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
60 views

Is this “truncating” matrix function well known?

I'm working with a kind of "truncating" matrix function $\tau_r:M_{n\times n}\to M_{n\times r}$, where $r\leq n$, defined by $\tau_r(A)=B$, where $b_{ij}=a_{ij}$ for $j\leq r$. Is this a well known ...
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2answers
39 views

Notation Question $n$ $ < <$ $m$

What does the following notation mean: $n< < m$ , where $n$ and $m$ are numbers?
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0answers
23 views

If $C^H$ is the conjugate transpose of $C$ then what is meant by $C^{-H}$?

If $C^H$ is the conjugate transpose of $C$, i.e., $C^H=\overline{C^T}$ then what is meant by $C^{-H}$?. Assume that $C$ is a square matrix. I can't find a definition for this anywhere?. Can anybody ...
2
votes
1answer
49 views

A Type of Union I do not understand

I am not able to read this following union. Could someone please help me to understand it? $\bigcup\limits_ {k \geq n}${${x \in X: |f_k(x)-f(x)|\geq q} $ }
1
vote
1answer
93 views

What does $\propto$ mean in the following equation?

I have seen this question but I still have problem with the meaning of this symbol. From this book: The time-dependent angle may be defined from the components of the wave vector in order to ...
1
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3answers
82 views

Acronyms and words as variables and in mathematical notation

I am unsure if this question is warranted. Often mathematical symbols and objects are represented by a single character, e.g. variables are most often single characters like $x$, and often to ...
1
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1answer
36 views

What is the “T” set?

I am reading an engineering paper and it references a "T" set in the same way that one would reference the set of complex numbers with $\mathbb{C}$, or the set of real numbers with $\mathbb{R}$". What ...
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0answers
42 views

Notation/definition problem for commutative binary operation

I'm trying to describe/define the commutative binary operation on a three-element set which when the operands are the same, gives the same element and when they are different gives the element which ...
1
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1answer
83 views

Use of exclamation point

I'm quite puzzled by the use of an exclamation point in this paper. The authors introduce the following linear constraints to a quadratic program: $ \sum_k a^{(l)}_k b_j (\mathbf{x}_k) = r_j^{(l)} $ ...
2
votes
2answers
112 views

What does $e$ mean in this expression?

I've seen this formula $$1RM = \frac{100 \cdot w}{48.8 + 53.8 \cdot e^{-0.075 \cdot r}}$$ but I don't know what does the $e$ means. The $w$ stands for weight. The $r$ for repetitions but I think ...
0
votes
1answer
30 views

Meaning of $^sB$, s an element, B a subgroup

Let $G = SL_2(\mathbb{F}_q)$, $B$ the subgroup of all upper triangular matrices, $s = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$. What does $^sB$ mean? I read it from page 4 of C. ...
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1answer
21 views

Notation in Kronecker-Weber theorem

Sorry for the dumb question but I don't understand a notation. I'm reading the notes of Culler about the Kronecker Weber theorem (see here) and at page 3 we have a finite extension of number field ...
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0answers
56 views

Mathematical notation for first and second maximum

I have a vector $f_x = f_{x_1}, f_{x_2},\cdots, f_{x_n} $ having the frequencies for bin $x = x_1,x_2,\cdots,x_n$. Now I want to address two bins having highest frequencies. I address the highest ...
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0answers
22 views

What is the mapping of Z-transform?

Recall that given a series $x(k)$, the Z-transform $\mathcal{Z}$ is defined as: $$\mathcal Z(x(k)) = \sum_{k =0}^{\infty} x(k) z^{-k}$$ where $x(k)$ satisfies $|x(k)| \leq M\rho^k$, $M, \rho$ real ...
2
votes
2answers
67 views

Notation of expectation and random variables

I'm trying to understand the notation used at p18 of The Elements of Statistical Learning. I suspect errors in notation. What do the authors mean and, if any notational errors, what would be the ...
3
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0answers
49 views

Standard notation for indices in group theory?

I've seen three notations for indices in group theory, namely $(G:H)$, $[G:H]$ and $|G:H|$. Is there any of these notations that is standard?
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0answers
21 views

Notation or theory on functions which reorder sequences

I wanted to come up with a simple way of reordering the elements in some sequence $a=\left[ a_{0}, a_{1} \cdots a_{n} \right]$ in a specific way. My solution was to have a sequence of integers ...
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0answers
19 views

Notation for functions returning probability distributions

Let $A$ and $B$ be two sets. If $f$ is a (deterministic) function from $A$ to $B$, I can write $f : A \rightarrow B$. What if $f$ was a stochastic function and could take different values for a ...
2
votes
1answer
95 views

Question about notion $d\mu = fdv$ in Real Analysis of Folland

I'm reading the book Real Analysis of Folland, chapter 3 about signed measure, and there's some notion that confused me. In this book, he defines that $dv = fd\mu$ if $v(E) = \int_E{fd\mu}$, and ...
0
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0answers
20 views

What is the notation for 'asymptoticly approximate mapping'? If any…

I've learned about the notation 'maps to': $\mapsto$ And also asymptotic approximation: $\simeq$ Is it valid to suggest the notion of 'asymptoticly approximate mapping'? If so, what is ...
2
votes
1answer
43 views

How to correctly write definite time integration of this function?

Last time I saw an integral was something like 10 years ago, and I am having doubts about the notation I should use. I want to describe the evolution of the volume difference between two cylinders ...
4
votes
1answer
69 views

Does writing $f(x)\sim \ell$ have a sense?

If $\lim_{x\to a}f(x)=\ell$, is it correct to say that $f(x)\sim_a \ell$ ? I would say yes since $\lim_{x\to a}\frac{f(x)}{f(a)}=1$, but on a test I wrote $e^{-t}\sim_0 1$ and the corrector said that ...
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1answer
75 views

How to simplify the equation of combination?

If there are three random variables and three related thresholds, how to simplify the following expression by summation or multiply or other operators? Thank you. ...
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1answer
39 views

Has anyone ever suggested a name or notation for this operation on multisets?

A basic multiset identity says: $$A+B = (A \cap B) + (A \cup B)$$ Allowing ourselves to use negative multiplicities and rearranging: $$A-(A \cap B) = (A \cup B)-B$$ But since $A \supseteq (A \cap ...
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vote
1answer
96 views

What if there is $\downarrow$ or $\uparrow$ notation in the limit instead of $\rightarrow$?

I saw a different notation in a limit in the book Elementary Differential Geometry by A. N. Pressley : $\qquad$ If the Möbius band were orientable, there would be a well defined unit normal $\bf ...
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2answers
81 views

Notation seen in “awfully sophisticated proof…” I don't understand

I want to understand what the definition of $f_n$ given here means? I tried to seek on the net but I not succeeded. I precise I do chemistry, maths are "just" a curiosity for me. I should be glad, ...
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0answers
26 views

mathematical notation for random selection of two integers

I want the shortest mathematical notation for the below: $x =$ random$(1,2)$ where there is equal probability of selecting 1 or 2. is it correct to state: $x \sim$ U$(\{1,2\})$. If I had more ...
1
vote
1answer
47 views

Notation for subspace of Hölder Space

As mentioned, this is largely a question on notation. I'm reading Fractional Integrals and Derivatives: Theory and Applications by Samko, Kilbas, and Marichev. I'm just starting and I'm curious about ...
1
vote
2answers
64 views

Why is the 'argument' of a function named as such?

When watching some videos on various bits of mathematics, I observed the word "argument" being used to describe what is in layman's terms 'the inside of the bracket'. I can understand the use of the ...
2
votes
2answers
78 views

Why sigma notation?

Repeated union is written as: $$\bigcup_{i=0}^na_i$$ Repeated logical conjunction is: $$\bigwedge_{i=0}^na_i$$ Etc. So why isn't repeated addition: $$\operatorname{\huge+}\limits_{i=0}^n{}^{\Large ...
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vote
2answers
31 views

Mathematical notation for 'value generated from normal distribution'

What is the correct mathematical notation for expressing that say 'x is a value generated from the given range with the probability given by normal distribution with given mu and sigma'? I am writing ...
0
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1answer
41 views

Identity element of word addition

I realize this is rather an arbitrary question, but it's important to me, that I understand it and get it right, and I'm not finding the answer anywhere else. I'm working through "A Book of Abstract ...
1
vote
1answer
63 views

What is $\mid\text{det}(A,G)\mid$?

I am reading an old paper dated back in 70', where I encounter this $$\mid\text{det}(A,G)\mid=(\text{det}\{(A,G)'(A,G)\})^{\frac{1}{2}}.$$ We compute the determinant of a single matrix, don't we? ...
0
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1answer
180 views

What do double parallel lines on vectors mean? [closed]

What do the lines mean in the notation $\|u\|$ where $u$ is a vector?
4
votes
0answers
49 views

Unique Conway notation for knots?

Is the Conway notation for a knot unique? Here are two rational tangles whose closures give the trefoil knot. However the Conway notation written for the trefoil knot is usually presented as 3 in ...
0
votes
1answer
51 views

repeated exponents sign

I'm wondering if there is a exponent version of $\sum$ or $\prod$ or I've even seen a big k used for repeated division. Is there a similar symbol for exponentiation and are there any useful ...
1
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0answers
36 views

Difference between $f(.)$ over $\mathbb{Z}_q$ and $f(x)$ for $x \in\mathbb{Z}_q$

What is the difference between the two following notations. function $f(.)$ over $\mathbb{Z}_q$ . function $f(x)$ where $x$ takes values from $\mathbb{Z}_q$ I think that both are same. Is there ...
0
votes
2answers
42 views

Confusion in notations of number theory

In several materials I saw the notation for complete residue system as follows $\mathbb{Z}_n=\{0,1,2,3,\cdots, n-1\}$ But in some other materials/ in the same material, It says that the above ...
3
votes
1answer
264 views

Set Theory ZF Axioms Doubt

I have a pretty basic question about the symbolic representation of the axiom of extensionality for set theory, which states that $$ \forall A \forall B [ \forall x (x\in A \iff x\in B)] \iff A = B ...
0
votes
2answers
54 views

Why are there many notations for expected value?

I saw from literature that the expected value of a random variable $f(X)$ is either $E f(X)$, $E(f(X))$ or $E[f(X)]$. Is there a standard which one notation should one use? Is the expected value a ...
27
votes
6answers
3k views

The logarithm is non-linear! Or isn't it?

The logarithm is non-linear Almost unexceptionally, I hear people say that the logarithm was a non-linear function. If asked to prove this, they often do something like this: We have $$ \ln(x + ...
1
vote
0answers
67 views

Proof Algebraic geometry R. Hartshorne

In book Algebraic geometry R. Hartshorne I'm confused in the proof of theorem 3.4 first chapter. 1) In the first paragraph of the proof the theorem 3.4: what is the significance of "this isomorphis ...
2
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0answers
58 views

What type of diagram could this be?

Some years ago, I saw a diagram somewhat like this somewhere on Wikipedia. I remember that it was supposedly used in some branch of mathematics. Unfortunately, neither Google Image nor trawling ...
1
vote
1answer
44 views

Given $f: A \times B \rightarrow C$, what is the notation for the induced function when the right factor is replaced by $B'$?

Given a function $f: B \rightarrow C$ and a bijection $g: B' \rightarrow B$, there is a naturally induced function $f': B' \rightarrow C$, namely the composition $f' = f \circ g$. Now, given a ...
0
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1answer
157 views

How to express rounding down/up to nearest multiplum of a number?

I've written an equation in a programming language which I need to express using maths: slots = (elements_count - (elements_count % slot_size) + slot_size) / slot_size In Excel, you can also ...
21
votes
13answers
2k views

Why do we use “congruent to” instead of equal to?

I'm more familiar with the notation $a \equiv b \pmod c$, but I think this is equivalent to $a \bmod c = b \bmod c $, which makes it clear that we should put a $=$ instead of $\equiv$. What's the ...
19
votes
10answers
3k views

Entering math through the side door [duplicate]

I am not really good at math, I'd say I'm a lot worse than good when it comes to math but I am a programmer so I have to learn to get over that fact. A lot of times if I want to implement some code I ...
5
votes
2answers
186 views

Is $e^x=\exp(x)$ and why?

In the comments to this question a discussion came up wether we have $e^x=\exp(x)$ by definition and what the "correct" definition of $\exp(x)$ is. Building on that, I want to line out the problem ...
0
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0answers
24 views

Change of Coordinate Notation

I'm reading through The Mathematical Theory if Finite Element Method by Brenner and Scott. On page 71 it remarks that We will often refer to the hyperplane $\{ x : L(x)=0\}$, where L is a ...
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3answers
114 views

Given $P(A) = .4, P(A\mid B) = .5$, and $P(A\mid B') = .2$, find $P(B\mid A)$

I have $P(A\mid B) = P(A \cap B) / P(B) = .5$, and $P(A\mid B') = P(A \cap B') / P(B') = .2$ I am trying to find $P(B|A) = P(B \cap A) / P(A) = P(B \cap A) /.4$ but I cannot find $P(B \cap A)$. I ...