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
16 views

Is there mathematical notation for representing a maximum output?

For example, something like the following: LowerOfTheTwo(a × b,1000) = c So, if a = 100 and ...
2
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1answer
56 views

Why is arcsin represented with the ^(-1) notation?

So in trigonometry, we have sin, secant (which is one over sin) and arcisn. Why is arcsin sometimes represented with sin^-1? sin^2 means sin to the second power, but sin^-1 explicitly does not mean ...
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3answers
43 views

The meaning of dot centered vertically, as in $3\cdot 5$

I just went to a site to practise some maths as I am studying some maths on my OU course in computing and IT and I ran into some symbols that I did not understand The questions were solve ...
1
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1answer
50 views

What is the meaning of the notation $]1, 1[$? [duplicate]

This may look like a silly question but I am struck in my work with this notation in one of the papers. What is meant by $]1,1[$ ?
4
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4answers
68 views

Question about $x\mapsto f(x)$ notation.

I'm trying to learn this notation, but I have some questions regarding its uses: Why is a "$:$" used instead of "$=$" when defining the function, e.g. $f: x\mapsto f(x)$ isntead of $f = x\mapsto ...
0
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0answers
9 views

List of hundreds of elements

In a formal writing I need to list the following elements in order: $a_1=[x_1,x_2,x_3],a_2=[x_1,x_3,x_2],a_3=[x_2,x_1,x_3],a_4=[x_2,x_3,x_1],a_5=[x_3,x_1,x_2],a_6=[x_3,x_2,x_1]$. ...
0
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0answers
14 views

Notation Explanation

Here, page $3$, there is this notation $\bar{P}^{\beta X}$. I know that $\beta X$ is the stone-Cech compactification of $X$, but authors do not define what is $\bar{P}^{\beta X}$. Is it the set of all ...
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0answers
29 views

Are ratio notations always equivalent?

Is there any case where the following ratio notations are not equivalent? For cases where the notations are equivalent, under what circumstances would the first notation be preferred? First ...
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1answer
44 views

How to notate higher anti-derivatives?

We can represent the $nth$ derivative of $y$ with the following notation: $$\frac{d^ny}{dx^n}$$ How can we represent the $nth$ anti-derivative of $y$?
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2answers
26 views

Big-O math Question

I'm having trouble with this question: Suppose that $f(x), g(x)$ and $h(x)$ are functions such that $f(x)$ is $O(g(x))$ and $g(x)$ is $O(h(x))$. Prove that $f(x)$ is $O(h(x))$. I have tried ...
2
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2answers
63 views

Is there a better way of writing differentiation and integration?

Differentiation is commonly written simply with a prime mark and an equation, as $(x^2)' = 2x$. Although I find this confusing and think it'd better be written $D(x\mapsto x^2) = x\mapsto 2x$, as ...
2
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4answers
120 views

Meaning of symbols $\vdash$ and $ \models$

I'm confused about the use of symbols $\vdash$ and $ \models$. Reading the answers to Notation Question: What does $\vdash$ mean in logic? and What is the meaning of the double turnstile symbol ...
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0answers
49 views

Does anyone use $\subset$ for proper subset anymore?

I belong the the group of people who still write (not necessarily proper) subset as $\subseteq$ to avoid any confusion with proper subset, which I notate $\subsetneq$; I usually do not use $\subset$ ...
0
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1answer
17 views

Substitution in Big-O notation

If I have two statements, one of the form $f\sim g$ and the other of the form $f=O(g)$ of which the definitions are: $$f\sim g\implies\lim_{x \to \infty}\left|\frac{f(x)}{g(x)}\right|=1 ...
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1answer
27 views

Big-O Math Problem [on hold]

I'm having trouble with a hard question, so, say that $f(x)$, $g(x)$ and $h(x)$ are functions such that $f(x)$ is $O(g(x))$ and $g(x)$ is $O(h(x))$. Prove that $f(x)$ is $O(h(x))$.
1
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1answer
18 views

Vector notation question

Just a short question regarding notation: If this matrix represents a vector and I want to solve it for $t=2$, may I write it as follows: $ \left( \begin{array}{ccc} vt\\ vt-gt\\ \end{array} ...
2
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3answers
70 views

Proving with Big O Notations

Is there a way I can prove that $O(3^{2n})$ does NOT equal $10^n$? How would that be done? Also, is it okay to simplify $O(3^{2n})$ to $O(9^n)$ to do so?
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1answer
15 views

Understanding relation between vector valued function and function objective in an multi objective optimization problem

I try to understand the relation between "vector-valued function" and "function objective" as used in optimization problem. I understand that objective function in a multi-objective problem can be ...
2
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0answers
19 views

A question about a notation used in the Folland Real Analysis

This is the exercise 11 in the Folland Real Analysis. Could anyone tell me what it means by f(x,・) and f(・,y)? I have never seen such notations before...
0
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1answer
44 views

What does $f(u)=\min!$ mean in calculus of variations?

I have a very simple notation related question. There are notes to calculus of variations [specifically: Zeidler's book "Nonlinear Functional Analysis and its Applications II/B" page 506] which states ...
5
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2answers
308 views

What is the proper notation for a general number of nested summations?

A sum over one index: $\sum_i f(i)$ A sum over two indices: $\sum_i \sum_j f(i,j)$ A sum over many indices: $\sum_{k_1} \sum_{k_2} \underbrace{\dots}_n \sum_{k_n} f(\mathbf k)$?
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2answers
46 views

What is the difference between $[H, g]$ and $[h, g]$?

I am working on this problem, where $[H, g]$ is the commutator group: Let $H$ be a subgroup of $G$, show that $[H, g] = [H, \langle g \rangle]$. Before solving it, I need to understand the ...
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0answers
23 views

Mathematical Notation: Bracket [on hold]

{M + 0.5[(24F/45) - M], M} For this formula, why is there a ", M}" What does that and the curly brackets mean? Someone told me it is a form of mathematical notation?
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0answers
21 views

Name the maps in a commutative diagram

When writing a formal paper sometimes one needs to construct complicated commutative diagrams, such as My question is, should one always give names to all maps in the diagram (perhaps except those ...
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1answer
30 views

What does “$C^{\infty}$” convergence mean?

I'm studying first notions about several complex variables. As a consequence of the (generalized form) of the Cauchy esteem for holomorphic functions, the book says that in the space $\mathcal ...
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1answer
30 views

Can one use the following notation in integrals?

I read from theoretical physics lecture notes the following: http://theory.physics.helsinki.fi/~fymmi/Luennot4_1-9.pdf $$\Gamma(p)\Gamma(q)=4\int_0^\infty dr r^{2p+2q+1}e^{-r^2}\int_0^{\pi/2}d\varphi ...
0
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0answers
6 views

Bring $ P(z_k | z_1, \ldots, z_{k-1},z_{k+1},\ldots,z_N) = e^\mathbf{z^Tb} / \sum_{z_k \in \{0,1\}} e^\mathbf{z^Tb} $ into sigmoidal form

Let $\mathbf{z} = \{z_1,\ldots,z_N\}$ be a state vector consisting of binary elements $z_i \in \{0,1\}$. Assume that I already did some work and found for a specific conditional distribution this: $ ...
0
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1answer
22 views

what is the name of this operation: $x^T\otimes B$

So the question is simple: how the following operation is commonly called? $x^T\otimes B$, each element of matrix B is multiplied by the array $x^T$, so the result is a matrix. I'm not even sure if I ...
1
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1answer
33 views

A quickie about set theory notation

I'm reading the first chapters of my discrete mathematics textbook and I couldn't help but wonder (perhaps I haven't seen enough examples) -- is it more appropriate to write that $a$ is an integer and ...
1
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1answer
27 views

What is the operator priority in set theory?

Say I have three arbitrary sets $A,B,C$. Which statement is true ? $A \times B \cup C = (A \times B) \cup C $ $\quad $ or $\quad$ $A \times B \cup C = A \times (B \cup C) $ And the same ...
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0answers
34 views

Mathmatical notation for a term of a polynomial

If I have a polynomial $f(x) = ax^n + bx^{n-1} + cx^{n-2} \ldots zx^0$, is there any mathematical notation for one term, such as the $x^3$ term. For example, if I have a polynomial of $f(x) = x^6 + ...
0
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1answer
15 views

Summation notation with ambiguous subscripts

I'm reading a paper which has the following description; Say we have a time series of correlated sequential observations of the random variable $X$ denoted $\{x_n\}_{n=1}^N$ from a stationary, time ...
1
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1answer
27 views

Need help with notation — finite set of random primes

I need help with notation for a finite set of random primes. Edit I've inserted my take on the format from the answer. Does it work? My attempt:$$\{X\in\binom{\mathbf P_{3,100}}{20}\},$$ ...
0
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0answers
23 views

is it okay in a journal to express the vector-scalar division like this

Assume you want to show that a vector is divided by a scalar and then the norm is taken, i.e. $\|\frac{x}{c}\|$ where x is the vector, and c is the scalar. So is it okay to show it like this? I ...
1
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0answers
26 views

Notating the components of the $\hat{\beta}$ matrix when $\hat{Y}$ is multidimensional

This is a question on The Elements of Statistical Learning. We have from the linear model $$\hat{Y} = X^{T}\hat{\beta}$$ where $\hat{Y}^{T} = \begin{bmatrix} \hat{Y}_1 & \hat{Y}_2 & \cdots ...
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3answers
138 views

What Does $y=A\exp(6x)$ mean?

So my professor used this and I don't really know what this equation means. $A$ is a positive constant, different $A$'s give different curves and these curves form a family $\mathcal{F}$. Given a ...
0
votes
1answer
48 views

Why is $(f(x))'$ shortened $f'(x)$

Why is $(f(x))'$ shortened $f'(x)$? This makes the chain rule look awkward, as $(f(g(x)))'\neq f'(g(x))$, but rather $f'(g(x))\!\times\! g(x)$, and makes it difficult to remember. It's also an ...
3
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1answer
99 views

What does a standalone $dx$ mean?

Some literature uses $dx$, in the context of differential equations, in a confusing way without defining what it really stands for: $Mdx + Ndy = 0$ Does it mean one of the following or something ...
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votes
1answer
44 views

$\bigcup_{i \in I} \mathcal{P} (A_i)$

This is Velleman 3.7, Problem 4 Below is the problem, verbatim. Suppose $ \{ A_i \mid i \in I\}$ is a family of sets. Prove that if $\mathcal{P}(\bigcup_{i \in I} A_i) \subseteq \bigcup_{i \in I} ...
0
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1answer
49 views

What is the name of this graph operation? (creating $k$ connected copies)

I'm looking for the name of this natural graph operation, which is kinda similar to Cartesian product, but not quite, as the copies of the graphs are not fully connected. Instead, it creates a $k$ ...
34
votes
6answers
3k views

What do mathematicians mean by “equipped”

I am a mathematical illiterate so I do not know what people mean when they say equipped. For example, I say that Hilbert space is a vector space equipped with a inner product. What does that ...
0
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3answers
40 views

What does the notation $\min_x$ mean?

I have a problem in which I need to find $\min_x(f(x))$. What does this notation mean?
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2answers
101 views

What is cos²(x)?

This looks odd to me. I need a definition. Is it just the square of $\cos(x) $ ? Like $\ \cos^2(x) = \cos(x) \cdot \cos(x) $ ? Then why don't you write it like that: $\cos(x)^2 $ ?
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1answer
30 views

Confusion about integration notation

This is probably a silly question but I've never seen this notation: For a > 0, compute $$\int\int_{x/y \leq a} 2e^{-(2x+y)} dx dy$$ What is $x/y \leq a$ there for? This is from my statistics ...
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2answers
14 views

Question about alternate subset notation

I am reading a new text, and I have come across the notation '$\Subset$' as well as '$\subset$'. Am I correct in assuming that '$\Subset$' is an alternative method of specifying an improper subset ...
1
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0answers
47 views

How to avoid fractions when writing expressions?

When I'm writing expressions in an articles the fractions when not segregated in a single equation usually are a problem. One example is $\frac{x}{\log y}$ that can be written as $x\log y^{-1}$. ...
1
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0answers
20 views

The maximum notation as regards the absolute value?

We know that $\max(\textbf{A})$ gives the maximum element of the array $\textbf{A}$. What is the notation, or a short formula, if we seek the element having the largest absolute value? e.g., ...
8
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2answers
1k views

Why is there this strange contradiction between the language of logic and that of set theory?

In standard probability theory events are represented by sets consisting of elementary events. Consider two events for which (as sets) $A \subset B$. If an elementary event $x \in A$ takes places then ...
7
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5answers
135 views

Does the interval notation $[a,b]$ imply that $a<b$?

If showing an interval $[a,b]$, are $a$ and $b$ implied to be such that $a,b\in\mathbb{R}$ and $a\le b$, by simply writing that, or must they be specified as such?
7
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4answers
354 views

What is $1 + 999999…$ (an infinite string of $9$s)?

I'm doing a programming assignment in Haskell, and it involves adding "infinite" lists. At the bottom of the assignment, our lecturer has written ... "in some sense an infinite string of $9$s is the ...