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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2
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3answers
48 views

meaning of powers on trig functions

I always forget this, when a trig function has an exponent does that mean multiply itself or apply itself to the result recursivly? e.g. does $\sin(x)^2=\sin(x)\sin(x)$ or $=\sin(\sin(x))$? What ...
1
vote
1answer
24 views

Notation of integral.

In some probability book I've come across this notation: $E(X)=\int_{-\infty}^{\infty}x d F(x)$, and it's very confusing, when I see other books defining the same concept as: ...
1
vote
1answer
59 views

How to write $\displaystyle\prod_{i<j} (j-i)$ as an explicit sum?

Let $I_n:=\{1, \ldots, n\}$ where $n\in\mathbb N$. I'm wondering whether is there a way to write $\displaystyle\prod_{i<j} (j-i)$ as a sum? The product above is taken over all pairs $(i, j)\in ...
1
vote
1answer
29 views

The rationale behind the oracle machine notation with brackets $\{e\}^A$

I would like to understand the rationale behind the oracle machine notation with brackets $\{e\}^A$ which is equivalent to $\phi_e^A$ where $A$ denotes the oracle set and $e$ denotes the index of the ...
1
vote
0answers
26 views

What’s the purpose of the styled digits in Unicode’s Mathematical Alphanumeric Symbols?

In Unicode there is a block called Mathematical Alphanumeric Symbols, which contains several variations (bold, italic, caligraphic, fraktur, blackboard bold, sans serif, monospace and certain ...
2
votes
1answer
46 views

Notation for difference of two dates

I am not looking for a formula to calculate the difference of two dates. I am looking for a notation to express the difference of two dates in a formula. Is there a common way to do that? If not what ...
2
votes
3answers
188 views

What is the word for set containing other sets?

For example, define $S = \{\{3\}, \{2,1\}, \{1,1,1\}\}$. What is the word for $S$? Multiset? Doesn't seem to be correct. Edit: Also, how can I denote the cardinality of a specific set within a ...
0
votes
1answer
22 views

How to denote the size of a list

Suppose I have a list (not set) with entires {x, x, x, y, z}, then the list is size of 5. What is the mathematical function that returns the number of elements? Does cardinality only work on sets?
2
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1answer
44 views

Kronecker Products and Powers notation

We are all familiar with the notation for powers, which represent repeated multiplication: $$x^n = \underbrace{x \times x \times \cdots \times x}_{n \text{ times}}$$ Is there something similar to ...
0
votes
1answer
48 views

What does this notation mean?

I am currently completing a Combinatorics homework and came across this question: "A $q$-ary $[n, k, d]$ code is a subset $C$ of $\mathbb{F}^n_q$ ..." What is the set $\mathbb{F}^n_q$?
0
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1answer
59 views

Number theory used in cryptography [duplicate]

I am entering the realm of cryptography and encountering Number Theory related stuff a lot (As expected). I have a good knowledge and background on mathematics but I have been away for a while. So if ...
0
votes
0answers
22 views

Matrix notation - sum of elements in one of the dimensions

I have what I think is a rather simple question related with matrix notations, but I've extensively searched and was not able to find an answer. If I have a two-dimensional matrix $A$, is there any ...
4
votes
1answer
44 views

Notation for Average of a Set?

In particular, I have some set $S = \{s_1, s_2, s_3, ..., s_n\}$ and a subset $S^\prime$, and I want to denote the average of the elements in $S^\prime$. I would generally just use ...
2
votes
2answers
68 views

Better scientific notation [closed]

It seems to me that scientific notation would be so much more useful if it were more succinct. Scientific notation: $7.24 × 10 ^{-4}$ Abbreviated form: $7.24{\scriptsize E}{-4}$ The abbreviated ...
0
votes
1answer
17 views

Unusual syntax for finite field

I found in an exercise the following syntax: Polynomial f(x) =..... is a polynomial in Fp with p = 2 mod 5 or p =3 mod 5. I have to show that it is irreducible. I don't know this Syntax p= 2 mode 5 ...
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vote
0answers
52 views

Why do I always seem unable to understand mathematical terminology?

As I ask more and more maths questions, the issue of terminology becomes ever greater for me. While I feel that my maths is progressing, and is in fact knowledge-wise beyond others people of my age, ...
2
votes
3answers
55 views

What does $R \rightarrow R$ means in functions?

I have a function. The function is: $$ f:R \rightarrow R $$ $$ f(x) = x^3$$ What does $R \rightarrow R$ means? I don't know what types of questions should I ask here. If it is not ok, the I will ...
0
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2answers
31 views

Matematical notation for showing even rows of matrix [closed]

I want to select an even rows of matrix. How can I show it using mathematical notations. Something like this: $X_{i:}$ where i is even.
1
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3answers
49 views

Mathematical notation: max of 5 values

I have 5 robots and for each new job, one of them finish last. What is the correct notation for getting the maximum of the times of the 5 robots for a job. is below acceptable? $MaxTime = ...
0
votes
1answer
32 views

notation: is not a factor of

I know that a factor can denoted by |, for e.g: if $x$ is divisible by $y$, then it can be notated by $x|y$. However, I do not know how to denote when $x$ is not a factor of $y$. What is the ...
3
votes
1answer
100 views

Why is modular inverse notation so ambiguous?

Consider $$\frac{a}{a}\pmod a,\ \ \ a\in\mathbb Z\setminus\{-1,0,1\}$$ There are two cases: $1)$ $\frac{a}{a}$ is the notation for the real number $1$. Then the expression is equivalent to $1$ ...
0
votes
0answers
21 views

What are best practices when writing (sub)equations?

I wonder when it's preferred or better to use subequations instead of normal equations. I.e. when to use 'normally' numbered equations (e.g. (1), (2), ...) and when to use subequations (e.g. (1a), ...
0
votes
0answers
58 views

What is this lazy sum notation supposed to mean?

I'm used to writing iterative summations like this: $$ \sum_{i=0}^3 f(i) $$ But I have a thermodynamics book that uses $$ \sum_s f(s) $$ And similar with no explanation. The Wikipedia article ...
1
vote
1answer
24 views

Exp lambda dot notation?

In a machine learning paper I'm reading, I came across the following notation: In our experiments we parameterize these potential functions as an exponential of a linear scoring function ...
1
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1answer
24 views

What's the name of a function of the form $y(x;p) = p f(x) + (1-p) g(x)$?

Is there a name for a function of the form $y(x;p) = p f(x) + (1-p) g(x)$, where $p$ is some scalar between 0 and 1, and $f$ and $g$ are functions?
0
votes
1answer
17 views

Notation question on $C(\mathbb R)$.

In a definition of Paley-Wiener space, I have read $$\{f\in L^2(\mathbb R)\cap C(\mathbb R),\ \operatorname{supp}\hat f\subset [-\pi,\pi] \}$$ I know $L^2(\mathbb R)$. What is $C(\mathbb R)$?
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1answer
35 views

Notation (Complex Analysis) function

Does this notation $${\Large \Im f(z)}$$ mean the imaginary part of a complex function?
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0answers
13 views

Notation: succinct way to denote piecewise continuous function

Is there a standard, agree upon (maybe even clever) way to indicate a function is piecewise continuous? i.e suppose $f \in \square $ where $\square$ is the set of piecewise continuous function
1
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2answers
48 views

Need help with a an unfamiliar mathematical operation

What does (9 over 3) mean? I can't type the exact operation; please see attached. Or can you direct me to a site where this operation is explained?
0
votes
3answers
111 views

What does $3\mathbb{Z}/12\mathbb{Z}$ mean?

What does $3\mathbb{Z}/12\mathbb{Z}$ mean? I must find all of its elements. Thank you
1
vote
1answer
43 views

Curiosity with the Cartesian Notation of the Vector Cross Product

In my opinion Hibbeler's book on statics (Engineering Mechanics Statics, 12th ed) is one of the most approachable on the subject. On pg.123 he defines the Vector Cross Product in its Cartesian ...
0
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1answer
13 views

mathematical notations - for selecting from a set under some constraints

I have a set $X = \{0, 1, ... , n\}$. I want to choose a number for each $Z_i (i = 1, ..., m)$, $m \leqslant n$, from the set $X$ such that $Z_i \neq Z_j (j = {1, ... ,m}, j \neq i)$ with the ...
1
vote
3answers
60 views

Do we sum over sets?

I'm writing my thesis on a topic in machine learning. In some parts I defined a summation over a set. I sent my thesis draft to my professor and then I met him. He briefly mentioned that "we don't sum ...
0
votes
2answers
42 views

How to interpret max(min(expression))??

I am reading this paper: ai.stanford.edu/~ang/papers/icml04-apprentice.pdf Step 2 of section 3 is to compute an expression of the form max(min(expr)). What does this mean? I made a simple example ...
0
votes
1answer
24 views

How is this norm $\|A\|_*$ called and what is it?

In my lecture notes I have found the notation $\|A\|_*$ for a matrix norm. Do you know the name of this norm (such that I can read the definition of it), or do you even know the definition of it? ...
0
votes
1answer
29 views

How do you write a division of a division when it can't be simplified?

I have an equation that cannot be simplified, but looks ugly written out. $N^y_j = \alpha_{y_j} + \Bigl\lfloor\frac{P^y_i}{\Bigl\lfloor{\frac{P^y_i}{N^y_j}\Bigr\rfloor}}\Bigr\rfloor$ I thought to ...
0
votes
1answer
31 views

What is the symbol you'd use for Boolean results?

What I mean is that $\mathbb{CRZ}$ etc. are used for different classes of numbers, allowing me to do stuff like this: $$f:\mathbb{R}\to\mathbb{R}$$ $$f:x\mapsto 3x$$ But say I have an expression ...
1
vote
1answer
34 views

Is there a notation to designate the quotient in integral domain?

Let $R$ be an integral domain and $p$ be a nonzero element of $R$. Let $p,r \in R$ such that $p$ is nonzero and $p|r$. Then, there exists a unique $q\in R$ such that $r=pq$. Is there a notation ...
2
votes
2answers
45 views

Denotation of existence of $n$ distinct $x$ such that $P(x)$?

I have that $\exists!x:P(x)$ means that there exists exactly one $x$ where $P(x)$ holds; this is a more specific version of existential quantification with $\exists$. My problem stands like this. I ...
3
votes
1answer
87 views

Tensor product notation for $(x,y)\mapsto f(x)g(y)$

I often stumbled across (variations of) the notation $f\otimes g$ for $(x,y)\mapsto f(x)g(x)$. If $f\in V^*$, $g\in W^*$ for vector spaces $V,W$ over ${\bf K}$ then $f\otimes g:x\otimes y\mapsto ...
1
vote
4answers
81 views

Can # be used to mean a repeating digit?

Is this an accepted way to represent larger repeated numbers: 4#40 + 3#25 = ? Is there a function for these maths?
0
votes
0answers
21 views

Standard notation for different variables?

I was wondering if there is a rule for choosing which letters to give to variables when naming or substituting them? In Gauss' Disquisitiones Arithmeticae, he uses many gothic lettering, but I haven't ...
1
vote
1answer
38 views

What does it mean when range is expressed between two “[”?

In this YouTube video the presenter writes $[0, 2^{128} [$ is this different than $[0, 2^{128} ]$ This happens around time 2:20 She also writes something that appears to be $[0, 16 [$ but there is ...
0
votes
1answer
27 views

What does $E^{2}$ mean in this context?

Let $P_{i} \in E^{2}$ be the vector location of demand point $i, i = 1,..., n$ What is $E^{2}$? Found it in a journal paper but not sure if I can link it.
2
votes
0answers
34 views

Under what context is notation $\frac{\delta f(x)}{\delta x}$ acceptable as a derivative?

$\frac{\delta f(x)}{\delta x}$ seems to be a totally abused notation whenever an author (usually in control theory or thermodynamics or some engineering discipline) decides to quantify "slight ...
0
votes
3answers
27 views

Notation for product expansion

Please excuse me in advance if this is the wrong type of question or too simple. I need to expand the following product for a proof: $ \left( \sum_{l=1}^{i} x_{l} \right) \left( \sum_{m=1}^{j} x_{m} ...
5
votes
3answers
138 views

Notation for sum of products.

I have a set of sucessive elements $\{a_1, a_2, a_3, a_4\}$ from an arithmetic progression and I need to sum all the possible product-combinations of two elements, i.e. $$ a_1\cdot a_2+a_1\cdot ...
1
vote
0answers
56 views

Does anyone know what this notation means?

Define $Z = N \times N$. For We wish to define a binary structure $+:Z \times Z \to Z$ by: For $x, y \in Z$ choose $(a, b) \in x$ and $(\alpha, \beta) \in y$ then define $x + y = \overline{(a + \alpha, b ...
1
vote
2answers
60 views

Meaning of $(\nabla_x + \nabla_\xi)^n$

what does $(\nabla_x + \nabla_\xi)^n$ mean? (In the context, $x,\xi\in \mathbb{R}^d$). In my notes, the author states this should be a tensor, but what exactly does he mean. Is this clear notation? ...
1
vote
1answer
44 views

Initial segments of trees

I am fairly sure this question will look quite trivial, but I have some trouble getting the reason behind the use of the symbole $\subset$ when we deal with sequences and initial segments of ...