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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2
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1answer
49 views

Seperation of variables justification?

I haven't found a similar question on Math SE, but I may not have looked enough because I find it hard to believe someone hasn't already asked this. Anyways, here goes: I'm studying mathematics, but ...
0
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0answers
56 views

What is the Δ above the = symbol?

I am reading this and at equation 4.21 it has an equal symbol with a Δ above it. Do you know how this is called, and what it does? Thanks
0
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1answer
35 views

How to define a set for a matrix

I have a big matrix and I have partitioned it. So, I want to say that I am taking the summation of entries that do not belong to the blocks in the diagonal. How can I say it mathematically. Is it ...
1
vote
1answer
57 views

Dot product with scalar equal to common symbol for multiplication

I'm in Algebra 2 now, and for about 3 years I have extensively $$ a \cdot b $$ Instead of $$ a \times b $$ Now, looking into vector math for shaders, I see this is also the dot symbol is also ...
1
vote
1answer
58 views

Set notation, what does it mean

Can sonbody explain to me what does set notation of $$ C_NM\\ $$ means. The C in given notation is not letter C, it is some kind of very narrow C. I Could not find the alternative, to write. ...
2
votes
2answers
68 views

Correct notation to indicate multiplying all elements within a set

Is there a correct notation to indicate multiplying all elements within a set? For example, if $M = \left\{n_0, n_1, ..., n_t\right\}$ be the set of elements where I want to multiply all the numbers ...
0
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0answers
89 views

Identity relation of many variables

The identity relation on a set $A$ is $\operatorname{id}_A = \{(x;x) \,|\, x\in A\}$. This can be generalized for any (possibly infinite) index set $N$ as $\{(\lambda i\in N: x) \,|\, x\in A\}$ (here ...
2
votes
2answers
107 views

What does “\” mean in math

In a Linear Algebra textbook I am reading, the following is stated: $b\notin \operatorname{span}(A \cup \{a\})\setminus \operatorname{span}(A)$. It does so without explaining what "$\setminus$" means. ...
0
votes
1answer
76 views

Convention in Riesz representation theorem vs. tempered distribution theory

We are working over the complex field here. Sometimes analysis textbooks say that every continuous linear functional on $L^p$ is integration against some $f \in L^{p'}$ for $p\in (1, \infty)$, rather ...
0
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1answer
167 views

The symbol $n$? Natural numbers?

This might seem like a very basic question, but it keeps bugging me. Does the symbol $n$ mean the set of natural numbers $\mathbb{N}$ shortened to $n$ to ease writing? Or is it rather the positive ...
11
votes
1answer
178 views

Why is $e$ the Identity?

Some authors use $e$ to be the identity element of a group instead of $1$. What is the origin of this notation? Was this before or after we used $e$ to represent the base of the natural logarithm? ...
2
votes
0answers
73 views

Integrating With Respect To $x$

Suppose I have the first derivative of the function $y$, $\displaystyle \frac{dy}{dx} = g(x)$. Furthermore, suppose I want to obtain the function $y$ by integrating with respect to $x$: ...
2
votes
3answers
186 views

Equation with the big O notation

How I can prove equality below? $$ \frac{1}{1 + O(n^{-1})} = 1 + O({n^{-1}}), $$ where $n \in \mathbb{N}$ and we are considering situation when $n \to \infty$. It is clearly that it is true. But I ...
9
votes
1answer
119 views

Why an integral symbol for the category of elements of a presheaf?

Let $\mathbf C$ be a category and $P \colon \mathbf C^{\rm op} \to \mathbf{Set}$ a presheaf. One can associate to $P$ the category of elements of $P$ (also called Grothendieck construction over $P$), ...
1
vote
0answers
40 views

Notation for number of tensor permutations

I have a tensor (or set if you will) that consists of N elements, and each element has a limited number of values it can take. For example: ...
0
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1answer
51 views

Notation for a subset of a powerset

If we have a set A containing all the integers between x and y, what is the correct notation for the subset B of the powerset of A where the sets contain between n and m elements? For example if x=1, ...
15
votes
3answers
369 views

Mathematical Notation and its importance

You can see how mathematical notation evolved during the last centuries here. I think everyone here knows that a bad notation can change an otherwise elementar problem into a difficult problem. Just ...
1
vote
0answers
32 views

Do we need to pay attention to the codomain of a differentiable function?

I came across the following definitions: We call $M\subset \mathbb R^N$ $m$-dimensional $C^k$-submanifold of $\mathbb R^N$ if for all $a\in M$ there is an open neighborhood $U$ of $0$ in $\mathbb ...
0
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1answer
64 views

Confused with probabilistic notation and precedence

Is $P(A|B,C) = P(A|(B \cap C))$ or $P((A|B) \cap C)$? In my book they do something like this in a proof regarding Markov models: $P(A|B_{1:t+1}) = P(A|B_{1:t},B_{t+1}) = ...
1
vote
1answer
89 views

Ambiguous set-builder notation

I apologize in advance for the Python code below. I don't know how to express this question unambiguously in the language of math. Let $\mathcal{F}$ be a family of sets. It seems to me that $$S(x) = ...
0
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1answer
34 views

Meaning of this notation - $T = \bigcup_{B \in \beta}B$

$$T = \bigcup_{B \in \beta}B$$ Does the $B \in \beta$ mean that $T$ is a union of some arbitrary subsets of $\beta$, or does it mean that $T$ is the union of all subsets of $\beta$?
3
votes
0answers
106 views

What does $\cos(n,t)$ mean?

In the book by JL Lions "Quelques methodes...", (Chapter 2, Section 3.3, page 197), he uses the notation $$\cos(n,t)$$ in a boundary condition on a domain $\Omega(t)$, where $n$ denotes the normal ...
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vote
3answers
76 views

Why is the notation for differentiation like this?

Consider the notation for denoting the differentiation of a function $f(x)$. $$\frac{d[f(x)]}{dx}$$ I mean, this notation doesn't make any sense. $dx$ means a vanishingly small $x$, which can be ...
0
votes
2answers
545 views

Probability of a Min/Max

I am studying probability for an exam and I am finding hard to understand the notion of $P(\min(X_1,X_2))$ and $P(\max(X_1,X_2))$, where $X$ is a discrete or a continuous variable. I have found in my ...
0
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1answer
129 views

Pearson's chi square test mathematical notation

Is there any way to translate the statement below in full mathematical / symbolic notation without using any words? For example to rewrite it as a function f(A,E,x). If possible can someone show me ...
0
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0answers
11 views

Equation form representation

In an equation, when I assume that a variable is given in a specific unit (e.g. ms), I write “x (ms)”. For example, consider the following equation: $$Y(ms)=2*z+x(ms)$$ Now, if I give x in ms, Y ...
0
votes
1answer
36 views

What does the notation $f(x-0) $ or $f(x+0)$ mean?

I'm studying a book by JL Lions. In it he uses this notation, what can it mean? An example context is $f$ has a jump point at $x$ with $k(x+0) > k(x-0)$ In this case, I believe it means ...
1
vote
0answers
27 views

Distinguishing definitions from equivalences.

I'm used to people using the symbol $\equiv$ when defining quantities. I might see expressions like $$\frac{df}{dx} \equiv \lim_{\delta\to 0} \frac{f(x+\delta) - f(x)}{\delta} = 2x \,.$$ where the ...
0
votes
1answer
44 views

what does the following expression mean?

I need to make a program to calculate the values of some variables, but i am stuck at this expression. I dont really understand the meaning of the last term (Xij). I already tried searching on ...
1
vote
1answer
55 views

Notation for a defining a grid of points

I evaluated a function over a grid of points in three-dimensions. I would like to know what the standard notation is to define my grid of points? In matlab notation the grid is defined by: ...
8
votes
1answer
282 views

What are the main changes between ISO 31-11 and ISO 80000-2? (math notation standards)

The international standard that defines mathematical signs and symbols, ISO 31-11, was superseded in 2009 by ISO 80000-2. What are the main changes?
0
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1answer
30 views

Doing an operation to every number in a subscript

I'm not good with words, and neither with math, but I'll do my best. (If someone has a better title for this then...). I've been learning about subscripts recently, and things like $\sum$ and $\prod$. ...
2
votes
1answer
55 views

Notation Question for summations

I came across this notation in a textbook of Algebra. With respect to the definition of linear independence in a Vector Space $V$. We define a subset $S = \{\alpha_i \ | \ i \in I\} \subset V$ as ...
0
votes
1answer
51 views

Is there a name for this theorem about the convergence of a function?

Let $f(x)$ be a continuous function over $\mathbb{R}$ such that for all $a < b$, we have $a < f(a) < b$. Then, for any $x < b$, the sequence $\{t_n\}$ defined by $t_0 = x, t_n = ...
2
votes
2answers
148 views

Multiplying subscripts

I'm not too good with math, but once in a while I like to fiddle around with it. But one question has been bugging me lately. Let's say I have $x_{1} = 1$, $x_{2} = 2$, etc, $x_{352} = 352$. Is there ...
0
votes
1answer
42 views

Is there another notation for a characteristic of a domain of a measurable function?

Let $(X,\Sigma,\mu)$ be a measure space and $E\in\Sigma$. In measure theory language, one can prove that $\int_E f d\mu = \int \chi_E f d\mu$. Here, $\chi_E$ is not a function, but it merely means ...
5
votes
2answers
107 views

Why do we make a distinction between derivatives and partial derivatives?

The definition of a partial derivative is the "derivative of a multi-variable function relative to a single variable when all other variables are held constant". But isn't the regular derivative (for ...
0
votes
5answers
4k views

why the square root of x equals x to the one half power [duplicate]

Could someone explain how/why the square root of $x$ equals $x$ to the one half power? I know by definition it does, but is there any mathematical process we can go through to get from one to the ...
3
votes
3answers
63 views

whats the difference between $|v|$ and $||v||$?

$v$ being a vector. I never understood what they mean and haven't found online resources. Just a quick question. Thought it was absolute and magnitude respectively when regarding vectors. need ...
1
vote
2answers
60 views

What is this form of 'notation' called?

I was reading some of Max Tegmark's lecture materials and I found this little thing. Is there a name for it? Specifically, I am talking about $S_1$ R $S_2$ & $S_1$ R $S_2$ and the matrix. Is ...
2
votes
1answer
97 views

What's the difference between ]a,b[ and (a,b)?

Is there any difference between $]a,b[$ and $(a,b)$? If there is no difference, what would be the motivation of using $]a,b[$ over $(a,b)$?
0
votes
1answer
53 views

What is meant by this notation?

I found the following question: Let $\large f(x)=e^{x^2}$. Find and simplify $\large{f^{(3)}(x)}$. Is it asking to find the third derivative of the function? Which rule is used to find the ...
0
votes
1answer
124 views

Notation Question (Meaning of double inclusion symbols)

What does the notation $\subset \subset$ mean? In my class notes, our prof writes $\Omega \subset \subset \mathbb{R}^{n}$ to mean that "$\Omega$ is a convex subset of $\mathbb{R}^{n}$". Is that all ...
2
votes
5answers
91 views

What does $a$ mean in Taylor series formula?

I'm trying to code the Taylor summation in MATLAB, being Taylor's formula the following: I've also seen $a$ denoted as $x_0$ in distinct bibliography. Problem is that I'm not sure how should I ...
9
votes
3answers
301 views

Regarding the notation $f: a \mapsto b$

While I have come to understand that $f:a\mapsto b$ means that for input from the set $a$, the function will return a value from the set $b$, I am curious as to how far one may "drag" this notation. ...
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vote
2answers
109 views

Ambiguity in Reverse Polish notation

Given the infix form: 1 * 2 * 3 What is the Reverse Polish notation? As I see things, two valid answers are: ...
1
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0answers
142 views

Tensor product symbol and convolution

The convolution of $f$ and $g$ is sometimes written as $f\ast g$ and sometimes as $f \otimes g$. Is convolution denoted by both of these symbols because the operations are related, or is it just ...
0
votes
2answers
51 views

Notational Question : (a) = (b)

What does the notation (a) = (b) mean? For context, a and b are elements of a ring. I have tried to find an answer by googling, but it's difficult to do this since I am not sure what to call it.
0
votes
1answer
26 views

A notation question on how to properly denote a function that takes inputs only of a certain form.

Suppose I have a set $B = \{n^2 + n + 1 : n \in \mathbf{N}\}$ and I want to define a function $g: B \rightarrow \mathbf{N}$ that only accepts as it's arguments numbers of the form $n^2 + n + 1$ for $n ...
0
votes
1answer
54 views

Name and notation convention for “unnormalized probability”

Given a finite set of non-negative numbers $S={s_1,...,s_n}$, we can divide them by a normalization constant $Z$ (i.e. their sum) to get a probability distribution. Then we typically say (and write) ...