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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27 views

Probability and calculus notation

I just need help to make sense of some notation that I have seen on a document related to monte carlo integration. There is a portion talking about expected values of a continuous random variable ...
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1answer
30 views

What does the notation $\equiv 1\ (\text{mod}\ p)$ mean?

I'm trying to understand the Fermat theory : $a^{p-1} \equiv 1\ (\text{mod}\ p)$ I know that $a\ (\text{mod}\ p)$ gives the remainder of division of $a$ by $p$. So what is $\equiv 1\ (\text{mod}\ ...
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0answers
27 views

Operator for scaling a function?

Let $\mathbb{F}$ denote the set of functions of the form $f: \mathbb{R} \to \mathbb{R}$. I am interested to know whether there exists a well-known linear map $T_\alpha: \mathbb{F} \to \mathbb{F}$ ...
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0answers
25 views

Product notation $\prod$ when product does not commute [duplicate]

This is kind of a dubious question, but is the product notation $\prod$ often used in noncommutative rings? For example, if $M_i$ are matrices, I guess the common definition of $\prod$ is $$\prod_i ...
2
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0answers
29 views

Better notation for a product

Let $A,B$ are two positive integers. Assuming that we have a product of the form $$ \prod_{\substack{a\mid A \\ \gcd(a,B)=1}}f(a). $$ Is there a better notation to be used instead of $a\mid A$ and ...
2
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1answer
34 views

What does the following set symbol notation mean

[6] x [6] -> Z I know it's the cartesian product of [6], but I don't quite understand what [6] means? Does it mean all numbers until 6, or is another way to write {6}?
2
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1answer
17 views

Incongruencies with derivatives and differencials

I read in Piskunov that the increment $\Delta y$ of a function can be written as: $\Delta y = f'(x) \Delta x + \alpha \Delta x$ And, when ${\Delta x\to 0}$ , $dy=f'(x)dx$ The problem is, doesn't ...
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1answer
52 views

When is Leibniz' notation for derivatives useful?

So Lagrange's $y'$ and Leibniz' $\frac{d}{dx}y$ seems to be the two most common notations for differentiation, but it seems puzzling to me that there are two notations for this. I've been taught ...
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0answers
17 views

Does the diagonal of a gradient exist?

If $\nabla \cdot \vec x$ is okay, why not $\text{diag}(\nabla)\vec x$? Should we write $\nabla \vec x$ or $\nabla \vec x^\intercal$ since the result is an outer product? E.g., if I want to write ...
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2answers
17 views

Notation for the “scalarization” of a vector with a single non-zero entry

Suppose I have a vector $v$ in the complex space $\mathbb{C}^N$ with only a single non-zero element. Is there a standard notation to replace the vector with a scalar equal to the non-zero value of ...
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1answer
44 views

Understanding a weird notation when proving a theorem

I'm reading a paper that's trying to prove a theorem. However there is a weird notation that I couldn't understand. First they present the theorem and then they present two claims. In the first claim ...
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0answers
49 views

What does $V^*$ represent in linear algebra?

If $V$ is a vector space, then what does the notation $V^*$ normally stand for? Thank-you
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0answers
16 views

Explaniation of symbols in Moment of Inertia

Im looking for an explaination of what the TWO axix symbols (x,y and z) in the down right next to the capital I (Moment of Inertia) mean. I have looked on google and youtube, all my math and physics ...
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3answers
52 views

What does “wedge” mean?

In Allen Hatcher's Algebraic Topology, $X\vee Y$ means the "wedge sum" of two (topological) spaces $X$ and $Y$. However, in $\LaTeX$, \wedge is the notation for ...
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0answers
25 views

Notation for gradients analogous to partial derivatives

Is there an equivalent of partial differentiation for functions taking multiple vectors as input? I mean the following. If we have a function $f(x,y)$, then a partial derivative is denoted as ...
7
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1answer
112 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 ...
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0answers
68 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 ...
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1answer
140 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 ...
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4answers
46 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)
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1answer
29 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?
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0answers
55 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..
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0answers
19 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 ...
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2answers
46 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
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1answer
30 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 ...
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2answers
202 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 ...
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2answers
56 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 ...
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1answer
65 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 ...
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2answers
31 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.
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0answers
16 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
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0answers
16 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): ...
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0answers
30 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 ...
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1answer
50 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 ...
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0answers
36 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 ...
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1answer
33 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
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2answers
57 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 ...
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1answer
36 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. ...
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3answers
111 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 ...
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0answers
9 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
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1answer
40 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 ...
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1answer
31 views

What does this matrix operation mean?

If T is matrix what is this operation? What's name of operation?
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4answers
66 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
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1answer
53 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 ...
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3answers
43 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
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0answers
48 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
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0answers
26 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 \ | \ i \in I \rangle $, where $I = \emptyset$? The family $\langle \mathbf{A}_i \ | \ i \in ...
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0answers
14 views

Limit of multi-variable function as we only change one variable?

What would the limit be of a multi-variable function as only one of the variables moves? E.g. $\lim \limits_{x \to 0} \frac{1}{x+y}$ Is this even defined? If yes, what does it "mean"? Do we ...
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2answers
30 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
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1answer
27 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 ...
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1answer
42 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 ...
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0answers
12 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 ...