mathbf{v})\mathbf{v} = \mathbf{u}^T(\mathbf{v}\mathbf{v})$ doesn't hold for $\mathbf{u}, \mathbf{v}\in\mathbb{R}^n$ - why?

Suppose I have vectors $\mathbf{u}$ and $\mathbf{v}$ in $\mathbb{R}^n$. It is well defined to write $5\mathbf{v}$ or $c\mathbf{v}$ for scalar $c$. Since the inner product of $\mathbf{u}$ and ...
1
vote
2answers
7k views

What does “-2E-07x” means? [duplicate]

I'm a programmer who had always been lacking some mathematical skills, yes it's a shame, I know. I'm making this little software for a biologist friend, and at some point I need to pull out a graph ...
0
votes
0answers
39 views

Can anybody recommend a comprehensive source for understanding mathematical notations?

I foten struggle with understanding some of the mathematics written down in papers. This stuggle is often due to notation used. Therefore, I was wondering whether somebody is aware of a resource that ...
2
votes
1answer
905 views

Resources for learning formal math notation

Does anyone know of some resources that provide a good introduction to common notation used in formal math? For example, I honestly don't know how to interpret $f: \mathbb{Z} \rightarrow \mathbb{Z}$. ...
2
votes
6answers
331 views

Function Notation

due to our national cirriculum (the way in which it was taught in high school). We just said that f(x) means a function. Though I understand this isn't necessarily correct? In high school we used ...
6
votes
2answers
324 views

What does the notation $\twoheadrightarrow$ mean?

I don't know what this double-arrow $\twoheadrightarrow$ means!
5
votes
1answer
63 views

What's the difference of naming a polynomial ring as $\mathbb{C}\{ x,y\}$ and $\mathbb{C} [x,y]$?

I sometimes see both notations and I am led (maybe misled) to believe that they are the same thing. What is the formal difference between both of them? Or there isn't any?
5
votes
2answers
3k views

Matrix rows notation

I'm working with a set of $M$ vectors $ \{\mathbf{w}_i \in \mathbb{R}^N, \, i = 1, \ldots, M \}$. Since single vectors are usually considered as column vectors, I'm defining a matrix $$ \mathbf{W} = ...
1
vote
1answer
517 views

Is this the correct notation?

$\left [ \left \{ 1,2,3,4 \right \}! \right]^{-1}$Is this the correct notation if one wanted to obtain the factorial for each number in a sequence and then take the sequence and inverse each number in ...
31
votes
11answers
8k views

What could be better than base 10?

Most people use base 10; it's obviously the common notation in the modern world. However, if we could change what became the common notation, would there be a better choice? I'm aware that it very ...
1
vote
0answers
44 views

Frequency of Math Symbols [duplicate]

Does anyone know of a study that has calculated the frequency of math symbols based on some popular mathematics journals or math corpus? For example in English you have letter frequencies of the most ...
5
votes
2answers
564 views

Frequency of Math Symbols

Does anyone know of a study that has calculated the frequency of math symbols based on some popular mathematics journals or math corpus? For example in English you have letter frequencies of the most ...
2
votes
1answer
124 views

Understanding some differential notations…

What this notation mean? (I know that is a partial derivative, but I don't understand the meaning of the evaluation bar at the right) $$\frac{\partial g}{\partial T}\Big|_{SA,p}$$ Is this relation ...
6
votes
1answer
4k views

what does z subscript something mean

Decide a positive integer $N \in\mathbb Z$. Generate a uniformly distributed random positive integer sequence: $$v_1, v_2, \ldots,v_n\in\mathbb Z_N$$ My question is, what does $\mathbb Z_N$ really ...
2
votes
1answer
116 views

Any name for an isosceles triangle sides

Is there an English translation for Finnish words kanta and kylki? Namely, if $ABC$ is an isosceles triangle with $AB=AC$ then $BC$ is kanta in Finnish and $AB$, $BC$ are both kylki.
0
votes
1answer
63 views

What is being maximised in the channel capacity formula?

The channel capacity formula is given as such: $$C=\max_{p(x)}I(X,Y)$$ Does this mean that it is the maximum probability multiplied by the mutual information, or is something else being maximised ...
1
vote
3answers
81 views

Difference between $\land$ and braces

I was wondering what are the difference between the $\land$ and $\begin{cases} \\ \\ \end{cases}$ symbol. As I know, they both mean "and". So far, I've noticed the $\land $ on statements (not sure ...
3
votes
3answers
820 views

Probability notation

Hey guys, I was just wondering why in my textbook(A First Course in Probability, 8th edition) and basically everywhere I've looked at when we have some random variable(assume for the sake of the ...
1
vote
1answer
31 views

How to name a matrix with restricted input values?

How should I refer to a matrix with a restricted domain of possible values that can be stored inside?
0
votes
2answers
585 views

Elementary Set Theory - Relations

I'm not exactly sure what to search for this problem I'm having, as I don't know the keywords, so I figured the best action would be to ask a question. I have this question: ...
1
vote
2answers
121 views

What does $\mathbb{\bar C}$ denote in complex analysis?

What does $\bar A$ denote when $ A \subseteq \mathbb{C}$? I've seen it used in some places as the algebraic closure, other places as $\bar A = A$ \ $ \partial A $ and other places again as $\bar A = ...
0
votes
2answers
35 views

Notation for number of value changes in a sequence

Let $A=\{a_{1}, a_{2}, a_{3}, a_{4}, ...,a_{n}\}$ be a finite sequence , where $a \in \mathbb{N}$. I would like to know the notation for something similar to a change rate. If I programmed, what I ...
4
votes
2answers
167 views

Summation and Product Bounds

If I have a sum or product whose upper index is less than its start index, how is this interpreted? For example: $$\sum_{k=2}^0a_k,\qquad \prod_{k=3}^1b_k$$ I want to say that they are equal to the ...
0
votes
1answer
154 views

Should brackets be placed around an exponentiated factorial?

For example, one can derive an approximation of $\pi$ from Stirling's approximation with one additional term as $$ \lim_{n \to \infty} \frac{72n(n!)^2}{n^{2n} e^{-2n} (12n+1)^2} $$ but is it correct ...
2
votes
1answer
55 views

Interpretation: existence of $2$ elements in a set. Simple question.

I'm ask to decide if there exists $2$ elements $a$,$b$ in a set such that $a+b =8$. It seems to me that many understand that $a$ and $b$ need to be two different elements. How should I understand ...
1
vote
1answer
28 views

Asymptotic Approximation and Sign Convention

When I write the asymptotic approximation of a function, does the sign convention matter? i.e. suppose I have (though the formula might not make sense) $$f_n(x)=x^2+\dots-O(n),$$ If my function is ...
0
votes
3answers
52 views

Reference a vector component

If I have the following cartesian vector: $$ \vec{v_1} = \pmatrix{1 \\ 2} $$ How would I reference the second vector component of: $$ \vec{v_1} $$ Is it okay to do it this way: $$ \vec{{v_1}_y} = 2 ...
2
votes
3answers
639 views

Notation: permutation and its inverse

Consider the sequence $S = (A, B, C, D, E)$ and the permutation $\pi = (4, 1, 3, 5, 2)$: Which of the following is true? $$ \pi(S) = (B, E, C, A, D) \quad and \quad \pi^{-1}(S) = (D, A, C, E, B) ...
0
votes
2answers
82 views

Inner product convention for $\ell^p$?

So I'm reading through some analysis problems and one is discussing $\ell^p$ (the space of $p$-summable sequences $x: \mathbb Z^+ \to \mathbb C$ such that $\sum_{n \in \mathbb Z^+}|x_n|^p < ...
1
vote
1answer
359 views

What does the notation $C(\mathbb{R})$ mean?

I thought that $C(\mathbb{R})$ was the set of all $$\mathbb{R}\to\mathbb{R}$$ functions that are continuous, but I may of seen a case that the function was $$\mathbb{R}\to\mathbb{C}$$ Was the use of ...
5
votes
1answer
2k views

What is the difference between a probability distribution on events and random variables?

For the purpose of simplicity, assume everything below is only in the discrete domain. A $\text{probability space}$ is usually defined as a triple $(\Omega , 2^\Omega , P)$ where $\Omega := ...
4
votes
1answer
83 views

Is the Knuth arrowup notation defined for non-natural exponents?

I recently found out about Knuth's arrowup notation. Wikipedia, among other websites, only shows a definition for $a \uparrow^n b$ where $n \in \Bbb{N}_0, a \in \Bbb{R}, b \in \Bbb{N}$ as following: ...
2
votes
2answers
382 views

Einstein Summation with multiple terms

I know the basics of Einstein Summation but i've got an equation here that is a little more complex than the easy examples i'm only finding on this subject: $C = (p-nT) \partial_\gamma u_\gamma + ...
3
votes
2answers
69 views

Help with unknown notation

In Ahlfors' Complex Analysis, page 19 it says (in relation with the Riemann sphere): "writing $z=x+iy$, we can verify that: $$x:y:-1=x_1:x_2:x_3-1, $$ and this means that the points ...
2
votes
0answers
329 views

French notational differences

I wish to read some French probability / measure theory papers. I do not wish to be caught out with different notations. For example if "compact" in French has a weaker meaning than in English ...
0
votes
1answer
115 views

congruence modulo and equality

why in cryptography most of the equalities written in the form of $$a:=b$$ why not we write $a=b$ why in congruence modulo $a \equiv c \pmod b$ that bracket is put. Is it refers the priority. can ...
1
vote
0answers
184 views

Is there a common notation for the labelled degree of a vertex?

Let $G$ be an undirected graph with labelled edges. The labelled degree of a vertex $v \in V(G)$ is the number of edges incident to $v$ with distinct labels. The definition of the labelled degree ...
2
votes
2answers
224 views

What is $\ln 0$?

What is $\ln 0$ ? Is it $-\infty$ or indeterminate?
1
vote
0answers
42 views

Notation for Restriction of Permutation

Suppose $\sigma$ and $\tau$ are permutations such that $\sigma(x)\not=x\implies \sigma(x)=\tau(x)$. Intuitively, I would like to think of $\sigma$ as a restriction (or projection) of $\tau$ onto a ...
1
vote
1answer
80 views

Notation in numerical methods

What are the differences in using $h$ and $\triangle t$ to represent a time step?
1
vote
1answer
80 views

Can we write $\sqrt[w]{z}=z^\frac{1}{w}$ when both $w$ and $z$ are complex numbers? [duplicate]

Let $w$ and $z$ be complex numbers defined in terms of real numbers $a$, $b$, $c$ and $d$ as follows: $$ w = a+bi \\ z = c+di $$ Can we analogically write $$ \sqrt[w]{z} = z^\frac{1}{w} \qquad ...
1
vote
1answer
66 views

Mixing asymptotic notations

I have a function $f(x) = g(x) - h(x)$ and I know that $g(x)=\Omega(\hat g(x))$ and $h(x)=O(\hat h(x))$. Is it well-defined to express this in asymptotic notation, as $f(x) = \Omega(\hat g(x))-O(\hat ...
1
vote
1answer
58 views

Limit of a seqence $\{f_n \}_{n\in \mathbb N}$ of functions?

I don't really know how mathematicians talk about this concept. I try to explain better what I mean with limit of a sequence of functions: Given a countable set of functions $\{f_n \}_{n\in \mathbb ...
2
votes
0answers
128 views

“Product” bundle notation.

Let $\newcommand{\Spin}{\operatorname{Spin}}M$ and $M'$ be two manifolds, equipped with a principal $\Spin_n$ and $\Spin_{n'}$ bundle called $P$ and $P'$, respectively. Then there is an induced ...
1
vote
0answers
56 views

Order of operations

Looking for a source that lists every possible proper order of operations. The reason for this is that I made a mistake with fractional exponents, I don't want to make this mistake again.
3
votes
1answer
130 views

What is Baire's zero-dimensional metric space?

I'm not familar with metrizable spaces. I met a notation: Baire's zero-dimensional metric space. Could somebody explain it for me? Thanks ahead:)
2
votes
0answers
77 views

What does the notation $\mathbf{Lt}$ signify in a limit?

The author of a book I'm reading defines the Dirac delta-function as $$ \delta(\omega_0-\omega) = \frac{2}{\pi}\mathbf{Lt}_{t\rightarrow \infty} \frac{\sin^2\left(\frac 1 2 ...
1
vote
3answers
429 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
votes
1answer
81 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
38 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 ...