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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7
votes
1answer
151 views

When do modifiers denote sub or super? Pseudo-, quasi-, ultra-, strong-, well-, pre-, c0- …

One only needs to search MMA.SE, math journals, wikipedia, or god-forbid, n-cat lab, for keywords listed in the title, which can be extended with: uniform-, regular-, complete-, local-, partial-, non- ...
2
votes
5answers
942 views

Mathematical notation for computer science

Can anyone point me in the direction of good introductory material on the use of mathematical notation in the field of computer science? I often come across notation in research papers that I don't ...
2
votes
2answers
1k views

Symbol for Euclidean norm (Euclidean distance)

Which symbol is more commonly used to denote the Euclidean norm: $ \left \| \textbf a \right \| $ or $ \left | \textbf b \right |$?
10
votes
2answers
259 views

Articles on ideas in the history of mathematics notation?

I'm teaching a course this term on the history of scripts (writing systems) and rather than talking interminably about Semitic and Chinese and their spawn, I'd like to give students a more varied ...
1
vote
1answer
247 views

Element of a sequence notation

I'm writing some equations dealing with sets and sequences. I have a sequence $S$ and want to show that $x$ is an element of $S$, however I am hesitant writing $x \in S$ because I don't want to ...
3
votes
2answers
320 views

Sum with $j \ne i$

I have seen notation like this, commonly in regard to matrix multiplication: $$ b_i = \sum_{j \ne i} A_{ij} x_j $$ So this is a matrix multiplication that excludes the diagonal ($j=i$). I'm kind of ...
1
vote
1answer
216 views

Combining primes

A friend felt the need to explore wikipedia and stumbled across "prime notation". I've been working with primes for awhile (cryptography programmer) and have never seen a notation for "combining ...
9
votes
4answers
218 views

Which parentheses are implied by $\prod$?

Which is correct? $$ \prod_a ab = \left[ \prod_a a\right]b $$ or $$ \prod_a ab = \prod_a \left[ ab \right] $$ I'd say the latter, but with $\sum$ we have $$\sum_a a + b = \left [ \sum_a a \right ] + ...
2
votes
3answers
244 views

Is there a reasoning behind the depiction of the numbers as they are $\{1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9\}$?

Is there a reasoning behind the depiction of the numbers as they are: $$\{1,2,3,4,5,6,7,8,9\}$$ Is there any other form of depiction for $6$ and $9$ other than $VI$ and $IX$?
2
votes
2answers
48 views

A list from each element of another?

Sorry to edit this so much at this late stage, but the question and answers are confused so much by my incorrect use of terminology and the such, I feel that I should clear this up. Where $a$ and ...
2
votes
2answers
86 views

Is there a sign for “x's negation equals y”?

For example, let M and N be two real numbers. M is smaller than N. Now I negate the inequality, such that now M is greater or equal to N. $M < N ≟ M \geq N$ Is there a sign to replace '≟' in the ...
10
votes
2answers
2k views

Which symbol should be used for an empty set?

Currently, a discussion started on the German Wikipedia article for Empty Set (the German discussion), whether $\emptyset$ or $\varnothing$ should be used or is more common as a symbol for an empty ...
4
votes
4answers
171 views

Why Does Finitely Generated Mean A Different Thing For Algebras?

I've always wondered why finitely generated modules are of form $$M=Ra_1+\dots+Ra_n$$ while finitely generated algebras have form $$R=k[a_1,\dots, a_n]$$ and finite algebras have form ...
1
vote
2answers
206 views

Manifold/Topology Notation

I have a basic notation related doubt as follows: Let $M\subset \mathbb{R}^N$ be a manifold. What does $C^\infty(M)$ denote in $f \in C^\infty(M)$?
0
votes
1answer
151 views

Notation question on empirical p-value computation

In calculating an empirical p-value for test statistic $T_{0}$ (in my case the KS test statistic, $D$) using a permutation test $\tilde{p}_{N}(x)=\frac{N\tilde{G}_N(x)+1}{N+1}$ $\quad$ (3.4) where ...
2
votes
2answers
845 views

What is the difference between $d$ and $\partial$?

After seeing the following equation in a lecture about tensor analysis, I became confused. $$ \frac{d\phi}{ds}=\frac{\partial \phi}{\partial x^m}\frac{dx^m}{ds} $$ What exactly is the difference ...
3
votes
1answer
113 views

Notation question, Stieltjes integral

I'm reading a signal processing textbook and they frequently write out formulas where if I have a Stieltjes integral: $$\int_a^b f(t) \, dX(t)$$ They'll write an explicit formula for $dX(t)$, such ...
1
vote
2answers
949 views

Set-builder notation: is there another symbol for “such that”?

My teacher is teaching us about sets, and he said that the '|', the ':' and the '\' symbols can be used to mean 'such that'. I'm certain of the first two, but I searched a little and couldn't find ...
3
votes
1answer
75 views

How to call simple expressions in a paper which do not need any proof?

I am using an expression in a paper which doesnt need a proof at all such as $$\sum_{i=k}^K\binom{K}{i}p^i(1-p)^{K-i}$$ is a decreasing function of $k$ and ...
0
votes
2answers
82 views

What is $|X|$ and $1n$?

I'm doing a course in calculus but I'm quite young so haven't learnt all the mathematical terms one should perhaps no before learning calculus, and these 2 terms keep coming up and I have no idea in ...
7
votes
2answers
357 views

Why does this text insist on changing the variable name here?

In What is mathematics? by Courant, Robbins, and Stewart, "5. An important inequality", the authors change $n$ in this example: $$(1+p)^n\geq1+np$$ to $r$ in this example: $$(1+p)^r\geq1+rp$$ In ...
3
votes
1answer
500 views

Convention of digit grouping after decimal point

I read that different cultures have different ways of grouping digits before the decimal point for readability e.g. 1234567890 can be grouped as 1 234 567 890 (English), 12 3456 7890 (Chinese) or 1 23 ...
1
vote
1answer
76 views

Notation and naming for two operations with $p$-form valued $n$-forms

While trying to answer my other question I found I never heard about vector-valued differential forms. I've been searching for them in various mathematical physics books, but didn't get too much. I'm ...
1
vote
1answer
111 views

Best Notation for Introducing Finite Numbers of Elements

What is the best way to quantify over a finite number of elements of a set? For instance, suppose that one wished to quantify over $n$ real numbers $a_1,\ldots,a_n$ in order to state a property of ...
0
votes
1answer
434 views

How would I express this code in math notation?

I'm writing a paper on an application I wrote, and I'm trying to describe mathematically what I did to determine the rotation of an object. What I did is really simple, but my math lags far behind my ...
6
votes
2answers
228 views

Why bother proving that a class is a set?

Fix a set theory, say ZFC. Now suppose you have a statement $P(x)$ written in the language of that theory, which has precisely one free variable $x$. We can conceive of the class of all $x$ in the ...
13
votes
6answers
935 views

Appropriate Notation: $\equiv$ versus $:=$

With respect to assignments/definitions, when is it appropriate to use $\equiv$ as in $$M \equiv \max\{b_1, b_2, \dots, b_n\}$$ which I encountered in my analysis textbook as opposed to the ...
0
votes
1answer
109 views

What does the $A(m)$ denote in Engelking's book?

Recently, I'm reading Engelking's book. In this book, it always uses as the example the space $A(m)$, see for instance the example 1.1.8, page 15. For this space, I'm not very clear, for the ...
13
votes
3answers
2k views

What does the notation $[0,1)$ mean?

I am studying the procedure for bucket sort from Introduction To Algorithms by Cormen et al, which assumes that the input is generated by a random process that distributes the elements uniformly and ...
2
votes
1answer
167 views

Notation for free graded resolutions of graded modules?

I am now reading a paper about Castelnuovo-Mumford regularity and in this paper, there is a notation as following: Let $S=k[x_1,...,x_{n}]$, by Hilbert's syzygy theorem, if $N$ is a graded module ...
0
votes
1answer
103 views

What does this notation represent

$${\bf w}_{k}\sim\mathcal{N}(0,{\bf Q})$$ Note that $\bf Q$ is $2\times2$ matrix. So what is ${\bf w}_k$? This is from Wikipedia- Kalman example application
0
votes
1answer
90 views

Operations on two conditions

Hi this is an extension of my previous question: Combining two equations for two conditions I was wanted to know if operations which were to be carried out on both conditions could be placed outside ...
2
votes
2answers
175 views

Writing inequalities in interval notation?

When writing the solution to an inequality in interval notation, say $x < 5$ as $(-\infty, 5)$, how can the $x$ be "involved"? Is it correct to just write $(-\infty, 5)$, or should it be ...
2
votes
1answer
443 views

Exponentiation and Set of Functions Notation.

Given arbitrary sets $A$ and $B$, the notation $A^{B}$ is mostly clear from context to mean $A^{B} = \{f : f : B \rightarrow A\}$. However, when these sets are ordinal or cardinals, especially ...
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 ...
2
votes
2answers
378 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
221 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
300 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
204 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
542 views

Question about math symbol $\bigsqcup$

Can someone tell me what this symbol means? $\bigsqcup$
5
votes
1answer
519 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
26k 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
86 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
948 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
296 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
171 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 ...