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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4
votes
2answers
244 views

Is there notation for “some two of the three statements are true”?

There are three propositions A, B, C and another condition "some two of these propositions are true and the third one is false", or, in other words, "exactly 2 of 3 propositions are true". Using truth ...
4
votes
4answers
2k views

What do the $+,-$ mean in limit notation, like$\lim\limits_{t \to 0^+}$ and $\lim\limits_{t \to 0^-}$?

I'm working on Laplace Transforms and have got to a section where they are talking about zero to the power plus or minus and that they are different. I can't remember what this means though. It's ...
3
votes
2answers
394 views

Best way to denote some trigonometric functions

What is the best way to denote tangent and other trigonometric functions: tg or tan, ctg or cot. What notation is commonly used and standardized?
2
votes
1answer
225 views

Set notation: subtracting elements with given cardinality from the powerset

I have a set $S = \{1,2,\ldots,n\}$ of $n$ elements and I denote with $P(S)$ the powerset of $S$. Which is a correct and accepted notation to say that the set $Z$ is composed by all the elements in ...
0
votes
1answer
89 views
1
vote
1answer
93 views

Am I talking right?

I'm trying to describe expected value. My paragraph goes: From probability theory we have $E[f(x)] = \int{f(x)p(x)dx}$. That is, the expected value of $f(x)$ is equal to the sum of infinitesimals ...
1
vote
2answers
305 views

What does the following notation mean: $\Bbb Q[x,y]$?

I came across this notation while at this MathOverflow thread and I could not find its meaning. It makes the biggest sense that $f(x,y) \in \Bbb Q[x,y] $ represents any continuous function on the ...
0
votes
5answers
205 views

What is the difference between set membership symbol $\in$ and $R$?

I know that $(a,b)\in R$ means an ordered pair of elements $a$ and $b$ belonging to the set $R$ but sometimes I see some expression like $a R b$ ? What does this notation/expression mean ? How to ...
1
vote
2answers
549 views

Question about math symbol $\bigsqcup$

Can someone tell me what this symbol means? $\bigsqcup$
5
votes
1answer
526 views

What is the $\tau$ symbol in the Bourbaki text?

I'm reading the first book by Bourbaki (set theory) and he introduces this logical symbol $\tau$ to later define the quantifiers with it. It is such that if $A$ is an assembly possibly contianing $x$ ...
8
votes
3answers
28k views

What does the letter epsilon signify in mathematics?

This letter "$\varepsilon$" is called epsilon right ? What does it signify in mathematics ?
1
vote
1answer
87 views

How can the set of the deducible WFF $\{\phi\mid\Sigma\vdash_K\phi\}$ be denoted?

I am relatively new to the formalism of Mathematical Logic, and don't know how denote the set of the wff logically deducible by a given set of premises $\Sigma$ in a predicate calculus $K.$ I have ...
2
votes
0answers
984 views

Submatrix Notation

I'm looking through some computer science papers and I see some notation that I'm just not familiar with. Consider an 5 x 6 matrix $$G = \begin{pmatrix} a_{0,0} & a_{0,1} & ...
2
votes
3answers
306 views

How to say the notation $ x_{i,j}^{ k}$

$ x_{i,j}^{ k}$ May I say the following to say the above notation? x sub i j to k ? x sub i j sup(prounced like "soup") k ? (Can I say "soup" for "superscript"? Could you please show me a ...
1
vote
1answer
172 views

Formal notation for function equality

Is there a short-hand notation for $$ f(x) = 1 \quad \forall x $$ ? I've seen $f\equiv 1$ being used before, but found some some might (mis)interpret that as $f:=1$ (in the sense of definition), ...
4
votes
1answer
117 views

Formal notation for a required statement

Is there a formal notation to distinguish an equality that is a true statement, e.g., [...] and hence, $$ x = x^2 - 1 $$ [...] from a demand, e.g., [...] so we require $$ x ...
1
vote
1answer
317 views

Explanation of this Cluster Entropy equation

I need to calcuate the cluster entropy to represent the distinctness of a phrase in a set of documents. I understand the meaning behind it but I don't understand the notation equation itself, as in ...
0
votes
2answers
246 views

Generator notation

I'm working through a proof (Bronstein, Symbolic Integration I, p.139) which uses generator notation. I am familiar with the following: $\langle t \rangle = \{ t^k : k \in \mathbb{Z} \} $, where ...
1
vote
1answer
226 views

How to write this in sigma notation?

Newton's formula for interpolation is $$P(x)=c_1+c_2(x-x_1)+c_3(x-x_1)(x-x_2)+c_4(x-x_1)(x-x_2)(x-x_3)+\cdots$$ I prefer sigma notation, when it is possible. Can this be written in sigma notation?
1
vote
2answers
359 views

What's the equivalent of the adjacency relation for a directed graph?

I've found several sources describing a relation notated $\sim$ signifying adjacency in an undirected graph, but nothing explicitly describing an equivalent for a directed graph. I've been using ...
4
votes
2answers
295 views

What is the Psi(x) variable binding operator?

In the Free Variable article on Wikipedia, it lists these: as variable-binding operators. I have seen all of them during my math studies, except for the psi operator. What does $\psi x$ mean in ...
0
votes
2answers
148 views

A notation question: $|\langle x,y\rangle|$

Someone please explain what is the meaning of the words in shade From Proof from the Book, 4th edition page 96: Let $q$ be a prime power, set $n=4q-2$, and let $$Q = \{x \in \{+1,-1\}^n: x_1 ...
0
votes
2answers
143 views

Notation for countable products of sets

Let $X$ be some set and $\Omega = \prod\limits_{i=0}^\infty X$, so that any element in $\Omega$ can be written as $$ \omega= (\omega_0,\omega_1,\dots) $$ where $\omega_i\in X$, $i \geq 0$. Given ...
2
votes
1answer
249 views

What does this notation, $x>x_0(\epsilon)$, mean?

What does this notation, $x>x_0(\epsilon)$, mean? I have seen this in several proofs and haven't quite figured it out.
1
vote
0answers
80 views

Is there any standard nomenclature for the sets of rational, algebraic, and elementary functions?

The rational functions of $X$ can be denoted $\mathbb{C}(X)$, i.e., quotients of polynomials. Is there a standard notation for the algebraic and elementary functions? By the set of elementary ...
3
votes
1answer
3k views

Notation for element-wise division of vectors

I am wondering if there is any standard notation for the element-wise division of vectors. I am going to use $\oslash$ for this purpose, similar to $\odot$ that is used in some texts for element-wise ...
0
votes
1answer
545 views

What does $K \Subset U$ mean?

What does $K \Subset U$ mean? I think that $K$ is a compact set with, $K \subset \subset U$ (precompact), where $U$ is an open set. Am I right? Thank you.
1
vote
1answer
97 views

2 quick notation questions re: vectors and transformations

Is it customary to omit one pair of parentheses and write $T \begin{pmatrix} 1\\2\\1\\1 \end{pmatrix} $ instead of $T \begin{pmatrix} \begin{pmatrix} 1\\2\\1\\1 \end{pmatrix} \end{pmatrix}$ to ...
1
vote
1answer
63 views

The product of a finite commutative subset of a non-commutative monoid

If $S$ is a finite subset of a commutative monoid, one can use the notation $\prod_{x \in S} {x}$ for denoting the product of all elements of $S$. It is rather obvious, that the same notation can ...
2
votes
2answers
149 views

derivative at a given point

I often see the following: $$ \left. \frac{\partial q}{\partial \alpha} \right|_{\alpha = 0} $$ Where $q$ is a function $q(q', t, \alpha)$. Is that just the same as that? $$ ...
2
votes
2answers
98 views

Indexing notation after $i$, $j$ and $k$ have been used?

If I have already used $i,j,k$ as indices, and need two more, where should I look? $l,m$?, $m$? I know from my previous questions that I can use anything I want as long as I define it, but I use $n$ ...
0
votes
2answers
67 views

Notation for a function from all members of a tuple minus one.

Is there any compact, mainstream notation for a function from all members of a tuple minus one? What I have in mind is $f\left(a_{1},\ldots,a_{n}\right)$ (except for $a_{i}$) $=a_{i}$
2
votes
1answer
69 views

What means the boundary of a space

By definition topological spaces are clopen and then their boundaries are empty, but for example, is said that the boundary of the closed unit interval is it's two endpoints a so on. whath is the ...
1
vote
1answer
105 views

Please explain this notation equation

I am confused by this equation as I rarely use math in my job but need this for a program that I am working on. What exactly does the full expression mean? Note that $m^*_i{_j}$ refers to a matrix ...
0
votes
3answers
110 views

Dumb percentage question?

Why do we multiply by 100 while calculating percentage ? example : 2/100 * 100 =2%
0
votes
1answer
72 views

Confusion with the meaning of a notation

An elliptic operator $L$ is called uniformly elliptic if $a^{ij}(x)\xi _i\xi_j \ge \theta|\xi|^2$. What does this notation mean? All I can find about it is that it is some kind of summation notation ...
2
votes
2answers
290 views

What does the notation “$\Omega \subset \mathbb{R}^n$ is $C^1$” mean?

In my calculus 2 lecture notes, we have the following definition: A region $\Omega \subset \mathbb{R}^n$ is $C^1$ (or $C_{pw}^1$ or $C^k$ respectively), if for each point $x_0 \in \partial \Omega$ ...
1
vote
2answers
74 views

What is the preferred symbol to indicate the least positive number to start a sequence?

I need a least positive number and I am considering $\delta$, $\epsilon$ and $\theta$. Which one would be best to start a sequence? Are there any others I should also consider? Edit: ...
0
votes
1answer
74 views

formal expression of $\tilde{z}$ is the nearest from z

$h = distance(z, \tilde{z})$, where $\tilde{z}$ is the element that is nearest from $z$ (that is, distance(z, $\tilde{z}$) is smaller than distance(z, any_other_z)). Is it possible to expression this ...
2
votes
2answers
129 views

Are there “variables/unknowns” for operations?

We use letters for unknowns/variables: $x^2=4$ Are there variables/unknowns for operations too? $8 \star 7 $ With the $\star $ being any operation.
1
vote
2answers
129 views

How do I have to interpret $\mathrm{nm}^2$?

My short question: How many $\mathrm{m}^2$ are $\mathrm{nm}^2$? Do I have to interpret it as $\mathrm{nm}^2=(\mathrm{nm})^2=(10^{-9}\mathrm{m})^2=10^{-18}\mathrm{m}^2$ or shall it be ...
1
vote
1answer
67 views

How is $I_{[0,\infty)}(t)$ defined?

How is $I_{[0,\infty)}(t)$ defined? This must be a notation in probabilty theory.
2
votes
1answer
62 views

Can ≈ be used to express an arbitrarily rounded rational number?

Is it a formally acceptable use of ≈ to express a rational number rounded to an arbitrary number of significant digits? For example, $\frac{4}{7}\approx0.57.$ If formally acceptable, is it expected? ...
2
votes
1answer
172 views

Question on meaning of a symbol: long thin C

I don't know how to write it in $\LaTeX.$ It is a tall skinny bold C. This is the context: A set is defined by: where $\complement\atop{\smash \scriptstyle i}$ is the thing I don't understand. The ...
0
votes
1answer
82 views

Do function with the following property have special name?

I'm writing "a structure preserving surjection" way too much when I need to refer a function of the following property: $$ Y \subseteq Z, X \subseteq Z. g: Z \to A, g \text{ is some fixed ...
44
votes
10answers
2k views

Have there been efforts to introduce non Greek or Latin alphabets into mathematics?

As a physics student, often I find when doing blackboard problems, the lecturer will struggle to find a good variable name for a variable e.g. "Oh, I cannot use B for this matrix, that's the magnetic ...
1
vote
1answer
81 views

What is the usual meaning of the notation $ \| f \|_{C^k (A)}$?

If $f \in C^k ( \mathbb R)$ and $A \subset \mathbb R$, what is the usual meaning of the notation below? $$ \| f \|_{C^k (A)} $$
0
votes
2answers
80 views

order of operations division

Very dumb question: What is the order of operations in the following: PEMDAS a/b+c = a : b + c (where ":" is the division symbol) 7/1+6 or 7:1+6 in the example below is it 1 or 13?
2
votes
2answers
574 views

Direct sum of Hilbert Space subspaces - Notation?

This is a really basic question sorry, I just need to make sure I have my understanding correct. Given an infinite dimensional Hilbert space $\mathcal{H}$ and two subspaces, also Hilbert spaces, ...
1
vote
2answers
41 views

Does $\beta_{0,i}$ mean the same as $\beta{_0}_i$?

I have two vectors of variables, $X$, and $\beta_0$ that I am writing about. Each are indexed by $i=1,\ldots,n$ If I want to talk about $X_i$ and $\beta_{0_i}$, using ...