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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1answer
27 views

Multiplication Notation based on Summation

Just want to ask a question This question becomes a hot topic in my country right now since someone upload a photo about his young brother's homework that marked wrong by his teacher okay this is the ...
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0answers
18 views

Are these proposed rules for the canonical factorization of algebraic integers complete?

In $\mathbb{Z}$, the rules are fairly well established, a few minor quibbles notwithstanding. But in, say, $\mathbb{Z}[\sqrt{7}]$, there are, as far as I can tell, no established rules. What I've seen ...
0
votes
1answer
15 views

Show that $n^a$ is in $O(n^b)$ but $n^b$ is not in $O(n^a)$, where $0 < a < b$.

Let $a$ and $b$ be real numbers such that $0 < a < b$. Show that $n^a$ is in $O(n^b)$ but $n^b$ is not in $O(n^a)$.
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3answers
48 views

Does the set given by $\{(1/n)\}_{n=1}^\infty$ include $0$?

Is there some sort of consensus on whether or not $$0 \in \{(1/n)\}_{n=1}^\infty?$$
1
vote
1answer
9 views

Notation for image of a discrete random variable?

Suppose we have a discrete probability space $(\Omega,\Sigma,\mathbb{R})$ and a discrete random variable $X:\Omega \to \mathbb{R}$. A usual way to denote the set of values that $X$ takes is simply ...
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2answers
66 views

Is it ever correct to say that $\vec{a}-\vec{a}=0$?

My textbooks define $$\begin{cases}0\cdot \vec{a}=\vec{0}\\(m+n)\vec{a}=m\vec{a}+n\vec{a}\end{cases}$$ Therefore, $\vec{a}-\vec{a}=(1-1)\vec{a}=0\cdot\vec{a}=\vec{0}$. But is it ever acceptable, ...
1
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1answer
29 views

A strange notation

In one of my papers I found a notation where 2 letters one under other are placed in brackets without any additional operation symbol - attached image (N m). What does this mean, is this a shortcut ...
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0answers
16 views

Symbol for “covers” in posets

Has there been any suggestions for a symbol for "cover" relation on posets? (For example on the poset $(\mathbb{Z}, \mid)$ number 12 covers number 6, but does not cover number 3.) Texts I have seen ...
3
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2answers
47 views

How do I read this definition of injective in English?

This is a different but related question to one I asked earlier. I link to it here: "To show that f is injective" - I don't get this statement I am pretty new to "functions" having ...
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0answers
14 views

Old Notation for Conditional Expectation

I am trying to read a somewhat "old" paper by Daniel Rudolph: "x2 x3 invariant measures and entropy". I have some problems trying to understand Rudolph's notation for conditional expectations. More ...
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2answers
57 views

How do you represent $\Im$ and $\Re$ on paper?

Do you draw $\Im$ and $\Re$ just like they are or you write $\mathtt {Im}$ and $\mathtt{Re}$?
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0answers
43 views

Can someone tell me what is this maths font? [on hold]

Can someone tell what is this font? Thank you!
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1answer
38 views

Euler-Lagrange equation notation: $\delta$ instead of $\partial$

I have seen the equation written as: $$\frac{\delta L}{\delta q} - \frac{d}{dx} (\frac{\delta L}{\delta \frac{dq}{dx}}) = 0$$ Here, "variation of $L$ divided by variation of $q$ or $\frac{dq}{dx}$" ...
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2answers
56 views

What does the notation $\bigcup_{n\in\mathbb N} A_n$ mean in sets?

$$\bigcup\limits_{n\in\mathbb N} A_n$$ The book is asking me to prove that $f(\bigcup\limits_{n\in\mathbb N} A_n) = \bigcup\limits_{n\in\mathbb N} A_n$. I'm able to prove that f(the notation ...
-2
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0answers
17 views

What kind of sets are described by $\{x: x \in S_i$ for at least one $i\}$ and $\{x: x \in S_i$ for every $i\}$. [on hold]

What kind of sets are described by $\{x: x \in S_i$ for at least one $i\}$ and $\{x: x \in S_i$ for every $i\}$> Specifically, how does one express these sets in non -set-builder notation? Here, ...
2
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3answers
40 views

Notation in regards to limits

Do we define infinity as a "limit"? Or do we simply say that the limit doesn't exist as the function/series diverges? I'm calculating the limit of a function, turns out to be infinity, but I am not ...
11
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4answers
784 views

Symbol for unknown relation?

When solving equations like $$\begin{align} 4x-4 &=\frac{(2x)^2}{x} \\ -4 &= \frac{4x^2}{x} -4x \\ -4 &= 4x -4x \\[0.2em] -4 &= 0\end{align}$$ using the equality-symbol feels like ...
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1answer
61 views

What does $R[[X]]$ and $R(X)$ stands for?

I'm reviewing Linear Algebra these days and I saw these two notations in my notes without definition. Those are, $R[[X]]$ and $R(X)$ where $R$ is a commutative ring with unity. I remember that one ...
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0answers
17 views

Notation Question with regard to functions

Let $f : N → N$ Let $E(f)$ be the function defined by $E(f)(n) = 2^{f(n)}$. Does $E(f)(n)$ mean $E(f(n))$? or $E(f)(n)$?
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3answers
68 views

Use of $\mapsto$ and $\to$

I'm confused as to when one uses $\mapsto$ and when one uses $\to$. From what I understand, we use $\to$ when dealing with sets and $\mapsto$ when dealing with elements but I'm not entirely sure. ...
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2answers
44 views

Reverse Polish notation in (abstract) algebra

If I have something like $\phi\circ \psi(x)$ this means first apply $\psi$ and then $\phi$. Going right to left is pretty contrary to my intuition. In computer science some programming languages (and ...
0
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1answer
21 views

Notation: Building a set from sequences of random variables, some a.s. equal

For $1 \leq i \leq n$ let $(\psi_{ij})_{1 \leq j \leq n_i}$ be sequences of random variables. Is there a better notation than $$\{\psi_{ij} : 1 \leq i \leq n, 1 \leq j \leq n_i\}$$ to build a set ...
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2answers
26 views

Truth table and the meaning of $\oplus$ in propositional logic

Could someone show me the truth table for this proposition? I think I have the last two down, but I'm not sure what the symbol in the following one is: $$p\oplus (p\wedge q)$$
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0answers
8 views

What do $A \upharpoonright x$ and $\mu s \ge x$ denote?

I am reading Computability Theory by Cooper and I do not understand the notation in the definition on the page 230: Let $\{A^s\}_{s \ge 0}$ be a $\Delta_2$-approximating sequence for $A \in ...
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0answers
35 views

Does an unambiguous (or less ambiguous) system of mathematical notation exist?

Fourteen years ago Stephen Wolfram propounded some preliminary ways of reducing ambiguity in mathematical notation in this talk: ...
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3answers
34 views

What does in:variable1;in:variable2; mean?

A question in my ODE textbook is as follows. Determine whether the given first-order differential equation is linear in the indicated dependent variable. $u dv+(v+uv-e^u)du = 0;$ in v; in u; ...
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3answers
43 views

Alternative notations for the function $f(a+b)$ to avoid confusion with $fa+fb$

What are some good alternatives to avoid mix-up with $f(x)$ where f is a function and $f(x)$ where f is a constant? I was thinking of some additional symbols to the f-symbol, $f_{x}(x)$, or maybe ...
1
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1answer
40 views

How would you describe category $\mathsf{Rel}$?

I encountered two definitions for a category denoted by $\mathsf{Rel}$: Objects are pairs $\left(A,R\right)$ where $A$ is a set and $R$ a relation on $A$. Arrows in ...
8
votes
0answers
68 views

$\sin$ vs. $sin$ - history and usage

One thing newcomers to TeX or MathJax often get wrong is that they write something like $sin(x)$ instead of $\sin(x)$ - the point being that common mathematical functions with names consisting of ...
0
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0answers
11 views

Counts symbol in mathematical notation

Is there specific symbol rather than Sigma, that I can show counts of an element ? Here I would like to say "g" contains elements of type "e", and "T" for all "e" are equal and the number of "e" ...
0
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1answer
28 views

What is the meaning of E and d in this formula?

I am trying to learn the information bottleneck method. On slide 15, they give this equation. I think I understand that X is a random variable (but do not understand the meaning of the exponent, n). I ...
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0answers
18 views

How to show proper set inclusion/exclusion? Please don't give me the solution.

I found this problem from an online source. I've just got two question 1) I think there is a typo in the solution, it should be $(x_n) \in \ell_1$ right? 2) I am guessing $c_0 \subsetneq ...
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0answers
9 views

Notation for expansion of multivariable functions

Let $ f: \mathbb{R}^2 \rightarrow \mathbb{R} $ be some analytic function. I want to say something like, as $ x, y \rightarrow 0 $, the taylor expansion looks like: $$ f(x,y) = a x^2 + b y^2 + ...
0
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1answer
17 views

Notation regarding the continuity equation for conservation of mass

I have the following equation for the net mass flow out of a control volume through a surface $S$ - $$\int \int_S p \overrightarrow{V} \cdot \overrightarrow{d}S$$ (Actually there should be an ellipse ...
2
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1answer
16 views

Can I write $[x_{i,j}]$ for the matrix whose $\{i,j\}$-th element is $x_{i,j}$?

Is it a general way to write $[x_{i,j}]$ for the matrix whose $\{i,j\}$-th element is $x_{i,j}$? Thanks.
0
votes
1answer
29 views

What does this notation mean for Expectation and Variance?

Let $f: \{-1,1\}^n \rightarrow \mathbb{R}$ Then the influence function of $x_i$ is defined by $$ \text{Inf}_i(f) = \mathbb{E}_{(x_1,...,x_{i-1},x_{i+1},...,x_n)}[\text{Var}_{x_i}[f]]$$ What does ...
6
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3answers
1k views

Ambiguity of notation: $\sin(x)^2$

Several people have told me that $\sin(x)^2 = \sin(x^2)$. However, on several computing platforms, such as the TI-84 and Wolfram|Alpha, $\sin(x)^2 = \sin^2(x)$. Can I safely conclude that the notation ...
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votes
1answer
37 views

function notations

can you explain how you get this answer? and explain the answer? the distance in feet $d(t)$ a dropped object falls in $t$ seconds is given by the function $d(t)=16t^2$. suppose you drop a ball from ...
3
votes
2answers
91 views

What does$ \|x\|_{\infty}$ mean?

In one of my homework-assignments in analysis, I have stumpled upon $ \|x\|_{\infty}$. I know x is a vector, but what does the infinity-symbol imply? The whole problem is actually this: $\| ...
0
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3answers
78 views

How to formulate “The $n$ smallest”

I know how to formulate the set of all $x$ with minimal distance to $y$ with $d(x,y)$ being the distance function: $\{x \mid \arg\min d(x,y)\}$ But how do I formulate the set of the $n$ closest $x$ ...
1
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3answers
68 views

Set notation and mappings question

Good evening. I have a question. Suppose I have two sets, $A=\{1,2,3,4\}$ and $B=\{5,6\}$. I want to write the notation for a function that takes each element in $A$ and assigns to it a value in $B$. ...
0
votes
2answers
49 views

Is there a symbol, or abbreviation for coefficient of x

Doing some binomial expansions with algebra where I need to equate different coefficients together but don't know what to write: [Coefficient of $x^3$] = _ $k=+1.5$
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2answers
34 views

Notation for writing down products of sets of combinations

I am writing a paper in which I come across an expression analagous to; $$ \prod_{k=0}^{n} (x-r_k) $$ I wanted a nice way of writing down how the $r_n$ relate to the coefficients in the resulting ...
3
votes
2answers
81 views

Weird integral symbol : $\mathrel{\int\!\!\!\!\!-}$

What does this integral sign mean ($\int$ with line going through the middle)? $$ \mathrel{\int\!\!\!\!\!\!-} $$ (It had something to do with the Beckenbach-Radó Theorem)
0
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1answer
42 views

Notation for a functor between comma categories

Suppose we have two categories $D$ and $S$, as well as two functors $K,L:D\to S$ and a natural transformation $\varphi:K\to L$. Given another category $C$ and a functor $Y:C\to S^D$, is there a nice ...
0
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2answers
44 views

Einstein Summation - does the following equality hold: $a_{ij} x_i y_j = a_{ij} y_i x_j$

Does equality hold when $x_i = y_i$ and $x_j=y_j,$ and $ i, j = 1, ..., n $.
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2answers
31 views

Einstein Summation: How do I show $a_{ij} (x_i + y_j) \not= a_{ij}x_i + a_{ij}y_j $?

Einstein Summation: How do I show $a_{ij} (x_i + y_j) \not= a_{ij}x_i + a_{ij}y_j $?
3
votes
0answers
42 views

Notation $(a,b)$ for $]a,b[$.

Is there any logic or justification for the notation $(a,b)$ to represent $]a,b[$? To me this notation is very ambiguous and confusing because it looks like a couple of numbers and not an interval. ...
2
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2answers
95 views

Some notation regarding “::”

I'm reading through some geometry proofs, and I can see something like $AB^2:PM\times EB::BC^2\ :CD\times PQ$ So I understand that $A:B$ is equivalent to $\frac{A}{B}$, but what does the $::$ mean?
2
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2answers
29 views

Notation on partial deriviatives

If I need to find $$\frac{\partial ^{2}g}{\partial u \partial v}$$ Then do I want to perform $$ \frac{\partial} { \partial v}\ \big( \frac{\partial g}{\partial u} \big) $$ or $$ \frac{\partial g} ...