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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0answers
33 views

Is there a notation for a set of angles?

Suppose that $f:[0,180]\to[-1,1]$ given by $\theta\mapsto\cos\theta$ I wondered whether there was a notation for this domain, the principle values of a trig function? For example we would use ...
4
votes
3answers
123 views

Integration by substitution notation question

Often with integration by substitution I see (and use) the notation $ x \to \frac{\pi}{2} - x $, for the simple reason that I don't have to rename the variable that I am integrating with respect to, ...
0
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0answers
19 views

What is the appropriate way to indicate that a long statement is continued on the next line?

When handwriting a long mathematical statement or equation, what is the clearest way to indicate that it is continued on the next line uninterrupted? I've considered defining a variable to equal ...
1
vote
2answers
44 views

What does the notation $\frac{\partial(x,y)}{\partial(u,v)}$ mean?

Suppose G$(u,v) = (x, y, z)$ In terms of derivatives, what does $\frac{\partial(x,y)}{\partial(u,v)}$ mean?
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5answers
161 views

What is the difference between the relations $\in$ and $\subseteq$?

Don't they both mean that something is an element of a set? Are they interchangeable in some or all situations? Like: $x \in A$ ($X$ is an element of the set $A, X$ is in $A, A$ contains $X$) $x ...
3
votes
2answers
60 views

Why is there no symbol for rounding to different precisions?

I was taught in a school that one uses rounding for different precision with just the symbol $\approx$, like $13.46\approx 13.5$ or $13.46\approx 13$ depending on the situation. Why are there no ...
0
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0answers
26 views

Making sense of the Big Oh notation

I know that when you write $f(x)=g(x)+O(h(x))$, it means that for all $x$ sufficiently large, we have $|f(x)-g(x)|<M|h(x)|$ for some positive constant $M$. What I don't understand is as follows: ...
0
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0answers
10 views

Correct mathematical notation for showing the selection procedure for multiple equation solution

I have an equation that solving it results in 4 solutions for $\theta$. Only one of these solutions is correct. So, in order to select the correct $\theta$, I use a function that I already know the ...
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3answers
43 views

How to show range in equation for multiple variables?

I'd like to show in the below equation that variables $i$ and $j$ need to be chosen from the range $1$ to $n$, but I am not sure how to properly show this. Can somebody please show me the proper ...
0
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0answers
29 views

Big $O$ notation and computations

Here all the functions of natural numbers are positive.$p$ is a prime number. Let $A(n)+B(n)=C(n)+D(n)$ where $B(n)=O(p^{5n})$. $ A(n)$ is always less that or equal to $C(n)$.$D(n)$ is known to be of ...
1
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1answer
59 views

Which way is best to solve: $T(n)=5T(n/5) + n\;?$

I'm not sure which way is best to solve $$T(n)=5T(n/5) + n$$ (recursion tree/master method/recurrence?) I would like some assistance, which way is easier and how can I be sure I got the right answer ...
0
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0answers
63 views

What's the meaning of the $\Sigma^{-1}\;?$

What's the meaning of the $\Sigma^{-1}\;?$ I studied years ago that means (calculates) something special, so I wrote it down. But I can't find its meaning What's the meaning of it in matrix ...
1
vote
1answer
24 views

Is a list and an ordered set (or multiset) the same thing in mathematics?

I've wondered whether a list is the same as an ordered set (or multiset) in mathematics ? Since a list can contain the same element more than once, the above can only be true for an ordered multiset ...
0
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0answers
26 views

Notation to represent the columns of a matrix

I have a matrix $\mathbf{Q}$ and would like to represent the $j^{th}$ column-vector of this matrix. Is there a standard mathematical-notation to do that? I have seen things like $Q_{*j}$, but I am not ...
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0answers
38 views

Best books about notation

I am reading A History of Mathematical Notations and I would love to read further about the trends and advantages of different notations in mathematics, pure or applied. Is there any good book or ...
0
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0answers
39 views

Derivative Notation as a factor

In the figure below, the author uses the notation D to replace the Leibniz's notation d/dt, and after that he rewrites the equation, disconnecting the symbol of the derivative, D, of its function, ...
1
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1answer
25 views

What is the notation (if any) for series probability inclusion?

In statistics, what is the notation to use for an event $A$ in $B$ in $C$ in $D$, etc., where the series may continue for a large number of events? The following works for a few events: $$A\cap B\cap ...
3
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0answers
81 views

Funny translations of mathematical words [closed]

As already noticed in this question there are some mathematical words that literally translated from a language to english (or from english to this language) means something totally different. A few ...
0
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1answer
76 views

How to translate math technical terms?

What is a good way to translate mathematical technical terms? This can sometimes be hard because some words have different meanings in some language. For example: "eigenwert" (= "eigenvalue" ...
1
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1answer
22 views

Conditional Probability Notation

I am writing a piece of work and have a situation where I have a 'double' conditional. e.g. The event of Y = y conditional on X = x; the event X = x is also conditional on parameter z. What's the ...
0
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1answer
49 views

Question about necessary and sufficient conditions?

I am working on a question which begins with The number $\alpha$ is a common root of the equations $x^2+ax+b=0$ and $x^2+cx+d=0$. Given that $a\neq c$, show that $$\alpha=-\frac{b-d}{a-c}$$ ...
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0answers
15 views

Flow Notation over Interval

Given a section of the flow $\Phi^t(x_0)$ (for finite $t$), I'd like to denote a subsection of this flow from times $\tau^{i-1}$ to time $\tau^{i}$ using similar notation. I was considering using ...
0
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1answer
19 views

Specific order sequence as subset of other sequence

I have a certain fitness function that evaluates a sequence. An example of such a sequence is: $h = [2\ 3\ 7\ 5\ 4\ 6]$. The fitness function is defined to be $0$ if the route $h$ does not include the ...
0
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2answers
26 views

Describing Notation of a set with an odd gradient

Hello how can you describe such a set: M = { 1 2 5 10 ...} The gradient is always odd in steps of 2 Gradient 1 + 3 + 5 + 7 + ... How can you describe such a set? I need somehow 2 variables to ...
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2answers
67 views

Is there a proper term for these?

The 'square root' sign is formally the 'radical symbol'. 'Brackets' are formally 'parentheses' Is there a formal term for the 'fraction sign' or say the 'absolute value bars'? EDIT: I can see some ...
2
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0answers
31 views

Can I denote $f'(g(x))=\frac{\text{d}}{\text{d}(g(x))} f(g(x))$?

Can I denote $f'(g(x))=\frac{\text{d}}{\text{d}(g(x))} f(g(x))$? Wikipedia avoids this by letting $y=f(u), u=g(x)$ and then denoting $f'(g(x))=\frac{\text{d}y}{\text{d}u}$.
2
votes
4answers
67 views

What does P in blackboard bold type of letter stand for? ℙ?

In the first post of the thread "Cardinal number subtraction", Cardinal number subtraction there is a symbol for some kind of set which looks like this: ℙ I am familiar with symbols for natural ...
1
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0answers
30 views

Notations for interior product

There are two symbols in the Unicode "Supplementary Mathematical Operators" range whose names intrigue me 2A3C: INTERIOR PRODUCT: ⨼ (like $\lnot$ upside down) 2A3D: RIGHTHAND INTERIOR PRODUCT: ⨽ ...
2
votes
0answers
78 views

About the differential notation in measure theory

Is there any good reason for which integrating according to a measure includes a $\mathrm d$ as in $\int f\mathrm d\mu$ ? Or is it just a manner to keep formal consistency with the traditional ...
2
votes
1answer
20 views

In notation for argmin

I saw this notation for $\in$ -- I'm assuming this means "defines", right? $$\hat{\theta} \in \underset{\theta}{\operatorname{argmin}} \dfrac{1}{2} \sum_{j=1}^n (\theta^T x^j - y^j)^2$$ Does anyone ...
2
votes
2answers
18 views

general sum notation considering also not incremental indexing

I need to write a formula with summation in a general case allowing also the case with not incremental indexing. Example: $ \sum_{i=\underline{i}}^\bar{i}$ where can be ...
1
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1answer
69 views

Is $\frac{1}{ \frac{1}{x-1}}$ equivalent to $x-1$ when $x=1$?

Is $\frac{1}{ \frac{1}{x-1}}$ equivalent to $x-1$ even when $x=1$?
1
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0answers
20 views

Help understanding Wiener filtering formula

I would like some help interpreting the following formula, equation 1 from this paper: https://www.math.uni-bielefeld.de/~rehmann/ECM/cdrom/3ecm/pdfs/pant3/strela.pdf $\hat{X} = ...
-1
votes
3answers
80 views

Can $a|b$ be used to mean $a$ can be divided by $b$? [closed]

Commonly $a|b$ means $a$ divides $b$, and I've seen $a\vdots b$ be written to mean $a$ can be divided by $b$ (meaning $b$ divides $a$). But how often would there be ambiguity if you wrote $a|b$ to ...
0
votes
1answer
21 views

Understanding notation of sets

What does it mean if you have a set suppose it is denoted $\theta = R \times (0,\infty)$. I'm a bit confused what the $\times$ represents?
1
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3answers
88 views

Mid '|' in math?

What does this equation mean? What does the $|$ mean? $446617991732222310 | mn(m^k - n^k)$ Here is the complete question for reference - What is the smallest positive integer $k$, such that for ...
0
votes
2answers
47 views

What's the notation for the intersection of stabilizer subgroups on a subset?

Let $G$ acting on the the (finite) set $S$, or the (finite dimensional) space $V$. Let $s \in S$, then the stabilizer $G_s:= \{ g \in G \ \vert \ gs = s \}$. Let $R \subset S$, then there are ...
0
votes
1answer
16 views

meaning of $f_{\chi_{E}}$

given $(X,\mathcal{M})$ a measurable space, I Have $E \subset X$ and $\chi_{E}$ is an indicator function. then what is meant by $f_{\chi_{E}}$ ? I am not very clear with this notation and meaning.
1
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2answers
54 views

Does \dots imply countable?

I am given an arbitrary set $S$. If I say the following: "Suppose that the elements of $S$ are labeled $x_1,x_2,x_3,\dots,$" am I notationally implying that the number of elements in $S$ is ...
1
vote
1answer
15 views

Expressing Sub-sequences of a sequence - notation

Given a sequence $b_n = \sin(\frac{n \pi}{2})$, I am trying to show that $(b_n)$ diverges. I have the idea down, I know exactly what to do, but just not HOW to do it. I know that any convergent ...
2
votes
0answers
25 views

Tensor notation in vectors

I have the following expression $\partial_{x_a}(\partial_{x_b} \rho \partial_{x_b}\rho) - \partial_{x_b}(\partial_{x_a}\rho\partial_{x_b}\rho)$ How do I write this in vector notation? At least the ...
2
votes
2answers
93 views

Quantifier for “there is at most one”?

As "there is at least one" and "there is exactly one" both have their symbols, I wonder what is the common notation for "there is at most one"? By "common" I mean the desired notation can be used ...
1
vote
0answers
22 views

Notation - continuity limit under an integral

I'm currently showing that the following integral is continuous: $$\int_{g_1(x)}^{g_2(x)} f(x,y) dy$$ Where $g_1, g_2, f$ are continuous. I am doing this by taking the following limit: $$\lim ...
6
votes
1answer
68 views

What does ∗⇒mean?

I am still really new to mathematical notations, and I am still having difficulty understanding most of the languages and notations. A recent notation I am very confused about ...
1
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0answers
44 views

Can I improve my Chain Rule (derivative) proof?

If $f'(g(x))$ and $g'(x)$ both exist, then $$f'(g(x))=\lim_{\Delta g(x)\to 0}\frac{\Delta f(g(x))}{\Delta g(x)}\stackrel{(1)}\implies \frac{\Delta f(g(x))}{\Delta g(x)}=f'(g(x))+\alpha(\Delta x),$$ ...
0
votes
0answers
49 views

What is this symbol ($\Vdash$) called?

This symbol: $$\Vdash$$ What is it called? It is often used in modal logic, like this: $W\Vdash$. I looked for it in wikipedia/modal logic and wikipedia/logic notation, but could not find it.
2
votes
1answer
43 views

What does the notation $U(\frak{g})[[\hbar]]$ mean?

I'm reading the following motivation for studying quantum group but I'm unfamiliar with the double bracket notation in $$U(\frak{g})[[\hbar]].$$ Is this a special set of polynomials with coefficient ...
1
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1answer
50 views

Nested radicals notation

Is there any convenient notation for things like: $\sqrt{1+\sqrt{2+{\sqrt{3+\cdots}}}}$ Maybe using limits? I'm asking purely notational-wise.
0
votes
1answer
57 views

A few questions about derivative notation

$1)$ How do I denote derivative of $ax^2+b$ in terms of $ax^2$? $(ax^2+b)'(ax^2)$ can easily be confused with $ax^2\cdot(ax^2+b)'$. $2)$ How do I denote the derivative of $ax^2+b$ in terms of ...
1
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1answer
42 views

Can I denote derivative of $f(g(x))$ in terms of $g(x)$ by $f'(g(x))_{g(x)}$?

How to denote derivative of $f(g(x))$ in terms of $g(x)$ in prime (with $'$ without $\text{d}$) notation? Is it conventional to denote derivative of, say, $\sin(\cos x)$ in terms of $\cos x$ in ...