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
votes
3answers
69 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? ...
1
vote
2answers
43 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.
1
vote
1answer
30 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
votes
1answer
30 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
votes
0answers
78 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 ...
-2
votes
4answers
203 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
vote
1answer
39 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
votes
2answers
50 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
52 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
190 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
46 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
43 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
1answer
85 views

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
148 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
vote
0answers
26 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
votes
1answer
26 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
votes
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
vote
1answer
31 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) ...
0
votes
2answers
56 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
votes
0answers
37 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
vote
1answer
53 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
37 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 ...
0
votes
1answer
62 views

How to mathematically describe a loop over a set with two indexes.

I have a set of sets $G = \{D_{0,0}\,D_{0,1}\,D_{0,2}\,D_{1,0},...,D_{n,0}\,D_{n,m}\} $ What I know want to express is a constraint that for each set in $ G $, if $ x \in D_{0,0} $ then the statement ...
-1
votes
1answer
81 views

What is varpi in Zhang's notation?

In his video from this summer at the IHES on bounded gaps between primes, T.Tao uses the $\varpi$ notation as shown here : When asked what his notation means in this context, he answers that he ...
0
votes
2answers
28 views

How to mathematically describe the number of Element x in a set

I am trying to formulate the following. I have a Set A={x, y, z}, I also have a Set B, C and D, which all are subsets of A. It is not exactly defined which elements are in B, C and D. I only want to ...
2
votes
2answers
43 views

Have I properly used $\,\exists !\,$ in this statement?

I want to express the following in logical notation. For every natural number, there is a unique natural number that succeeds it. Does the following statement express that proposition? ...
0
votes
0answers
26 views

Function Notations

Let $f:X\to Y$ be a function and let $x\in X$. For the image of $x$ under $f$, a popular notation is $f(x)$; while some author prefers $(x)f$. To me, $(x)f$ is far more natural as if we apply a ...
2
votes
1answer
68 views

suggest a topic about history of mathematics

Can you suggest a topic (the history of mathematics) concerning the evolution of a given concept from a document written in English from varied scientific resources What do you think of the ...
2
votes
2answers
31 views

Why $E^2$ instead of $\Bbb R^2$

I was reading a paper earlier where whenever the author would discuss vectors in polar coordinates, he'd call the space $E^2$. He'd even give a function of vectors in that space as $f:E^2 \to \Bbb ...
3
votes
1answer
224 views

Interpretation of hint for Exercise 2.19b of Eisenbud

I am doing exercise 2.19b of Eisenbud's Commutative Algebra with a View Towards Algebraic Geometry. Here we have an $R$-module $M$ and elements $\{f_i\}$ which generate the unit ideal. The exercise ...
1
vote
1answer
24 views

Clarification on notation

For a graph $G$, put $δ(G) = \text{min}\{\deg_{G} (v) : v \in V\}$ (the minimum degree of $G$). Prove $χ(G) \leq 1 + \text{max}\{δ(G ) : G' \subseteq G\}$, where $G' \subseteq G$ means that $G$ is a ...
92
votes
22answers
10k views

Most ambiguous and inconsistent phrases and notations in maths

What are some examples of notations and words in maths which have been overused or abused to the point of them being almost completely ambiguous when presented in new contexts? For instance, a ...
0
votes
1answer
59 views

Incomplete statement of commutativity of summation in Concrete Mathematics?

My text (p. 30, eq. 2.17) states the "commutative law" for sums as $$\sum\limits_{k\in K}{a_k} = \sum\limits_{p(k)\in K}{a_{p(k)}}$$ where $p$ is a permutation and $K$ is a set of integers. While ...
2
votes
1answer
86 views

What does single parentheses mean?

I see look at Changing a number between arbitrary bases, Math Gems answer and see such annotation : 1⋅6+2=10)6=60)+1)=61)6=446)+3=451 What does 10)6 mean? What single ")" mean? Mathematics teacher ...
1
vote
1answer
30 views

about $\nabla^{4}\Phi=0$, write down this equation in terms if Cartesian Coordinates

$\nabla^{4}\Phi=0$, write down this equation in terms if Cartesian Coordinates(x,y). I am a bit confused here, the question doesn't tell you if $\Phi$ is scalar or vector, but i think it is a vector, ...
2
votes
3answers
42 views

Does every element of the empty list posses every property?

Suppose we have a list of elements $v_1, v_2, \ldots, v_n$. Then, as I've understood, setting $n=0$ above results in the empty list $v_1, v_2, \ldots, v_0$ of no elements (please correct me if I'm ...
2
votes
4answers
48 views

Let $S$ be a set. How is $f(S) = S$ different from $f(s) = s$ for all $S$?

Usually, $f$ denotes a function, $f(x)$ is an image of $x$ under $f$. But what's $f(X)$ if $X$ is a set? edit: Please, disregard the body of this question. I had to put something here to be able to ...
1
vote
0answers
25 views

Intersection of Elements from Sets of Sets

Say I have 2 sets of sets: $$ X = \left \{ \left \{ 1,2 \right \}, \left \{ 3,4 \right \} \right \} $$ $$ Y = \left \{ \left \{ 1,3 \right \}, \left \{ 2,4 \right \} \right \} $$ I want to express ...
1
vote
1answer
87 views

How correctly define the pixel intensity of an image?

Let's do easy: I have an image IM and p(i,j) is the discrete intensity value of a pixel in the image IM (not necessarily 2-dimensional)..... How can I mathematically correctly define this? Thank you ...
2
votes
3answers
413 views

“sup” in an equation

I am currently reading through JC Lagarias' "The $3x+1$ Problem and its Generalizations" and have come across some notation reading : $$\sup_{K \ge 0} T^{(K)}(N)$$ Now I assume that this means ...
0
votes
1answer
57 views

What does $Du$ mean in a differential equation?

I'm very interested in the following work: http://maths-people.anu.edu.au/~andrews/HSU_Survey141105.pdf . Unfortunately, the author uses (in this and other papers I'm interested in) the notation $Du$. ...
3
votes
2answers
41 views

Can I say that a fixed constant is less or equal infinity?

Mathematically speaking, given $c\in\mathbb{R}$, can I say that: $c\leq\infty$? E.g., is $10 \leq \infty$ a correct mathematical statement? I know this comparison is true in computer arithmetic, ...
2
votes
2answers
36 views

Help me evaluate this equation in Scientific Notation

How do i solve this using Scientific Notation? $$ \frac{3\times 10^8}{4\times 10^{-5}} $$ I have been trying for hours now! Help please
0
votes
0answers
48 views

Notation for a sum product

I'm struggling with notation for a sum product. Let $f:Z^+\rightarrow Z^+$. I am interested in a sum where each term is the product of functions whose sum of arguments equals $n$. For example if $n=3$ ...
14
votes
1answer
275 views

Did Einstein introduce anything new to mathematics? [duplicate]

Newton introduced calculus, so I am wondering, did Einstein introduce anything important to mathematics?
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0answers
22 views

What is the mathematical notation for the mode of a distribution?

Am writing an economics paper wherein defining a dummy variable as a taking the value one if the value of one variable is greater than the mode of another. What would be the best way to write this ...
6
votes
3answers
141 views

In logic, do the $\Longrightarrow$ and $\rightarrow$ signify different things?

In logic, do the $\Longrightarrow$ and $\rightarrow$ signify different things? Are there contexts where one is more appropriate than the other? I had believed that the $\Longrightarrow$ was for ...
1
vote
1answer
50 views

How to write notation for this function?

Say $X=(x_1,x_2,x_3,..,x_n)$, and there is a function of $X$, which is $f(X)=g(h(c,X))$ where $c$ is constant. Now in my case, given a $X_0$,there will be a function $i_1(x_1)$, which takes $x_1$ in ...
0
votes
1answer
23 views

How do you use mathematic logical notation to notate a function whose output positively correlates with the input?

Suppose the amount of weight John gains from a meal is a function of the number of calories he eats, and that John will gain X weight, such that X>A, if he consumes Y calories, such that Y>B, where A ...
0
votes
1answer
44 views

Question about Set Notation and Minimization: $\colon, \mid$

I see many different notations in context of sets, minimization. For example $$\min_{x \in X} f(x),$$ $$\min \{ f(x) \mid x \in X \}$$ $$\min \{ f(x) \colon x \in X\}$$ and so on.. Is there any ...