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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34 views

Notation for the subset of a set without the last elements

I have an ordered set $S=\{23,45,32,56\}$ I would like to make an ordered subset $M=\{23,45,32\}$ which contains the elements of $S$ except the last one. In this case. How do I represent this formally ...
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1answer
20 views

ordered set notation in functions

Do please forgive me, if this question is a duplicate. How does one correctly notate a function $f$, which takes a ordered subset $S$ from the field $\mathbb{K}$ and returns an other (ordered) subset ...
0
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1answer
17 views

Asymptotic notation basics

Say that we have the function $$ f(n)=kn, \, k>0 $$ does that imply the following? $$f(n) \in O(n), \, f(n) \in \Theta(n) \text{ and } f(n) \in \Omega(n)$$ I'm fairly new to these notations and am ...
3
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1answer
55 views

What does $(0:x)$ mean?

The following excerpt is from Eisenbud's "Commutative Algebra with a view toward Algebraic Geometry" on pg. 424 We can decide whether an element $x\in R$ is a nonzerodivisor from the homology of ...
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1answer
39 views

Question on the Notation of an Abstract Algebra Question

The following is a question that I came across in a textbook I'm reviewing for self-study. The book is "Introduction to Abstract Algebra", 4th Edition, by W. Keith Nicholson. I have a question both ...
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1answer
25 views

Concerning the notation $\chi (U)$ in one of the hypothesis for some properties of curl and divergence

I have the following exercise: Let $U \subset \mathbb{R}^3$ be open, $X \in \chi (U)$ and $f \in C^{\infty}(U)$, prove the following: $$curl(\nabla f)=0 \\ div(curl(X))=0 \\ curl(f.X)= f.curl(X)+(\...
1
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1answer
23 views

Partitions: reading skew diagrams?

Consider the following two partitions. Partition $\lambda=4^4=(4,4,4,4)$ o o o o o o o o o o o o o o o o And partition $\mu=(4,2,1,0)$ ...
3
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2answers
77 views

$A^\dagger$ - how to handwrite this?!

In one book I came across the notation $A^\dagger := \overline{A}^T$. But how does one usually handwrite it? When I try to do it, it seems so similar to $A^+$
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1answer
46 views

Is there a blackboard bold letter for the set of Boolean numbers? [duplicate]

Is there a symbol (e.g. $\mathbb{B}$) for the special set of Boolean numbers or values; ${0,1}$ or ${True,False}$?
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3answers
55 views

What is $\mathbb{Z_{n}}\left [ x \right ]$

Question: Show that $\mathbb{Z_{n}}\left [ x \right ]$ has characteristic $n$. What does $\mathbb{Z_{n}}\left [ x \right ]$ stands for? I'm very sure this is not the gaussian ring.
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1answer
28 views

Enunciating utility maximization problem using set theory

I need to enunciate a problem using set theory and I am not sure how to start. The problem goes like this: You are a car manufacturer and need to decide how many colours to use in your next bash of ...
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1answer
15 views

How does variable ordering in expressions work when creating functions from an equation?

I'm having a really hard time understanding some aspects of functions, i've tried looking around on Khan academy and haven't quite found something to answer my question, i'm sure i'm overlooking ...
1
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1answer
54 views

What mathematical notation can use for this formula

I just played around with archimedes $\pi$ formula and ended up with $\pi = \lim\limits_{n \to \infty} 6 \cdot 2^n \cdot \sqrt{2 - \sqrt{2 + \sqrt{2 + ...n times... \sqrt{2 + \sqrt{3}}}}}$ I want to ...
2
votes
2answers
53 views

$\ln(x)$ and Big O notation

I have tried to assert that $\ln(x)=O(x^0)$ a few times, but it seems fairly obvious that this statement should be false, and so I've been faced with some rightful speculation. My reason is that $$\...
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0answers
33 views

What does the middle dot in parentheses mean?

The below picture is from section 3.3.1 in this paper; I'm not familiar with the notation of using middle dots in square parenthesis. Are the authors using this simply to indicate that any two ...
2
votes
1answer
97 views

What does $ f ^ {n} (x ^ {1/n}) = … $ mean?

I was asked to check whether the sequence of functions $ \{ x_{n} (t) \} $ defined as $$ x ^{n} _{n}(t ^ \frac{1}{n}) = \begin{cases}n, & t \leq \frac{1}{n} \\\frac{1}{n},& t > \frac{1}{n}...
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2answers
72 views

Is this notation on the restriction of a function in group theory common?

If $f: X \rightarrow Y$ is a function between sets $X$ and $Y$, then a common notation to use when we want to restrict $f$ to a certain domain $X' \subset X$ is $f|_{X'}: X' \rightarrow Y$. I'm doing ...
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1answer
45 views

What the sign ' | ' stand for?

Going through a proof of a theorem, I encountered the following statement: $e\mid a/d$, $e\mid b/d$ Then, $a/d = ex$, $b/d = ey$ where $x,y$ belongs to $\mathbb{Z}$. However, my question ...
2
votes
1answer
42 views

What does $X_j \approx X$ mean when used in this blog post?

I was trying to learn disjoint union topology and used the following blog : https://drexel28.wordpress.com/2010/04/02/disjoint-union-topology/ The second theorem about disjoint topology says that if ...
0
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0answers
27 views

2 dimensional Real space set notation

Is there such notation as: $\Bbb R^2_+$ Like $\Bbb R^2$ but with strictly positive numbers? Or is there better notation for such a set?
5
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1answer
104 views

Who introduced the notation $\lesssim$?

Who in history introduced the notation $X\lesssim Y$ for meaning $X\leq CY$ for some constant $C$? I've seen this notation in modern literature in PDE a lot. (See for instance the notation section of ...
0
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1answer
51 views

What does $q\%p$ mean

Sorry for such a simple question. In notes on quadratic reciprocity there was a phrase replace $q$ by $q$%$p$. $p$, $q$ are odd primes. What does that mean? Thanks
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0answers
39 views

Applying Bayes Theorem to find the probability of a finite intersection of events

I have a notation problem. Let $A$ and $B$ be events such that $P(B)\ne 0$. The by Bayes' theorem, $$ P(A \cap B) = P(A|B)P(B)~~~~~~~~~(1) $$ Similarly, $$ P(A\cap B \cap C) = P(A|B \cap C)P(B\cap C)...
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0answers
14 views

Nested conditional function

I have a number of equations that I am solving in steps so that the answer to preceeding steps affects the answer to the current and future steps. This leads to a number of conditional functions, but ...
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1answer
44 views

Gröbner basis is not a vector basis?

We use the same notation for Gröbner basis and vector basis. I recall that $\langle 1\rangle_{GR}$ is the largest Gröbner basis while $\langle 1\rangle_{vector}$ is the smallest vector basis. So for ...
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0answers
34 views

Basis of all real polynomials?

I am studying the book Topics in Algebraic Graph Theory by Beineke et all and the page 12. By the book, the set of all real polynomials can be generated by the set $\{1,x,x^2,\ldots\}$ which I ...
3
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0answers
34 views

Why does (h,k) generally represent the center of a circle?

Why are h and k generally used to denote the coordinates of the center of a circle? After a bit of research, we found that h may represent "horizontal shift" or "horizontal translation", but we're ...
2
votes
1answer
52 views

A little help on mathematical notation and on the definition of a manifold

I was going through the mathematical definition of manifold and it defined it as follow : " A topological space, $\ M $ is an n-dimensional real manifold if there is a family of subsets $\ U _\alpha $...
26
votes
3answers
4k views

Is there a sign for 'not less than', 'not greater than', etc.?

I was wondering about this, just now, because I was trying to write something like: $880$ is not greater than $950$. I am wondering this because there is a 'not equal to': $\not=$ Not equal to is an ...
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0answers
43 views

The notation of 'greater than or equal to'.

I've known that the following marks are equal. However, both marks are used in the same book. I was wondering whether there is some difference between them.
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0answers
35 views

Why “deformation retracts to” instead of “deformationally retracts to”?

First, correct me if I'm wrong: I grammatically understand "X deformation retracts to Y" as "X(subject) deformation(adverbial) retracts to(verb) Y(object)". But I just don't understand why we don't ...
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1answer
31 views

Is $\forall x \in U: f(x) \in V$ the same as $x \in U \implies f(x) \in V$?

As the title says, do the following two statements have the same meaning? $$\forall x \in U: f(x) \in V \text{ (for all $x \in U$, $f(x) \in V$)}$$ $$x \in U \implies f(x) \in V \text{ ($x \in U$ ...
2
votes
1answer
78 views

Notation i.i.d sample

I am learning measure theory and sometimes I am not sure if I am using the correct notations, especially with respect to distributions of random variables. In the following I try to formulate the ...
2
votes
2answers
67 views

Is there any difference between $\sum_{ij}$ and $\sum_i\sum_j\;?$

I was reading Tensors by Feynman, where he said: [...]$$u_P=\tfrac{1}{2}\sum_i\sum_j\alpha_{ij}E_iE_j\;.\tag{31.7}$$ The energy density $u_P$ is a number independent of the choice of axes, so ...
0
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2answers
33 views

How to express that one interval is included in another interval?

Would the symbol "$\in$" work for denoting that one interval is included in another interval? Like this: $(x>2) \in (x>0)$
1
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2answers
33 views

Quantum group notation

I was jumping into the deep end and reading a few papers and lectures on quantum groups. My knowledge on Lie algebras is a bit thin but I was just wondering the notation used in the starting of this ...
0
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2answers
15 views

Name for opposing (complementary) multisets (bags)

I am looking for the accepted mathematical name for opposing multisets (or complementary multisets). I have done a Google search and a Stack Exchange search, and have come up empty. These are the ...
3
votes
2answers
47 views

What's the notation of the one-sided differential of a function?

Assume $$f(x)=\left \{\begin{matrix} x-1 & x \leq 0\\ x+1 & x > 0 \end{matrix} \right.$$ Obviously, $df(x)/dx$ do not exists at $x=0$ but the one-sided differential exists. What's the ...
0
votes
0answers
27 views

Show that $(\log(n))! = \Omega(n^3)$

I want to prove that $(\log_{2}(n))! = \Omega(n^3)$. I Think that $(\log_{2}(n))! = \Theta({\log_{2}(n)}^{\log_{2}(n)})$ But, I dont know how to continue. Someone has an idea ? Thanks
0
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2answers
40 views

How are these different types of notation called?

My teacher used to give questions on integrals of vector fields with different notation to get us used to seeing things in different forms. I'm just wondering what these three different forms of ...
3
votes
0answers
32 views

Origin/history of mixed number notation with misleading hyphen, e.g. 1-1/2

So there is a system of writing mixed numbers (that is, a combination of whole number and fraction, used instead of an “improper” fraction) used in cases where typing vulgar fractions (e.g. ½) ...
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votes
3answers
99 views

What does the mathematical symbol with an underline below the variable name mean?

I have been reading a research paper. The author has used a variable '$x$' with an underline beneath '$x$'. I know that a variable with with a line on top of it implies it's arithmetic mean. But I ...
2
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1answer
73 views

which odd integers $n$ divides $3^{n}+1$?

I don't understand this solution to this problem. Can anyone explain why d divides n?
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1answer
45 views

How to represent a nested loop using mathematical formulae [closed]

Excluding the context of summation or product, how can one represent a nested loop within mathematical notation? For instance, if every element of an array X is being compared to one another as part ...
1
vote
1answer
46 views

What is the origin of PEMDAS?

While working on a compiler's grammar to follow this, It occurred to me that although it's something we are all taught to and simply follow, I don't know the origin or the reason we do it in the first ...
3
votes
2answers
66 views

What does $\mathbb{Z}/n \mathbb{Z}$ mean in abstract algebra?

If you look at this wiki page under the image on top of right hand side, you see $\mathbb{Z}/ \mathbb{8Z}$. What does it mean and give example if possible please thanks.
5
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2answers
87 views

Is it weird to say $A \in B \in C$?

I've just noticed that I've never seen any text say $A \in B \in C$, which is why when writing it myself it immediately looked weird. For context, I was proving a result about the topology $\mathcal{...
1
vote
1answer
29 views

Two different notations for inner product

In my linear algebra course on the faculty of mathematics, we used the following notation for the inner product: $$\langle v, w \rangle$$ On the other hand, my friends from the faculty of physics ...
0
votes
1answer
32 views

Why the separate notation for norm

One usually denotes the norm as $\|\cdot\| $, $\| v\| := \sqrt{\langle v, v \rangle}.$ However, in metric spaces, one often writes $d(x,y) \equiv \lvert x-y \rvert$. Since the norm canonically ...
11
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6answers
762 views

When can we not treat differentials as fractions? And when is it perfectly OK?

I am a first year calculus student so I would prefer if answers remained in Layman's terms. It is common knowledge and seems to me a mantra that I keep hearing over and over again to "not treat ...