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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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
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2answers
44 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
43 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
16 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
14 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 ...
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0answers
35 views

Does anyone use the notation $\mathrm d^3(x,y,z)$?

I am working on a LaTeX package for typesetting differentials (yes, I know it will be only one of many). I aim at covering many different situations that may arise when dealing with differentials. I ...
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1answer
80 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 ...
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0answers
11 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 ...
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1answer
35 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 ...
3
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1answer
64 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
35 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
32 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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0answers
44 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 : what do both of $\downarrow$ and $\uparrow$ mean?
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2answers
67 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
18 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 ...
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1answer
28 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 ...
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2answers
44 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 ...
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2answers
57 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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2answers
22 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 ...
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1answer
22 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 ...
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1answer
54 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? ...
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1answer
40 views

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

What do the lines mean in the notation $\|u\|$ where $u$ is a vector?
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27 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 ...
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1answer
40 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 ...
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0answers
31 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 ...
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2answers
39 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 ...
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1answer
235 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 ...
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2answers
42 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 ...
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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 simething like this: $$\ln(x + y) \neq ...
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0answers
45 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
49 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 ...
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1answer
37 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 ...
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1answer
29 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 ...
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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 ...
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10answers
2k 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 ...
4
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2answers
152 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 ...
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0answers
14 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
89 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 ...
0
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1answer
18 views

standard notation to handle representation of a real number on a computer

Is there a standard notation to handle the effective representation of some real number $x$ on a finite machine ? I have in mind some kind of braces, but I am not sure it is appropriate. Let me try to ...
1
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1answer
35 views

Fourier series… delta notation

I'm going through the answer to a Fourier series question and have come across some notation which I haven't seen before. The question is to represent the periodic function $$f(x) = ...
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3answers
38 views

How to notate a sequence of decimals

I would like to know if there is a mathematically correct way of describing a sequence of decimal points of a given number. e.g. position 35-46 of π
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0answers
92 views

Notation/terminology for “independent” subspaces/subalgebras

Let $V$ denote a vector space (or any other kind of algebraic structure). Question. Letting $I$ denote a fixed set and $X$ denote an $I$-indexed family of subspaces (subalgebras) of $V$, is there ...
1
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1answer
60 views

Is there a “greater than about” symbol?

To indicate approximate equality, one can use ≃, ≅, ~, ♎, or ≒. I need to indicate an approximate inequality. Specifically, I know A is greater than a quantity of approximately B. Is there a way to ...
0
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1answer
9 views

Equal or approximation after initial approximation sign

I'm wondering what notation of the following two is preferred: A) $\frac{1}{3}+0.7 \approx 0.3 + 0.7 = 1.0$ B) $\frac{1}{3}+0.7 \approx 0.3 + 0.7 \approx 1.0$ I guess it depends on if you ...
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1answer
98 views

What does “span” looks like in infinite dimensional spaces? [closed]

I noticed that my prof loves to write $S = span\{v\}$ Instead of $\sum \alpha v$ or $a_1v_1 + a_2v_2+...$. Is he using "span" in a general way? What would span look like in infinite dimensional ...
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0answers
44 views

Is there a name or symbol for continuous and bounded functions?

For example, I have a function $f$ that is continuous and satisfies $|f| \leq M \lt \infty$ Is there a succinct notation to decribe this function without having to specify continuity and boundedness ...
3
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2answers
134 views

Matrix product notation

My lecturer has used some notation that I've never seen before: it is a (matrix) product symbol with a left-to-right arrow over the top. Does anybody know what this means? Thanks in advance. Edit: ...
3
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0answers
31 views

Regarding the construction of the tensor bundle

Recall the construction of the tangent bundle: we write $$TM = \bigsqcup_{p \in M}T_p M$$ and define it as the prevector bundle with local trivializations $[\gamma] \mapsto (\gamma(0), (x\gamma)'(0))$ ...
0
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0answers
52 views

Standard notation for the transform that turns a function $A \rightarrow (B \rightarrow C)$ into a function $B \rightarrow (A \rightarrow C).$

Suppose we're given sets $A,B$ and $C$. Then to each function $f : A \rightarrow (B \rightarrow C)$, we can assign another function $F : B \rightarrow (A \rightarrow C)$ by defining: $$F(b)(a) = ...
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31 views

What does $\textrm{soc}$ stand for?

I'm reading something where for an algebra $A$, there is a claim that the unique minimal, two-sided nonzero ideal is $\operatorname{soc}(A)$. What does $\mathrm{soc}$ stand for and mean in this ...