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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2answers
182 views

Power correct notation

Ok, I know this may sound dumb, but I am trying to understand which is the correct (most beauty) notation for the power function ${\rm pow}(f(x),n)$. This is the correct one: $[f(x)]^n$ From ...
7
votes
2answers
923 views

Notation for a relation

I'm reading up on "Set Theory and Logic" by Stoll and came upon notation for relations that I haven't seen before. I've seen $x\sim{y},$ and $xRy$ before but Stoll uses this one. $$(x,y)\in{\rho}$$ ...
3
votes
2answers
150 views

Why use the non-exclusive or sign in equations?

$x^2=4 \Leftrightarrow x = 2 \lor x=-2$, but $x$ can't be equal to both $2$ and $-2$, unlike what the inclusive-or symbol ($\lor$) implies. Although it may seem obvious, it's just wrong to say that ...
1
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3answers
90 views

How to make sense of $A+B$ where $A$ and $B$ are sets.

Suppose $A$ and $B$ are compact subsets of the complex plane $ \mathbb{C}$. How do I make sense of $A + B$ ? My first thougt: If one of the sets consist only of one point, say $A = \{ z: |z| \leq R ...
1
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1answer
76 views

Show that a partial differential eqution is satisfied (is my notation okay?)

Let: $f:\mathbb{R}\rightarrow\mathbb{R}$ be differentiable. $u:\mathbb{R}^2\rightarrow\mathbb{R}$ and $u(x,y)=e^{-y}f(x+y^2)$ Show that: ...
5
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1answer
145 views

Meaning of the following integal

What does $\int d^3 x $ mean? I found this in a lecture on quantum field theory, and it was not explained.
0
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2answers
91 views

About notation of function

Suppose I have a function $f:[a,b] \to \mathbb{R}$. I am writing this: $f$ is a nice function. Is this sentence the same as the sentence $t \mapsto f(t)$ is a nice function. In other ...
1
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1answer
133 views

Problems with tensor notation

I've got a question for the mathematically more educated for I am a humble engineer having a hard time: $\kappa = \left( \delta_{ij}-n_in_j\right)\displaystyle\frac{\partial u_i}{\partial xj} - ...
0
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2answers
126 views

What does $U \in \mathbb R^n \times \mathbb R$ mean?

Ok so I get the basics of this, I just can't put it all together. $U$ is contained in the cartesian product of $\mathbb R^n \times \mathbb R$. What is $\mathbb R^n \times \mathbb R$ though? I know ...
8
votes
3answers
348 views

Is $d^2y/dx$ a valid mathematical notation?

I have often seen "the second derivative of y with respect to x" written as $${d^2y\over dx^2},$$ but I don't understand the reason for this notation. I have always seen it written as $${d^2y\over ...
1
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1answer
188 views

Notation of complement of set

Given, $U=\{1,2,3,4,5,6\},A=\{1,2,3\}$. We have to find the complement of the set A. We start by, Since set $A=\{1,2,3\}$, so $A'=\{1,2,3\}'=\{4,5,6\}$ Is the second part where I write ...
1
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2answers
154 views

How to understand sum symbol?

I have searched google for an answer but I'm not sure what I'm asking. I know that Sigma means sum but there is an 'n' above Sigma and an 'i=1' under sigma. how can i understand this? thank you!
1
vote
1answer
150 views

What are common notations for the endomorphism group of a vector space?

Given a vector space $V$, the set of endomorphisms in $V$ can be denoted $$\text{End}(V)=\left\{L:V\rightarrow V:L\text{ is linear}\right\},$$ particularly when one wants to be completely unambiguous. ...
3
votes
3answers
191 views

Conventional set notation for integers between m,n CS Theory/Math literature

This is a pretty simple, straightforward question. I've seen in the literature $[n]=\{0,1,2,\dots,n-1\}$ and $[n]=\{1,2,3,\dots,n\}$. Is there a similar convention for ...
1
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0answers
93 views

decimal digit grouping delimiters

I feel a bit silly having to ask this but I just can't seem to find any resources that give an answer to this. When dealing with decimal values that have a large number of digits to the right of the ...
5
votes
4answers
566 views

Leibniz notation for high-order derivatives

What is the reason for the positioning of the superscript $n$ in an $n$-order derivative $\frac{d^ny}{dx^n}$? Is it just a convention or does it have some mathematical meaning?
4
votes
3answers
564 views

What's the meaning of $\dagger$

In some books I've seen this symbol $\dagger$, next to some theorem's name, and I don't know what it means. I've googled it with no results which makes me suspect it's not standard. Does anybody know ...
2
votes
2answers
113 views

How to indicate keeping the sign when squaring a number.

I have a vector $x$, which I wish to transform according the the following computer code xstar = sign(x) * x^2 with $x^*$ preserving the positiveness or ...
0
votes
2answers
73 views

Is this use of product notation legal?

So I'm trying to prove something, I came across a sub-question that lead me to another question I thought of. Is the following legal? $$\prod_{k=1}^{n} \left(1-\frac{1}{2k}\right)/ \prod_{k=1}^{n} ...
1
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1answer
443 views

Minimum notation of modified set elements analog to Sum notation

I'm currently trying to simplify a calculation that takes the minimum of all elements in a set. However the elements should not be taken as they are but be modifiable: $$ S = \{{A}, {B}, {C}\}\\ ...
1
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1answer
72 views

What is the notation for separable states or independent variables?

Is there any specific notation that two quantum states are separable or that two random variables are independent?
0
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2answers
53 views

Is there a convention for precedence of operators in an additive category?

The laws for an additive category are that there must be a zero object, binary products, that every Hom-set is an abelian group, and that the morphism addition distributes over composition. My ...
3
votes
0answers
64 views

Curve of centers of curvature

I really can't find the English name of the curve of the centers of curvature of a curve. Formulated more precisely: Suppose $\alpha$ is a regular curve in $\mathbb{E}^2$ and $||\alpha(t)'||=1$. How ...
3
votes
3answers
495 views

Different of mapsto and right arrow

Could someone please explain to me what is the difference in the two arrows$$\rightarrow$$ and $$\mapsto$$ For example in Probability wih Martingales (Willams) Thank you.
0
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1answer
209 views

How to write the expression with multi-index notation?

I need some help for writing the following expression with multi-index notation, $$\sum_{i_1, \ldots, i_p=1}^n \frac{\partial^{2p}}{\partial x_{i_1}^2\ldots \partial x_{i_p}^2}f(x, \xi),$$ where ...
2
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1answer
3k views

Bar symbol over a matrix

So I am reading a paper (not online) and I come across a definition: $$\mathbb E=R\bar R$$ Where R is a complex matrix. I am thinking that it means complex conjugate, but I honestly have never seen ...
3
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1answer
73 views

Turning preorders into partial orders

Given a preorder $\preceq$ we can define a partial order $\leq$ as: $x<y$ iff $x\preceq y$ and not $y\preceq x$ $x\leq y$ iff $x<y$ or $x=y$ Transitivity is inherited from $\preceq$, ...
2
votes
3answers
147 views

Notation for set of all possible bijections

I have two finite sets: $S$and $S'$. I know $\mathrm{card}(S) = \mathrm{card}(S')$ I have a function $colour()$ that produces some colour for each element of $S$and $S'$. I know that there is at ...
0
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1answer
52 views

Stochastic Infinitesimal Generator Definition Confusion

I have seen an operator $A$ called the Infinitesimal Generator. Given $b: \mathbb{R}^n \rightarrow \mathbb{R}^n$ and $\sigma: \mathbb{R}^n \rightarrow \mathbb{R}^{n m}$ and $f:\mathbb{R} ...
1
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1answer
121 views

Cartesian Product

Given sets $A_1,A_2,\ldots, A_n$ how do I describe its Cartesian product $$C = A_1 \times A_2 \times \ldots \times A_n$$ in a succinct fashion? An example would be $C = \times_{i=1}^n A_i$ or $C = ...
2
votes
2answers
169 views

Understanding notation difference between mutual information and information divergance

The mutual information is defined on random variables. That is, $I(X;Y)$ denotes the mutual information between random variables $X$ and $Y$. On the other hand, the the Kullback-Leibler divergence is ...
3
votes
3answers
656 views

About plus-minus sign

If, say, we know that $x=1$, is then the expression $x=\pm 1$ mathematically incorrect? I ask this because when we use $\pm$ sign in the discriminant formula we imply that any of the plus or minus ...
5
votes
4answers
250 views

What is a suitable name for numbers like $a + b\sqrt{c}$

The motivation for this is to find a succinct name for a data type in a Python module. Suppose I choose an integer $c$ and I want to talk about the set of numbers of the form $a + b\sqrt{c}$, where ...
2
votes
2answers
268 views

Is there an “and” symbol?

I was wondering if there was a symbol for "and"? For example, I want to say something like $\therefore a = b \, \text{and} \, c = d $ Then can I replace "and" with a symbol? Thanks!
3
votes
4answers
104 views

inf of a finite set

I often see the notation $$\inf \{x_1,..,.x_n\}$$ or $$\inf\{s,t\}$$ Is this considered appropriate notation or is it considered better to use $\min$ in these cases?
2
votes
2answers
36 views

What does the notation $\sup_{x\in X}\inf_{y\in Y}d(x,y)$ mean?

Say you have two disjoint closed sets $X$ and $Y$ in a metric space. I'm trying to interpret what $$\sup_{x\in X}\inf_{y\in Y}d(x,y)$$ means. Does it mean that you pick a fixed $x\in X$, and then ...
2
votes
1answer
1k views

How to denote matrix concatenation?

Trivial question: Is there any standard notation for the concatenation of two or more matrices? Example: $$A = \left(\begin{array}[c c] - a_1 & a_2\\ a_3 & a_4 \end{array}\right),$$ $$B = ...
0
votes
0answers
88 views

Is there a special name for planar graphs, when the outer face has the highest degree?

Is there a special name for planar graphs, when the outer face has the highest degree? $\hskip1.3in$ Like $a)$, where $f_{\text{outer}}=6$; not like $b)$, where $f_{\text{outer}}=4$...
7
votes
4answers
256 views

Is there an established notation, either modern or historical, for any unit of measure which is then further subdivided into 360 degrees or parts?

This question about notation is simple as dirt, but would be useful for me regardless, because of some work that I'm doing in music theory. Basically, while there's a notation for subdividing the ...
0
votes
1answer
44 views

Module Notation $Dx$

Let $K$ be a field, and let $D$ be a subring of $K$ with identity. Let $K^*$ be the multiplicative group of nonzero elements of $K$. The group $U$ of units of $D$ is a subgroup of $K^*$. We take ...
2
votes
1answer
545 views

What do these symbols mean?

I was reading this pdf booklet I found on the internet from MIT to teach myself probability, but they use these symbols to represent DeMorgan's laws: I know and understand the laws, but not the ...
1
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3answers
220 views

What is the answer to $(1/10000000)^{455}$ in scientific notation?

I'm trying to figure out the odds of a random generator generating the same list of numbers $455$ times in a row. The random numbers are in a range from $0-1.999999$ ($6$ decimal points) I figure ...
2
votes
6answers
101 views

Why $\vec{r}$ is commonly use for vector equation?

I'm wondering why $\vec{r}$ is commonly use in mathematics (vector calculus, line integrals) and physics for denote the vector equation. Edit/Added clarification: I'm wondering why the letter $r$ is ...
0
votes
1answer
52 views

Binary “star” operator

I'm in the process of implementing a decoder, and I found this formula in the official specification: In context, X and Y can be interpreted as either two integers, or two arrays of integers (byte ...
1
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1answer
22 views

Name of Mathsyntax 12 4 / result: 3

I'm searching the name of a math syntax printed similar to this: term: 3 4 + result: 7 term: 12 3 / result: 4 the operator is at the end of the term Thanks ...
49
votes
17answers
3k views

Notations that are mnemonic outside of English

Some conventional math notations seem arbitrary to English speakers but were mnemonic to non-English speakers who started them. To give a simple example, Z is the symbol for integers because of the ...
8
votes
1answer
133 views

What classification of countable ordinals above $\omega_1^{CK}$ exists?

What classification of countable ordinals above the Church–Kleene ordinal $\omega_1^{CK}$ exists? Are there such things as $\omega_2^{CK}$, $\omega_{\omega_\omega^{CK}}^{CK}$ or ...
3
votes
0answers
81 views

partial derivative notation question

I'm reading a book called Correlated Data Analysis, Analytics, and Applications and I simply don't understand some notation. The author says, in chapter 2, page 26: A unit deviance is called ...
5
votes
1answer
157 views

Notation of derivatives…

I asked my teacher the difference between this notations. (1) $$\frac{dy}{dx}$$ (2) $$\frac{\delta y}{\delta x}$$ (3) $$\frac{\Delta y}{\Delta x}$$ He told me that there is no difference. I really ...
1
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1answer
679 views

What does $P(\overline{N})$ mean?

Sorry, this must be laughably trivial, but I have to be sure. I am a grade 12 math tutor, and while running through some older exam questions I encountered this problem: $$\text{If } P\left(N\right) ...