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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0
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3answers
108 views

Dumb percentage question?

Why do we multiply by 100 while calculating percentage ? example : 2/100 * 100 =2%
0
votes
1answer
72 views

Confusion with the meaning of a notation

An elliptic operator $L$ is called uniformly elliptic if $a^{ij}(x)\xi _i\xi_j \ge \theta|\xi|^2$. What does this notation mean? All I can find about it is that it is some kind of summation notation ...
2
votes
2answers
284 views

What does the notation “$\Omega \subset \mathbb{R}^n$ is $C^1$” mean?

In my calculus 2 lecture notes, we have the following definition: A region $\Omega \subset \mathbb{R}^n$ is $C^1$ (or $C_{pw}^1$ or $C^k$ respectively), if for each point $x_0 \in \partial \Omega$ ...
1
vote
2answers
73 views

What is the preferred symbol to indicate the least positive number to start a sequence?

I need a least positive number and I am considering $\delta$, $\epsilon$ and $\theta$. Which one would be best to start a sequence? Are there any others I should also consider? Edit: ...
0
votes
1answer
74 views

formal expression of $\tilde{z}$ is the nearest from z

$h = distance(z, \tilde{z})$, where $\tilde{z}$ is the element that is nearest from $z$ (that is, distance(z, $\tilde{z}$) is smaller than distance(z, any_other_z)). Is it possible to expression this ...
2
votes
2answers
129 views

Are there “variables/unknowns” for operations?

We use letters for unknowns/variables: $x^2=4$ Are there variables/unknowns for operations too? $8 \star 7 $ With the $\star $ being any operation.
1
vote
2answers
128 views

How do I have to interpret $\mathrm{nm}^2$?

My short question: How many $\mathrm{m}^2$ are $\mathrm{nm}^2$? Do I have to interpret it as $\mathrm{nm}^2=(\mathrm{nm})^2=(10^{-9}\mathrm{m})^2=10^{-18}\mathrm{m}^2$ or shall it be ...
1
vote
1answer
67 views

How is $I_{[0,\infty)}(t)$ defined?

How is $I_{[0,\infty)}(t)$ defined? This must be a notation in probabilty theory.
2
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1answer
62 views

Can ≈ be used to express an arbitrarily rounded rational number?

Is it a formally acceptable use of ≈ to express a rational number rounded to an arbitrary number of significant digits? For example, $\frac{4}{7}\approx0.57.$ If formally acceptable, is it expected? ...
2
votes
1answer
164 views

Question on meaning of a symbol: long thin C

I don't know how to write it in $\LaTeX.$ It is a tall skinny bold C. This is the context: A set is defined by: where $\complement\atop{\smash \scriptstyle i}$ is the thing I don't understand. The ...
0
votes
1answer
80 views

Do function with the following property have special name?

I'm writing "a structure preserving surjection" way too much when I need to refer a function of the following property: $$ Y \subseteq Z, X \subseteq Z. g: Z \to A, g \text{ is some fixed ...
44
votes
10answers
2k views

Have there been efforts to introduce non Greek or Latin alphabets into mathematics?

As a physics student, often I find when doing blackboard problems, the lecturer will struggle to find a good variable name for a variable e.g. "Oh, I cannot use B for this matrix, that's the magnetic ...
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1answer
78 views

What is the usual meaning of the notation $ \| f \|_{C^k (A)}$?

If $f \in C^k ( \mathbb R)$ and $A \subset \mathbb R$, what is the usual meaning of the notation below? $$ \| f \|_{C^k (A)} $$
0
votes
2answers
80 views

order of operations division

Very dumb question: What is the order of operations in the following: PEMDAS a/b+c = a : b + c (where ":" is the division symbol) 7/1+6 or 7:1+6 in the example below is it 1 or 13?
2
votes
2answers
558 views

Direct sum of Hilbert Space subspaces - Notation?

This is a really basic question sorry, I just need to make sure I have my understanding correct. Given an infinite dimensional Hilbert space $\mathcal{H}$ and two subspaces, also Hilbert spaces, ...
1
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2answers
41 views

Does $\beta_{0,i}$ mean the same as $\beta{_0}_i$?

I have two vectors of variables, $X$, and $\beta_0$ that I am writing about. Each are indexed by $i=1,\ldots,n$ If I want to talk about $X_i$ and $\beta_{0_i}$, using ...
7
votes
2answers
1k views

What is the meaning of $\bigvee$ (bigvee) operator

What do mean $\bigvee$ operator in page 6 of this document. It is a Variable-sized Math Operator. What about $\bigwedge$?
1
vote
2answers
217 views

What does this mean: $\mathbb{Z_{q}^{n}}$?

I can't understand the notation $\mathbb{Z}_{q}^{n} \times \mathbb{T}$ as defined below. As far as I know $\mathbb{Z_{q}}$ comprises all integers modulo $q$. But with $n$ as a power symbol I can't ...
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0answers
2k views

Capital and small letter function notations

Why are some functions denoted by capital letters? For example, an ODE is represented by the equation $F(t, y, y',\ldots, y^n) = 0$. Here, what I understand is that F is actually a multivariate ...
3
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0answers
89 views

What's this called? $\mathbb{C}[d/dx]$

The 'ring of differential operators wrt x' ? Thx.
1
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2answers
198 views

How to denote a “boolean” (on/off, 1/0) variable in mathematics?

Is there any conventional notation for variables that can only take the value 0 or 1? (I'm looking for something of the nature of an overbar, a caret, etc.)
1
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1answer
134 views

Expanding out summation signs

I am trying to follow along in a textbook (Boas: Mathematical Methods in the Physical Sciences) and I have a problem understanding how to expand the following summation signs. (They are unrelated to ...
2
votes
5answers
876 views

Notation for powers of trigonometric functions [duplicate]

Possible Duplicate: $\arcsin$ written as $\sin^{-1}(x)$ When I learnt the trig identity $\sin^2\theta + \cos^2\theta \equiv 1$, I learnt that $\sin^2\theta = (\sin\theta)^2$. So why isn't ...
1
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0answers
142 views

Notation for Cartesian power, an oddity in the international standard

The Cartesian product of $A$ with itself $n$ times is normally denoted using superscript notation $A^n$, and this what ISO 31-11 defined as standard. However, ISO 31-11 has been superseded by ISO ...
3
votes
2answers
108 views

Definition of S(n) for graded ring S

In Hartshorne's Algebraic Geometry, the twisting sheaf of Serre $\mathscr{O}(n)$ is defined to be $S(n)^\sim$, where $S$ is an $\mathbb{N}$-graded ring. But I couldn't find the definition of $S(n)$ ...
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2answers
884 views

What does sup mean?

I found this formula regarding calories burned: Rate per Pound (Cal/lb-min)=A+BV+CV.sup.2 +KDV.sup.3 where: V=Running Speed (mph)--limited to a minimum of 3 mph and a maximum of 14 mph ...
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1answer
313 views

$\int f(x) dx $ is appearing as $\int dx f(x)$. Why? [duplicate]

A few of us over on MITx have noticed that $\int f(x) dx $ is appearing as $\int dx f(x)$. It's not the maths of it that worries me. It's just I recently read a justification (analytical?) of the ...
7
votes
3answers
3k views

What is the difference between plus-minus and minus-plus? [duplicate]

Possible Duplicate: What is the purpose of the $\mp$ symbol in mathematical usage? Just as the title explains. I've seen my professor actually differentiating between those two. Do they not ...
1
vote
0answers
122 views

What does “depends $C^{m}$-ly on parameters” mean?

Context is probably not important. What does it mean to say "$u_{a,b}$ depends $C^{m}$-ly on $a$ and $b$"? I know what it means to say a solution depends continuously on the data (change in solutions ...
1
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0answers
48 views

Notation for a derived function that map from power set to power set [duplicate]

Possible Duplicate: Notation for image and preimage Is there a standard notation for the function $F$? $f:X\to Y$, define $F:2^X \to 2^Y$ as $F(S) = \{f(x)|x\in S\}$. Recently I have to ...
6
votes
4answers
8k views

Is there a mathematical symbol for “For every element”?

Is there a mathematical symbol that means "For every element"? I want the meaning to have similar function as an iteration, say for loop.
1
vote
3answers
126 views

Notation question. Piecewise function.

I have observed the below statement in a report. $ f(x,y) = \left\{ \begin{array}{lr} f<0 & : (x,y) \in A\\ f = 0 & : (x,y) \in B \\ f>0 & : (x,y) ...
16
votes
5answers
4k views

Contradiction! Any Symbol for?

Perhaps, this question has been answered ago but I don't aware of its existing answer. Is there any international icon or symbol for showing Contradiction or reacing a contradiction in Mathematical ...
8
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4answers
5k views

Symbol for finite

I understand there is a symbol for infinite. Is there one for finite? I searched and found there is none. How is finite represented symbolically?
2
votes
3answers
63 views

Let $p^k$ be the $p$-component of $a^t - 1$ i.e. $p^k\|a^t - 1$

I read the above recently. What is this '$p$-component'? What does the double '$\|$' mean? It looks like divide '$|$' but not quite. I understand $p^k | a^t - 1$ but not $p^k\|a^t - 1$
1
vote
0answers
299 views

Notations for array operations

There are some common array operations that are used in programming, which I have a difficult time writing out in mathematical notation without using explicitly-indexed scalars. Some include: ...
3
votes
1answer
451 views

Notation in Munkres' $\textit{Analysis on Manifolds}$

I am trying to understand Theorem 9.1 of 1991 copy of Munkres' Analysis on Manifolds. I have stated what I don't understand below; there is a heading in bold. This theorem is a precursor to the ...
1
vote
2answers
92 views

Notation for an indecomposable module.

If $V$ is a 21-dimensional indecomposable module for a group algebra $kG$ (21-dimensional when considered as a vector space over $k$), which has a single submodule of dimension 1, what is the most ...
8
votes
1answer
273 views

$\operatorname{arsinh}$ vs $\operatorname{arcsinh}$

I note that some people like to write the inverse hyperbolic functions not with the prefix "arc" (like regular inverse trigonometric functions), but rather "ar". This is because the prefix "arc" (for ...
2
votes
2answers
106 views

Why parametrise a curve in this way (on the unit circle)?

I saw papers saying something like "let $\gamma:S^1 \times [0,T] \to \mathbb{R}^2$ parametrise a curve. The second interval above just makes it time dependent, but why parametrise (for fixed time) the ...
3
votes
1answer
88 views

Need help understanding notation

The textual description of the space $G$ is as follows: $G(\mathbb{R}^2)$ is the Banach space composed of the distributions $f$ which can be written as $f = \mathrm{div}(g)$, where ...
1
vote
0answers
89 views

Confusion with vectors and notation

Could someone please explain to me why $$\nabla (\dot{r}\cdot A)$$ take the following form in index notation? $$\left({\partial A_i\over \partial r^k}-{\partial A_k\over \partial ...
2
votes
1answer
387 views

Index notation clarification

Previously, I have seen matrix notation of the form $T_{ij}$ and all the indices have been in the form of subscripts, such that $T_{ij}x_j$ implies contraction over $j$. However, recently I saw ...
6
votes
2answers
507 views

Big Oh notation Question in calculus

In my text book, they state the following: $$\begin{align*}f(x) &= (\frac{1}{x} + \frac{1}{2}) (x-\frac{1}{2}x^2+\frac{1}{3}x^3+O(x^4))-1& ,x \rightarrow 0\\&= ...
3
votes
1answer
406 views

mathematical notation for a logical statement

The proof of the statement below is a homework question, however I did not tag this question as such since I don't need the actual proof: I have already proved the statement wring and don't need a ...
0
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2answers
107 views

How do I read this?

I received the following equation. It is supposed to contain clues to something I have to solve. I am not familiar with the math symbols used here. How do I read the following: ...
3
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1answer
108 views

Confusion with (notation in) a surface integral problem.

I encountered the following problem in a practice Advanced Calc exam, and I have an issue. Suppose $\phi:\mathbb{R}^3\to\mathbb{R}$ is a strictly positive function satisfying ...
2
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1answer
62 views

is $\frac{\{1, \ldots ,n\}}{n+1}$ proper notation when $n\geq1$?

I am trying to explain R code: (1:n)/(n+1) such that: > n <- 4 > (1:n)/(n+1) [1] 0.2 0.4 0.6 0.8 I might use ...
1
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1answer
125 views

Given an interval $I$, what does the notation $\overline{I}$ mean?

I have below a beginning of a theorem: If a function $f:I \rightarrow \mathbb{C}$ defined on an interval $I$ of length $p$ can be expanded to a piecewise differentiable function on $\overline{I}$, ...
2
votes
0answers
234 views

Understanding notation (linear continuous functional on $C[a,b]$)

Let $C = C([a,b],\mathbb{R}^n)$ be a space of continuous vectorvalued functions on $[a,b]$. Let $y \in C$, $\Phi \in C^*$ and $f \in C(\mathbb{R}^n, \mathbb{R}^n)$. What does mean a notation $$ A = ...