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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7
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1answer
118 views

The meaning of a definition involving multiple sums with Bernoulli numbers

Reading a paper regarding Bernoulli numbers, and I stumbled onto a definition. First let $$\frac{x}{e^x-1}=\sum_{k=0}^{\infty}B_k\frac{x^k}{k!}$$ The author then goes on to define new terms. Let ...
0
votes
0answers
79 views

Does there exist some kind of irreversible transfomations on maths?

I know that this kind of transformation by itself without control can lead to contradiction because its value changes depending on the state of the function where you do the transformation. Anyway I ...
4
votes
1answer
167 views

Unfamiliar notation in an AoPS paper

Here it is, from this paper: Proposition 5.1.1. The number of skyline polyominoes of area $A$ and width $w$ is $\left(\!\binom{w}{A-W}\!\right) = \binom{A-1}{w-1}$. I'm referring to the first ...
0
votes
4answers
57 views

Can someone explain the meaning of \ in operations with sets? [duplicate]

I have never faced with such operator... what does '\' mean? Does this expression make any sense? (A ∪ B) \ C = A ∪ (B \ C)
0
votes
1answer
30 views

Question about sums with a negative limit for the index

To me, it looks like we have $\;\sum_{i = 1}^{0} x_i = 0\;$ and $\;\sum_{i = 1}^{1} x_i = x_1\;$. What happens if I write the following? $$\;\sum_{i = 1}^{-123} x_i\;$$ Would this be defined?
0
votes
0answers
60 views

Is there a notation for the set of zero divisors?

While the multiplicative subgroup $R^*$ denotes the set of units, I wonder whether there is a notation for the set of zero divisors. It's quite painful to me everytime I write down zero divisors..
0
votes
0answers
27 views

Notation for bounds on derivative

I am working on a problem where the assumptions are that some derivatives are bounded. I want to refer to the individual bounds in the proof but there are about 7 of them in total. I am wondering if ...
0
votes
2answers
89 views

Correct notation for union of all elements in a set?

Say I have a set $H$ and I want to describe the union of all elements in $H$. How would I write that? I believe I've seen a big U with a subscript used before.
2
votes
1answer
87 views

Confusion about Notation for Bayesian Statistics

I'm currently trying to learn Bayesian Statistics but I keep losing time trying to figure out what exactly is meant by notation. Could someone answer the following for me? Let's say $X \sim ...
2
votes
2answers
291 views

Shorthand notation for partial?

If I am taking a regular derivative, and I want to show the process in detail, I'll do something of the sort $f'(x) = g'(x) + h'(x) - l'(x) ..... $, etc, using that "prime" notation. However, what ...
1
vote
2answers
321 views

Meaning of : Set is closed under finite intersections and arbitrary unions

I have been working through "Set theory for working mathematician" and near the end of chapter about real numbers there is a small bit of topology. Namely the natural topology $\tau$ on euclidean ...
2
votes
1answer
91 views

Is this notation nonsensical?

I know personally made notations are generally a bad thing, but I've not seen any reason to stop using the notation I've made, and it feels more natural to use. Now, this my seem like a biased ...
1
vote
2answers
65 views

Notation: is a factor of

How can one write $x$ is a factor of $y$ (as a constraint)? I am also not sure what else to add to meet the question quality requirements.
0
votes
0answers
19 views

Notation for operator that returns square of a function?

Let $F$ denote the vector space of all real-valued continuous functions on the real line. Suppose I have an operator $T:F\to F$ such that for any input function $f \in F$, $T$ returns the square ...
2
votes
0answers
28 views

Hadamard original notation for global inversion theorem

I'm reading the original article of J. Hadamard: "Sur les transformations ponctuelles" (1906). He considers "la plus petite valeur du rapport" (the minimum value of the ratio): ...
2
votes
1answer
87 views

Probability notation question: differences between undergraduate and graduate texts

Suppose $X$ is a random variable. In most undergraduate math texts, one writes the expected value of $X$ as $\text{E}X$ or $\text{E}[X]$. Similarly, the probability that $X$ is greater than some value ...
1
vote
1answer
76 views

Unit vector symbols/names

I am currently studying vectors and matrices in 3 dimensions, my book calls the unit vectors i j and k, however I have seen them being called in other ways, such as: x-hat, y-hat and z-hat; or simply ...
1
vote
0answers
42 views

Using upshape (non-italic) variables in mathematics

I was reading some answers from this user of MSE: http://math.stackexchange.com/users/242/bill-dubuque And I noticed that this user sometimes uses italic variable names, and sometimes he uses upshape ...
1
vote
1answer
40 views

clarification of notation for partial derivatives

its been a while since i did vector calculus and i am a little bit rusty on the notation, can someone please tell me if this is true: $\nabla_\mathbf{a} C = \dfrac{\partial C}{\partial \mathbf{a}}$ ...
2
votes
2answers
62 views

If $q$ is a prime $\leq p$, then $q$ divides $p\# − q$

If $q$ is a prime $\leq p$, then $q$ divides $p\# − q$ What does this mean? I know that it is related to something which I have been studying, but what does $p\# − q$ mean? I am only beginning to ...
1
vote
1answer
40 views

Group Theory Formatting Question

I apologize if this was posted already somewhere. I looked but had trouble describing it. My only question is what the overline means in this situation. I do not need help with the actual problem. ...
7
votes
3answers
139 views

Notation For Complex Numbers

I have seen many different notations used for complex numbers. Does it make a difference which notation is used, or is any one notation more standard than another? I see a+bi at ...
0
votes
0answers
75 views

Notation for ensemble average with respect to variable or index?

If I have a variable $x_{ij}$ I want to ensemble average with respect to $i$, what is the standard way to write this? Is a subscript often used with angle brackets? \begin{equation} y_j = \langle ...
1
vote
1answer
54 views

One Half of a Primorial

Is there a name for a half primorial? How should a half primorial be notated? The first three primorials are 2,6, and 30. The first three half primorials are 1,3, and 15. I have found that the half ...
1
vote
1answer
33 views

What does this matrix operation mean?

If T is matrix what is this operation? What's name of operation?
1
vote
4answers
80 views

Why is $\frac{d^n}{dx^n}(y(x))$ the notation for the $n$th derivative of $y(x)$, instead of $\frac{d^n}{d^nx}(y(x))$?

I've always wondered why the numerator is $d^n$ while the denominator is $dx^n$ instead of $d^nx$ like the numerator. I must be missing something very obvious or fundamental. Is this notation derived ...
0
votes
1answer
87 views

How can I write the given statement using mathematical symbols

How do I write this in mathematical symbols: "Result is equal to the sum of product of $a(i)$ and $b(j)$ when $i,j$ are natural numbers and satisfy the property $i+j = k$"? I forgot to add one more ...
1
vote
3answers
49 views

Notation For the $n$th Prime

What is the standard notation for the $n$th prime? How would I notate the prime that is $n$ more or less than the $n$th prime? I have seen notation for the $n$th prime on various webpages, but I am ...
0
votes
0answers
54 views

What is the meaning of this notation in algebraic geometry (from /): $k\left[x_{1},\ldots,x_{r}\right]\mathbf{/\left(f_{1},\ldots,f_{r}\right)}$?

I have stumbled on something is apparently a trivial concept, but the difficulty is that I haven't seen this notation before. Here is the fragment of a text from lecture notes: Let us call $\rho$ ...
3
votes
0answers
32 views

What is the product of an empty family of similiar algebras, that is $\prod\langle \mathbf{A}_i \ | \ i \in I \rangle $, where $I = \emptyset$?

What is the product of an empty family of similiar algebras, that is $\prod\langle \mathbf{A}_i \mid i \in I \rangle $, where $I = \emptyset$? The family $\langle \mathbf{A}_i \mid i \in \emptyset ...
1
vote
2answers
37 views

Clarification over product of products $\prod$ notation

This might be a trivial question to ask in this forum but I would like some clarification over a particular formula. Suppose we are given $$f^{eq}_i=\rho ...
0
votes
1answer
32 views

Confused by indicial notation term $u_{j,ij}$

I am confused by the indicial term $u_{j,ij}$ and cannot find it treated in discussions of tensor/indicial/Einstein notation even though it is an important term in linear elasticity. Working off ...
0
votes
1answer
51 views

Notation in Hartshorne book about monoidal transformations (blow-ups of surfaces along points)

I'm starting the process of learning the concept of blow-up for surfaces along a point. At page 386 of Hartshorne's book, the author defines the monoidal transformation of a surface $X$. But at the ...
0
votes
1answer
50 views

Notation with regards to percentage and order of magnitude - little dot next to percentage sign.

Is anyone able to tell me if there is some notation that means 'an order of magnitude' or '/10' on a percentage value? I have a graph (see below) from a journal and the y-axis values are more than I ...
-5
votes
2answers
155 views

What is a short hand for random variable X, Y independent?

In some of the textbook problems, it would say, suppose X and Y are zero mean, unit variance independent Gaussians... I would usually just write $$X,Y \sim \mathcal N(0,1)$$ and this is a nice short ...
1
vote
1answer
52 views

Notation interpretation

Consider the set $$\Bbb R^n :=\{x=(x_1,...,x_n):x_1,...,x_n \in \Bbb R \}.$$ For $x,y\in \Bbb R^n$, we define $<$ as below: $$ x<y \iff \exists j \in \{1,..,n \} \left( x_j<y_j \wedge ...
1
vote
1answer
64 views

Meaning of $S^{-1}R$ notation

Here are objects defined in an exercise: Let $R$ be a commutative ring. Let $A$ be an ideal of $R$ and $S=\{1+a\mid a\in A\}$. The exercise then makes reference to the prime ideals of $S^{-1}R$. ...
6
votes
3answers
208 views

What does $23_4$ mean?

I just saw this on a mathematical clock for $11$, i.e $23_4=11$: http://ecx.images-amazon.com/images/I/51nsaGqFoUL.jpg I guess it is some notation from algebra. But since algebra was never my ...
0
votes
2answers
72 views

Birational map and birational morphism in algebraic geometry

In algebraic geometry do the two terms "birational map" and "birational morphism" indicate the same object? By reading wikipedia the answer seems to be NO: A birational map from $X$ to $Y$ is a ...
0
votes
3answers
193 views

What is the meaning of $\log^2n$ and how should it be read in word form?

$\log^2n$ is what I need assistance with. How is this read in word form? What exactly does this mean? No matter how much I read about logarithms, they still seem new to me.
0
votes
2answers
149 views

Best practices in notation

I have already read A Primer of Mathematical Writing, by Steven Krantz which gives extremely good advice about writing mathematics. But I would like to collect some more specific suggestion about ...
1
vote
1answer
55 views

Is there a name and/or notation for arbitrary sum of sums?

I am looking for information about sums of the form: $$\sum_{i=1}^n \sum_{j=1}^i f(j)$$ But not just that form, but arbitrarily many stacked sums. Even just a name would help. To be specific about ...
0
votes
1answer
31 views

Is $y(x)=\alpha \sin^2(\beta x+\gamma)$ a sinusoidal function?

Is $$y(x)=\alpha \sin^2(\beta x+\gamma)$$ a sinusoidal function? I know it can be alternatively represented as $$y(x)=\frac12 (\alpha-\alpha \cos(2\beta x+2 \gamma))$$ Can this be transformed to ...
1
vote
2answers
10 views

Notation for an Unknown in an Equation that Represents a New Variable with Every Invocation?

If you have: a*a*a you can represent it as: a^3 Is there a similar notation to collapse ...
2
votes
1answer
186 views

What Notation Do I Use To Fix Ambiguity Writing Chain Rule

I'm a calculus noob learning over the internet. I think the best way to ask my question is just to put up a little diagram I made in paint. Now this is my attempt to write the chain rule using d/dx ...
0
votes
1answer
23 views

What would the Big oh be of (1/2)^n

Is it just (1/2)^n? The function itself gets closer and closer to 0 as x > infinity but I don't know what its classification would be in terms of big oh. O(1)?
0
votes
2answers
25 views

Notation for summation while skipping elements

Suppose I have a summation like so: $\sum_{i =0}^n l^i$ Except I don't want to compute for all $0 \leq i \leq n$. I just want to compute it for the arithmetic sequence: $1, 3, 5, 7, 9...$ How do I ...
3
votes
1answer
55 views

What is (DIVIDE TIMES) for?

I looked "⋇" up on Google and now I know that it's Unicode U+22c7 but when would it be used? I am guessing that 5 ⋇ 5 = 25 and one...?
0
votes
0answers
27 views

Module notation

Suppose I have a ring $R$ whose underlying group is $G$. Now suppose I read the definition: Let $M$ be an $n$-dimensional left module over $R$. Is this a conventional way of defining $M$ as ...
0
votes
0answers
56 views

Notation of measures $d \mu$

I am reading the paper http://www.ams.org/mathscinet-getitem?mr=3246935 and there some notation that I have found a bit confusing on page 1503 between Lemma 4.2 and 4.3. I'll give as much context as I ...