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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53 views

Symbol for “Take Highest Number”

As the title states, is there a symbol for taking the highest value? Let's say we have two variables $a=2$ and $b=3$ now I want $aXb$ (where $X$ is the symbol I am looking for) and I want that answer ...
1
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2answers
31 views

Is “foot of $X$” a common term in math? General questions about the foot?

I moved and started taking classes at a new university. One term that has come up several times in class is the "foot of $X$" which has notation similar to a bracket but with the top bits cut off. ...
1
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2answers
26 views

What do gradient, curl, and div input and output?

What do gradient, curl, and div input and output? (e.g. vector field or scalar function of several variables)
5
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2answers
370 views

Vertical bar sign in Discrete mathematics

I am little bit confused about the sign " | ". Some people call it the division sign and some call it "such that". In computer programming, it's known as pipe. ...
0
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0answers
15 views

What is the correct term (and symbolic representation) of specific “un-modded” values?

Given $x \in \mathbb{R}$ such that $x \equiv x+k\cdot(b_u-b_l),\,\forall k\in\mathbb{Z}$, are there terms to describe the functions $$f:[b_l, b_u) \to[b_u, b_u+(b_u-b_l)):x\mapsto x+(b_u-b_l)$$ and ...
5
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3answers
48 views

Subsets of $\{1,2,3,4,5,6,7,8\}$ with at least 1 odd and 1 even number

How can I formally write the number of subsets of $S=\{1,2,3,4,5,6,7,8\}$ with at least 1 odd and 1 even number? I know if I take the subset with even numbers, $E =\{2,4,6,8\}$, there are $2^4-1$ ...
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2answers
52 views

Notation of exactness

I'm doubting my recent Facebook comment concerning the acceptance of 2 + 2 = 5: The trick is that without a decimal dot, those numbers could be up to 0.5 bigger or smaller, depending on rounding ...
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4answers
2k views

Symbols for “odd” and “even”

Let $A$ be a sequence of letters $\langle a,b,c,d,e,f \rangle$. I want to create two subsequences, one with the values with odd index and other with the values with even index: $A_{odd} = \langle ...
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2answers
52 views

“Subset of above not equal to” $ \subsetneqq $ Symbol

I was reviewing my Algebra diary, and I noticed a symbol that I was not familiar to: $ \subsetneqq $. After some reseach on the internet I eventualy found it (through UNICODE), and found that the ...
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0answers
9 views

parsing prefix notation

I am trying to write a program to evaluate prefix notation expressions, but apparently I'm not grasping the concept correctly. The test program I was given passes $({+} (- 6) ({*} 2 3 4) (/ (+ 3) (* ...
2
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1answer
58 views

Are the definitions of dot product and cross product the wrong way round?

This is something that has been bugging me since I started studying again. It seems to me that the definitions and symbols for the dot and cross products are backwards. When I first learnt ...
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2answers
19 views

Summation of values with odd index in a sequence

Given a sequence of numbers $S = \langle s_1,\dots,s_n \rangle$ I want to sum all the elements of S that the index is odd. Would the following be a good notation or is there a more compact (and ...
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2answers
41 views

Can you help me simplify this summation notation?

$$\sum_{i=1}^n \frac{n}{n+1}i^2$$ and $$\sum_{i=1}^n \frac{i}{n}$$ (n is a constant)
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1answer
27 views

Notation for power of prime in prime factorization

What's the accepted shorthand for the power of a prime in the prime factorization of a natural number? For example, $35 000 = 2^3 5^4 7$, so what would the notation be for $f_5(35 000) = 4, f_2(35 ...
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1answer
48 views

Are there any sets that cannot be constructed using the symbols $\{$ and $\}$?

It seems to me all sets in mathematics can be constructed via these two symbols only. For instance, the natural numbers are defined as $0 = \varnothing = \{\}, 1 = \{0\}$, $2 = \{0, 1\}, 3 = \{0, 1, ...
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1answer
67 views

How to write “there exists an infinite number of”?

We all know that means “there exists” and ∃! means “there exists exactly one”. Is there a similar notation for existence of an ...
1
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0answers
8 views

Compare all elements of a set with all elements of the set

I have a set $ X = \{a,b,c,d\} $ where all elements of the set are tuples $ (x,y), x \in \mathbb{N}, y \in \mathbb{N} $. In this case the elements of the tuple would represent a timeslot where start ...
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2answers
32 views

Notation laplace operator squared $\Delta^2$

I have the following expression (in a numerical context) $$\Delta_h u(x) = \Delta u(x) + \frac{h^2}{12} \Delta^2 u(x) + O(h^4)$$ The $\Delta$ is the Laplace operator so $\Delta u = u_{xx}+u_{yy}$. ...
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1answer
34 views

$dx$-notation in analysis

In the context of integrals and differential equations, often the symbol $df$ or $dy$ appears, where in some previous steps $f$ and $y$ were functions. What do these symbols mean $df$ and $dy$? ...
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0answers
24 views

Composite residuosity statement.

Consider the following definition. A number $z$ is said to be $n$-th residue modulo $n^2$ , if there exists a number $y \in \mathbb{Z}_{n^2}^*$ such that $$z\equiv y^n \mod n^2$$ Let us take $n=6$ ...
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1answer
55 views

Meaning of symbol $:=$

Can anyone tell me the meaning of this symbol $:=$ I couldn't find it online. It came up while I was studying joint probability of Gaussian random variables.
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1answer
39 views

What is this symbol used for?

I have seen the symbol $\subsetneqq$ in a Probability exercise. What is it used for? In the exercise it seemed to mean "proper subset of", but then in what is it different from $\subsetneq$?
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1answer
32 views

Question about correct notation

Is the following way to define a set correct: $\{A_p|A_p\in Z_2\&(\forall A_q \in Z_3)(A_p \cap A_q = 0)\}$ or is it better to write it this way: $\{A_p|A_p\in Z_2\&(\forall A_q \in Z_3) ...
2
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1answer
17 views

Notation of sigmas

When one writes $$\sum_{i+j=4} a_i a_j$$ is that then equal to $$a_0a_4 + a_1a_3 + a_2^2$$ or $$\sum_{i=0}^4 a_i a_{4-i}=2a_0a_4+2a_1a_3 + a_2^2$$ I suddenly got confused while writing these sigmas ...
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2answers
56 views

Confusion in notation of functions.

Let us consider the following notations for $x \in X,y\in Y ,z \in Z$. $$F(x,y,z)=x^yy^z$$ $$F_x(y,z)=x^yy^z$$ I am clear with former notation , but I saw latter one too , what's the difference ...
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1answer
28 views

Notation: $\sum\limits_{i=m}^n i$, with $m>n$.

I came across with that notation in one book. They defined $$\overline{X_n}=\frac{X_1+...+X_n}{n}.$$ Then they define $n\in \mathbb N$, $k_n\in\mathbb Z$ such that: $$[k_n]^2\leq n\leq ...
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0answers
8 views

How to create a total order of a set of triplets

I have a set $ M = \{a_1,...,a_n\} $ where every $a$ is a triplet $ a = (x,y,z) $. I know want to do some things with this. I want to build a set $ N \subseteq M $ which contains all triplets that ...
2
votes
3answers
58 views

Explain to me the difference between the notation $\mathbb{Q}( \sqrt2) $and$ \mathbb{Q}[ \sqrt2]$

Please explain to me the difference between the notation $\mathbb{Q}( \sqrt2) $and$ \mathbb{Q}[ \sqrt2]$. I know that these two fields are equal. But what difference do the different brackets imply? ...
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2answers
35 views

Set notation query

What do square brackets mean next to sets? Like $\mathbb{Z}[\sqrt{-5}]$, for instance. I'm starting to assume it depends on context because google is of no use.
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1answer
19 views

Notation with random variable $\overline{X}_{n^2}$ in Strong Law of Large Numbers proof.

I'm reading the proof for the strong law of large numbers. It says: Let $X_1,X_2,\ldots$ be a sequence of independent and i.i.d. random variables with finite mean $\mu$ and finite variance ...
0
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1answer
24 views

“$H_2/G_2$” and “$G_1/H_1$” meaning

I have the following problem: Let $f \colon G_1 \rightarrow G_2$ be an epimorphism, $H_2/G_2$ and $H_1=f^{-1}(H_2)$. Prove that $G_1/H_1 \cong G_2/H_2$. Is this still true if $f$ isn't surjective? ...
2
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0answers
47 views

What are numbers with E in them called?

I know that this is a very stupid question, and that I will get flamed for it, but I cannot find any information what-so-ever about it on the internet, because Google doesn't include some characters ...
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4answers
195 views

What is the product of magnitudes $\frac{\partial }{\partial x}$ and $x$?

I know that $\frac{\partial}{\partial x}\space (x)=1$, here I am not talking about it. Consider: $$(\widehat{e}_x\frac{\partial}{\partial x}).(\widehat{e}_x x)=(\frac{\partial }{\partial ...
1
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1answer
35 views

How can I write in Landau notation (or the like) that $2^x/x$ rises almost as fast as $2^x$?

Since $2^x \not\in O(2^x/x)$, we do not have $O(2^x/x)=O(2^x)$. But since $x$ rises linearly and $2^x$ exponentially, $2^x/x$ rises almost as fast as $2^x$. Can I somehow express this in Landau ...
0
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2answers
30 views

Vector notation for “not including” index

I was wondering how to write vector notation with an index which is not included in the vector. In sets we can write, $$ A=\{0,1,2,3,4\},$$ then if we don't want to include the element $\{0\}$ we ...
2
votes
2answers
48 views

What might be meant by $\left\{0,1,2\right\}^{\mathbb{Z}}$?

What might be meant by $\left\{0,1,2\right\}^{\mathbb{Z}}$? I do not know what this notation means-
2
votes
4answers
100 views

When an equation has no solutions, denote it with $x\in\varnothing$.

My teacher claims that when an equation in variables $x_1,x_2,\ldots,x_n$ has no solutions, you should denote this fact with $(x_1,x_2,\ldots,x_n)\in\varnothing$. An empty set can't have an element ...
0
votes
1answer
44 views

What's the name of this function?

Does the function $f(x)=\log(-\log(x))$, $x\in(0,1)$ has a name? Equivalently, the function $g(y)=f^{-1}(y)=\exp(-\exp(y))$, $y\in{\mathbb R}$. The only thing I want to know if whether this function ...
0
votes
1answer
21 views

Summation of the Max Distance between the elements of two sets

I have a situation where I need to sum of the max distance of all elements of a Set $A$ comparing with all the elements of a set $B$. For example: let's say that $dist(a,b)$ is the euclidean ...
0
votes
0answers
11 views

What is $F_i^p(e_j)$?

$F_i^p$ is the face opposite the $i^{\text{th}}$ vertex in a $p$-simplex. My book mentions the term $F_i^p(e_j)$, where $e_j$ is a vertex in the simplex. What is $F_i^p(e_j)$?
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25 views
+50

Is there any convention regarding the order of operation of the binary modulo operator?

Is there any predominant convention as to where the binary modulo operator (i.e., the variant of the modulo operator that is not applied to a whole equation) ranks in the order of operations, in ...
2
votes
3answers
43 views

Is modular arithmetic defined for all rational numbers (with denominators coprime to modulus)?

In the expression $\frac{1}{b}\pmod m$, where $(b,m)=1$, is $\frac{1}{b}$: a) a rational number (and so rational numbers are defined in modulo arithmetic using multiplicative inverses)? b) just ...
1
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0answers
18 views

Classification of discontinuities of multidimensional functions/maps

I know that for functions $f: \mathbb{R} \rightarrow \mathbb{R}$ there exist plenty of references which describe various discontinuities that such functions can exhibit (e.g. jump, asymptotic, etc). ...
0
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1answer
14 views

How to read this superscripted minus sign in a PMF formula

I was glancing at a probability and statistics review, and I saw some notation that I hadn't seen before. Naturally, I am curious as to how to properly read it and/or use it in the future. My question ...
0
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2answers
22 views

Functions and its powers

Given a map $\pi: A \rightarrow B$ what is the definition of $\pi^n$ where $n$ is a positive integer? For example if $\pi(a)=b$ then is $\pi^n(a)=b^n$? Ok so if $n=3$ then ...
1
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1answer
13 views

Confusing delta notation for multivariate expectation

I'm seeing this odd notation describing process error covariance in an extended Kalman filter over a time interval $(t, t')$. It says that $$ Q(t) = \left[ \begin{matrix} Q_1(t) ...
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2answers
47 views

Is there a mathematical for “for every fixed element”

I've noticed that "for every fixed element" has come up enough for me to ask is there a mathematical sign for this? If not, why not? I can think of plenty of times when it comes up and such a notation ...
2
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0answers
25 views

Use of absolute value sign for determinants

I was wondering if there is a connection with the use of absolute value signs with the notation of a matrix's determinant. I understand there is some quantifying characteristic with the determinant ...
1
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1answer
45 views

what does this summation mean?

I apologize if this question has been asked. I know several similar ones have been asked but I cannot find one answering this in particular. I want to know what this summation means: ...
2
votes
1answer
34 views

Is there any good reason against referring to employed equations over the relation sign when establishing a new relation?

I need to write down a complicated proof for a paper, for which I need to employ equations that I established earlier for almost every new relation I show. I would consider it best for the reader, if ...