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
415 views

How to prove $2^n = \omega (n^k)$

I'm trying to prove $2^n = \omega (n^k)$ but the problem is that, I could not find any examples of proving little/ small omega, and what makes it confusing is that I could not even find a way to deal ...
-3
votes
1answer
86 views

What is this symbol?

This symbol: I found on the Wikipedia page for the Law of Cosines. It looks kind of like a lowercase Gamma (γ), but it doesn't specify so I'll wait to see what you guys think. Thanks
0
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0answers
154 views

Notation for domain-restricted function

When restricting the domain of a function $f: A \to B$ it is common to write $f|_{E}$, to mean $f$ domain-restricted to $E \subseteq A$. This notation is used in Wikipedia and also for example in this ...
0
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0answers
168 views

Order of operations: summation and exponenets

I'm reading a paper that includes the following expression: $$\sum^c_{k=1}\left(\frac{||x_i - c_j||}{||x_i - c_k||}\right)^\frac{2}{m-1}$$ Should I read that the exponentiation to apply to the whole ...
2
votes
2answers
107 views

What exactly does the $d$ represent in $\frac{d}{dx}$?

When taking the derivative, such as $\frac{d}{dx}$, what exactly does the $d$ represent? The best answer so far is in for example $\frac{dy}{dx}$, the $d$ stands for change in and what follows the ...
0
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2answers
84 views

Indexed families and arbitrary sets, notation

I wonder if there's some advantage of using the notation of indexed families when taliking about arbitrary sets or this is just a matter of style. For example to denote $\bigcup A$ and operate over ...
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6answers
98 views

Which one is preferred: $r2^m$ or $2^m r$? [closed]

Which is preferable to write: $r2^m$ or $2^m r$?
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1answer
66 views

Intervals and sets

I never took calculus until now, but as a stat major I have sometimes used the notation $x\in [a, b]$ as an alternative way of writing $a\leq x \leq b$. Does it make sense to express it like this, or ...
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2answers
519 views

Learning math symbols

I am taking linear algebra and none of this stuff is expained. I found this helpful link http://www.math.ucla.edu/~pskoufra/M115A-Notation.pdf but it is missing a lot of what I need to know. Just ...
2
votes
2answers
53 views

What does ${N\choose\mu}$ mean where $\mu = (\mu_1, … , \mu_n)$ be the vector of nonnegative integers for which $\sum_{i=1}^n \mu_i = N$?

When I've read Cohn et al. paper 2005, I've met a strange object in lemma 1.1 that looks like number of combinations: ${N\choose\mu}$ where $\mu = (\mu_1, ... , \mu_n)$ be the vector of nonnegative ...
4
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1answer
257 views

Derivative $\Delta x$ and $dx$ difference

This may seems like a dummy question but I need to ask it. Consider the definition of derivative: $$\frac{d}{dx}F(x) = \lim_{\Delta x->0}\frac{F(x+\Delta x) - F(x)}{\Delta x} = f(x)$$ Also: ...
2
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2answers
102 views

Is “iff” the same as equality if each member is a predicate?

"Iff" - if and only if ($\Leftrightarrow$ or $\leftrightarrow$, although the first usually carries a "meta" meaning, something that is not evaluated) - is used in $2x=3\Leftrightarrow x=\frac32$, ...
3
votes
2answers
1k views

What does the Big intersection or union sign of a set means?

Normally what I know is that you can make a union or an intersection between 2 sets. In this expression Its a big union of a set. I'm asking about the meaning of such expression, What does it mean. ...
0
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1answer
81 views

Mathematical notation for computer codes

How to write in mathematical notation the following procedure? 1) For each element of matrix A assign the sum of distances between it and all other elements. Distance is simply difference in ...
0
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1answer
147 views

Asymptotic notation meaning in transitive relation

I'm attempting to prove the transitive relation on $\theta$ and I'm having trouble understanding the meaning of one of the symbols used. Here is the transitive relation: $f(n) = \theta(g(n)) ...
0
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3answers
83 views

Math notation for sum of the last $n$ numbers in a vector

I have a vector of numbers, $x_0, x_1, x_2, \dots, x_n$. I'm trying to figure out how I can denote the sum of the last 3 numbers in the vector. For example, consider the vector: ...
1
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2answers
106 views

Matrix (correct) notation

Say I have a real $m \times n$ matrix $\mathbf{M}$. Shall I write $\mathbf{M} \in \mathbb{R}^{m \times n}$ or $\mathbf{M} \in \mathbb{R}^{m,n}$? What is commonly accepted and most beautiful and ...
1
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2answers
54 views

Power correct notation

Ok, I know this may sound dumb, but I am trying to understand which is the correct (most beauty) notation for the power function ${\rm pow}(f(x),n)$. This is the correct one: $[f(x)]^n$ From ...
6
votes
2answers
195 views

Notation for a relation

I'm reading up on "Set Theory and Logic" by Stoll and came upon notation for relations that I haven't seen before. I've seen $x\sim{y},$ and $xRy$ before but Stoll uses this one. $$(x,y)\in{\rho}$$ ...
3
votes
2answers
112 views

Why use the non-exclusive or sign in equations?

$x^2=4 \Leftrightarrow x = 2 \lor x=-2$, but $x$ can't be equal to both $2$ and $-2$, unlike what the inclusive-or symbol ($\lor$) implies. Although it may seem obvious, it's just wrong to say that ...
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3answers
86 views

How to make sense of $A+B$ where $A$ and $B$ are sets.

Suppose $A$ and $B$ are compact subsets of the complex plane $ \mathbb{C}$. How do I make sense of $A + B$ ? My first thougt: If one of the sets consist only of one point, say $A = \{ z: |z| \leq R ...
1
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1answer
66 views

Show that a partial differential eqution is satisfied (is my notation okay?)

Let: $f:\mathbb{R}\rightarrow\mathbb{R}$ be differentiable. $u:\mathbb{R}^2\rightarrow\mathbb{R}$ and $u(x,y)=e^{-y}f(x+y^2)$ Show that: ...
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1answer
99 views

Meaning of the following integal

What does $\int d^3 x $ mean? I found this in a lecture on quantum field theory, and it was not explained.
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2answers
68 views

About notation of function

Suppose I have a function $f:[a,b] \to \mathbb{R}$. I am writing this: $f$ is a nice function. Is this sentence the same as the sentence $t \mapsto f(t)$ is a nice function. In other ...
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1answer
82 views

Problems with tensor notation

I've got a question for the mathematically more educated for I am a humble engineer having a hard time: $\kappa = \left( \delta_{ij}-n_in_j\right)\displaystyle\frac{\partial u_i}{\partial xj} - ...
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2answers
115 views

What does $U \in \mathbb R^n \times \mathbb R$ mean?

Ok so I get the basics of this, I just can't put it all together. $U$ is contained in the cartesian product of $\mathbb R^n \times \mathbb R$. What is $\mathbb R^n \times \mathbb R$ though? I know ...
8
votes
3answers
239 views

Is $d^2y/dx$ a valid mathematical notation?

I have often seen "the second derivative of y with respect to x" written as $${d^2y\over dx^2},$$ but I don't understand the reason for this notation. I have always seen it written as $${d^2y\over ...
1
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1answer
118 views

Notation of complement of set

Given, $U=\{1,2,3,4,5,6\},A=\{1,2,3\}$. We have to find the complement of the set A. We start by, Since set $A=\{1,2,3\}$, so $A'=\{1,2,3\}'=\{4,5,6\}$ Is the second part where I write ...
1
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2answers
110 views

How to understand sum symbol?

I have searched google for an answer but I'm not sure what I'm asking. I know that Sigma means sum but there is an 'n' above Sigma and an 'i=1' under sigma. how can i understand this? thank you!
2
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2answers
85 views

How to represent objects formally? [closed]

Computer indexed arrays can be represented formally using vector notation. x= [1,3,2] $x=(1,3,2)$ How can I show an object/associative array mathematically? y=['a'=>5,'b'=>4] ~ ?
1
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1answer
88 views

What are common notations for the endomorphism group of a vector space?

Given a vector space $V$, the set of endomorphisms in $V$ can be denoted $$\text{End}(V)=\left\{L:V\rightarrow V:L\text{ is linear}\right\},$$ particularly when one wants to be completely unambiguous. ...
3
votes
3answers
100 views

Conventional set notation for integers between m,n CS Theory/Math literature

This is a pretty simple, straightforward question. I've seen in the literature $[n]=\{0,1,2,\dots,n-1\}$ and $[n]=\{1,2,3,\dots,n\}$. Is there a similar convention for ...
1
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0answers
46 views

decimal digit grouping delimiters

I feel a bit silly having to ask this but I just can't seem to find any resources that give an answer to this. When dealing with decimal values that have a large number of digits to the right of the ...
4
votes
4answers
231 views

Leibniz notation for high-order derivatives

What is the reason for the positioning of the superscript $n$ in an $n$-order derivative $\frac{d^ny}{dx^n}$? Is it just a convention or does it have some mathematical meaning?
4
votes
3answers
251 views

What's the meaning of $\dagger$

In some books I've seen this symbol $\dagger$, next to some theorem's name, and I don't know what it means. I've googled it with no results which makes me suspect it's not standard. Does anybody know ...
2
votes
2answers
102 views

How to indicate keeping the sign when squaring a number.

I have a vector $x$, which I wish to transform according the the following computer code xstar = sign(x) * x^2 with $x^*$ preserving the positiveness or ...
0
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2answers
63 views

Is this use of product notation legal?

So I'm trying to prove something, I came across a sub-question that lead me to another question I thought of. Is the following legal? $$\prod_{k=1}^{n} \left(1-\frac{1}{2k}\right)/ \prod_{k=1}^{n} ...
1
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1answer
130 views

Minimum notation of modified set elements analog to Sum notation

I'm currently trying to simplify a calculation that takes the minimum of all elements in a set. However the elements should not be taken as they are but be modifiable: $$ S = \{{A}, {B}, {C}\}\\ ...
1
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1answer
57 views

What is the notation for separable states or independent variables?

Is there any specific notation that two quantum states are separable or that two random variables are independent?
0
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2answers
41 views

Is there a convention for precedence of operators in an additive category?

The laws for an additive category are that there must be a zero object, binary products, that every Hom-set is an abelian group, and that the morphism addition distributes over composition. My ...
3
votes
0answers
51 views

Curve of centers of curvature

I really can't find the English name of the curve of the centers of curvature of a curve. Formulated more precisely: Suppose $\alpha$ is a regular curve in $\mathbb{E}^2$ and $||\alpha(t)'||=1$. How ...
3
votes
3answers
153 views

Different of mapsto and right arrow

Could someone please explain to me what is the difference in the two arrows$$\rightarrow$$ and $$\mapsto$$ For example in Probability wih Martingales (Willams) Thank you.
0
votes
1answer
151 views

How to write the expression with multi-index notation?

I need some help for writing the following expression with multi-index notation, $$\sum_{i_1, \ldots, i_p=1}^n \frac{\partial^{2p}}{\partial x_{i_1}^2\ldots \partial x_{i_p}^2}f(x, \xi),$$ where ...
2
votes
2answers
641 views

Bar symbol over a matrix

So I am reading a paper (not online) and I come across a definition: $$\mathbb E=R\bar R$$ Where R is a complex matrix. I am thinking that it means complex conjugate, but I honestly have never seen ...
3
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1answer
48 views

Turning preorders into partial orders

Given a preorder $\preceq$ we can define a partial order $\leq$ as: $x<y$ iff $x\preceq y$ and not $y\preceq x$ $x\leq y$ iff $x<y$ or $x=y$ Transitivity is inherited from $\preceq$, ...
2
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3answers
115 views

Notation for set of all possible bijections

I have two finite sets: $S$and $S'$. I know $\mathrm{card}(S) = \mathrm{card}(S')$ I have a function $colour()$ that produces some colour for each element of $S$and $S'$. I know that there is at ...
0
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1answer
38 views

Stochastic Infinitesimal Generator Definition Confusion

I have seen an operator $A$ called the Infinitesimal Generator. Given $b: \mathbb{R}^n \rightarrow \mathbb{R}^n$ and $\sigma: \mathbb{R}^n \rightarrow \mathbb{R}^{n m}$ and $f:\mathbb{R} ...
1
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1answer
69 views

Cartesian Product

Given sets $A_1,A_2,\ldots, A_n$ how do I describe its Cartesian product $$C = A_1 \times A_2 \times \ldots \times A_n$$ in a succinct fashion? An example would be $C = \times_{i=1}^n A_i$ or $C = ...
2
votes
2answers
107 views

Understanding notation difference between mutual information and information divergance

The mutual information is defined on random variables. That is, $I(X;Y)$ denotes the mutual information between random variables $X$ and $Y$. On the other hand, the the Kullback-Leibler divergence is ...
3
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3answers
121 views

About plus-minus sign

If, say, we know that $x=1$, is then the expression $x=\pm 1$ mathematically incorrect? I ask this because when we use $\pm$ sign in the discriminant formula we imply that any of the plus or minus ...