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
45 views

Looking Portable Mathematical Notation(s) [LaTeX, Mathematica, Maple, Macsyma] that are open

I'm looking for a portable Mathematical notation. What I mean by that is: I want to create a collection of (open-source) math problems that can be: Rendered for the Web or say in ePS format for ...
1
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3answers
34 views

Meaning of the word dom.

Let X be a set and $\sum$ a $\sigma$ algebra of subsets of X. Let f and g be real valued functions defined on domains : dom $f$ and dom $g$ $\subseteq X$. If $f$ and $g$ are measurable , so is $f+g$ ...
1
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3answers
54 views

Meaning of $f(x, \cdot)$

Let $(X,Σ, \mu)$ be a measure space and $(a,b)$ non empty open interval in $\mathbb{R}$. Let $f:X \times (a,b) \to \mathbb{C}$ be a function and suppose that the integral $F(t) = \int f(x,t) dx$ is ...
1
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1answer
18 views

Exercise in Taylor (PDE, volume 1) - Notation

I struggle to understand the following question. I expect I'm simply being dense about something. Let $F$ be a vector field on $U$, open in $\mathbb R^3,$ $F = \sum_1^3 f_j (x) ...
1
vote
1answer
29 views

Set builder and interval notation

My rather basic question is related to an example from Spanos (1986, p.41), which I quote (verbatim) below. Let $S$ be the real line $\mathbb{R} = \{x : -\infty<x<\infty\}$ and the set of ...
1
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3answers
30 views

Intrepreting tuples as functions

I have been mulling over this for a while now. I am told $\mathbb R^n$ can be interpreted as a set of functions. Take $\mathbb R^2$, for example I can see how we might interpret it as a set containing ...
1
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0answers
26 views

Expressing through summation subscript

I am trying to define an equation to model a psychological phenomenon such as e.g.: $B=\sum_{i=1}^k (P_{ij} T_j)$ Where $B$ is boredom, $j$ is an attribute of a given situation, $i$ is a stimulus in ...
2
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0answers
36 views

Notation of the set of subspaces

I have a very simple question. Let $W$ be a vector space over a finite field $\mathbb{F}_{q^m}$. Now consider the set of subspaces of $W$: $$\{V\:|\: V\subseteq W \; \text{is subspace}\;\}.$$ Is there ...
2
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1answer
29 views

Function representation

I am learning something about functions. So far I have only seen this kind of a prescription: $f(x)=x^2 + 2$ , for example. I am currently reading a book about functions. However, this kind of a ...
-3
votes
2answers
93 views

Can $60+60\times0+1$ be both $1$ and $61$ [closed]

The expression under debate is $60+60\times0+1$. I'm in a debate on Facebook and people that are saying $61$ and that the people that are saying $1$ are and vice versa but I'm saying they are both ...
5
votes
4answers
165 views

How does $-[-\pi]$ equal 4?

For Christmas I got a math watch and for 4 it was $-[-\pi]$. I know that $\pi$ does not equal 4 so how does $-[-\pi]$ equal 4? Thank you.
6
votes
3answers
308 views

Express “if true, then 1 else 0” in a formula suitable for Desmos calculator

In programming, often the value of True is also 1, and False is 0. This means that: (x>5)*4 will return 4 if x is greater than 5 (because ...
0
votes
2answers
80 views

Meaning of $\overline {g(x)}$

What is the meaning of $\overline {g(x)}$? To put this into context, in my notes I have, $$\langle f,g\rangle_{L_2 (\mathbb{R})}= \int_\mathbb{R} f(x) \overline{g(x)} \, dx$$ How is $g(x)$ ...
1
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1answer
17 views

In signals processing why is the discrete sequence x[n] undefined (as opposed to 0) when n is not an integer?

In Oppenheim & Schafer's "Discrete Time Signals Processing" it's written that: ... it is important to recognize that x[n] is defined only for integer values of n. It is not correct to think of ...
1
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1answer
44 views

What is the meaning of $\mathbb{N_0}$?

What is the meaning of $\mathbb{N_0}$? To put it into context, I have in my notes, $f^{(k)}$, $k \in \mathbb{N_0}$ is a continuous function on $[-\pi, \pi]$. How is it different to saying $k \in ...
0
votes
1answer
20 views

Notation for eigenvalues

Is there a specific notation for eigenvalues? specifically, I'd like to write: $$m\equiv \text{smallest eigenvaue of }H$$ I've seen some sources write this as: $H\succeq mI$, where "$\succeq0$" means ...
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2answers
35 views

What is the dot product of a function and a differential?

In a few theorems with integrals it looks like they are taking the dot product of a vector valued function or vector field and the differential. $\oint_C \textbf{F} ⋅ d \textbf{r}$ from here and ...
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2answers
37 views

What is $\sup_n f_n$?

Let $\{f_n\}$ a sequence of measurable functions on $\mathbb R^d$. What is the significance of $\sup_n f_n$ ? Is it $$\sup\{f_n(x)\mid n\in\mathbb N, x\in \mathbb R^d\}\ \ ?$$
3
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2answers
90 views

What does $\therefore$ mean

Question: I recently read the symbol $\therefore$ in a couple of posts. Unfortunately i can't find the posts anymore. Does this have any special mathematical meaning?
6
votes
5answers
147 views

What is the rule for using $| \cdot |$ and $\| \cdot \|$ in Cauchy-Schwarz inequality

In this widely cited and wildly popular proof of the Cauchy-Schwarz inequality, the authors write (http://www.math.lsa.umich.edu/~speyer/417/CauchySchwartz.pdf) Let $u$ and $v$ be two vectors in ...
1
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1answer
37 views

Notation for square root of positive-definite matrix

Why is the real square root notation $\sqrt{~~~}$ not used for matrices (as far as I know)? The square root of a matrix is not uniquely defined in general, but could the notation $\sqrt{~~~}$ be used ...
0
votes
1answer
55 views

Question about Inversion of Partial Derivatives

If I want to calculate $ \frac{\partial x }{\partial u}$ and $ \frac{\partial x }{\partial v}$ where $$u = \frac{y}{x^3}, v = \frac{x}{y^3}$$ could I calculate $ \frac{\partial u }{\partial x}$ and $ ...
0
votes
2answers
39 views

What is the difference between set notation and interval notation?

I was wondering if there is a difference between set notation and interval notation. For example is it the same to write $\{0,\infty\}$ and $(0,\infty)$? I am asking this because in variable ...
3
votes
1answer
40 views

Is there a standard notation for a sum (or product) over the elements of a set?

I would like to know if there is a standard notation for the sum/product of a function over the elements of a set. I have used the following notations before: $$\sum_{x\in S}f(x)$$ $$\prod_{x\in ...
3
votes
1answer
52 views

What does a power of $|\nabla|$ mean in the context of PDE?

I've seen the notation $|\nabla|^\alpha f$ used in a PDE setting, where $f$ is some function on $\mathbb R^n$. Could someone tell me what that means? For example in this discussion on Math Overflow ...
0
votes
1answer
89 views

Is there a recommended symbol for the empty set?

The symbols $\varnothing$ (\varnothing) and $\emptyset$ (\emptyset) are both used for the empty set. Is there an official ...
0
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0answers
15 views

Expression of $[V,W]^\mu$ for two given vector fields

I'm taking a course in general relativity and I'm trying to find an expression for the components of $[V,W]$ where $V= V^\mu \partial_\mu$ and $W= W^\mu \partial_\mu$. I am not used to the physicist's ...
7
votes
5answers
80 views

Is there a notation for saying that $x_n\geq c$ from some $n$ and on?

I am looking for something like $\lim\inf x_n \geq c$, but I need that from some point and on it is $\geq c$, not just that the limit is $\geq c$.
0
votes
0answers
23 views

Notation involving “Smooth Functions of Compact Support.”

I'm reading a paper that regularly refers to the space: $\mathcal{C}_c(\mathbb{R}^n)$ as "Smooth functions of compact support." For added context, it's used in such a way as to illustrate a special ...
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2answers
80 views

efficient way to express large numbers

I recently watched the walkthrough of Graham's Number on YouTube (Numberphile). Mind-blowing of course. I then puttered around in other large number topics like Ackerman and Tree(3) and fast growing ...
2
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0answers
36 views

Center of a Ring Notation (or lack of)

Quick question that I did not see on line or in the book I'm working out of (Abstract Algebra by Dummit & Foote). There is an example that defines the center of a ring $R$ as $$\{z\in R\mid ...
0
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1answer
13 views

Function relation notation with the cartesian product.

This excerpt comes from one of my lectures: I'm assuming that the sets A and B are example sets? If so, does that mean that if I was working with the sets X and Z I could rewrite the above as: ...
0
votes
1answer
21 views

Which are correct between notated, represented, and expressed?

I hesitated to ask this question here because this is mathematics cite. However, I think this is related to mathematical expression. My question is like the following: $$ x(t) \mbox{ can be ...
1
vote
2answers
26 views

Simple functional notation issue

I didn't learn functional notation very well and I'm not sure exactly where to find the answer for this so if someone doesn't mind explaining some pretty simple stuff that would be greatly ...
2
votes
1answer
44 views

Implication of mathematical notation

I'm a bit confused by the rules of writing in mathematical notation. In general, if I wrote $\forall x \in (0,3)$ Is it implied that the possible values of $x$ are only real numbers, or could the ...
3
votes
2answers
89 views

Notation in analysis

Could someone please explain the following notation $$||f_j||_{\infty}$$ Its used in convergence theorems but I dont understand the double lines or the infinity symbol.
0
votes
1answer
47 views

What does the following notation $\mathbb{Q}(\sqrt{3})$ mean?

I came across the notation while looking at solutions to a problem. So without going through the entire problem, I solved some polynomials and found solutions to be $$(\pm1,\pm1),(\pm \sqrt{3},0)$$ ...
2
votes
2answers
35 views

If $A \subset \mathbb{R}$, $x_0 \in \mathbb{R}$ and $h$ is an affine map, what does $h^{-1}(x_0 - A)$ mean?

I am reading a book, and it suddenly says: A distribution $\nu$ is symmetric around a point $x_0 \in \mathbb{R}$ if $h(\nu) = \nu$ where $h$ is the affine map given by $h(x) = 2x_0 - x$. As ...
3
votes
2answers
46 views

Justification for manipulations according to Leibniz-notation

Is there a way to justify the manipulations according to Leibniz-notation without nonstandard-analysis. E.g. $\frac{dy}{dx} = x \\ dy = x dx\\ \int dy = \int x dx\\ y = \frac{1}{2} x^2$
3
votes
4answers
71 views

What does $\langle X\rangle$ mean?

My notes has the following. Let $G$ be a group. Let $J = \{G_i\}_{i∈I}$ to be the collection of all subgroups of $G$ containing the subset $X ⊆ G$. We note that $G$ is nonempty, since $G$ itself ...
0
votes
1answer
29 views

Question about the notation of vectors in respect to their domains

A column vector $a$ is said to an element of R^(4) when $a$ is [1, 2, 3, 4]' (Transpose of this row vector). Therefore my question lies in the fact that I do not understand how row vectors can be ...
1
vote
0answers
35 views

On the little oh notation.

I have been told that in a fraction if we only have little ohs then we can't conclude anything taking the limit. As an example say we have $$ \lim_{x \rightarrow 0}\frac{o(x^3)}{o(x^2)}$$ then we ...
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vote
4answers
86 views

Good explanation of $\mathbb{R}^3\rightarrow\mathbb{R}^2$

I see this pretty much everywhere, but I'm still not really sure what it means. I've heard the explanation that it "maps the third dimension onto the second dimension," but even that doesn't make ...
1
vote
1answer
35 views

How do you write a function 'such that' in purely mathematical terms?

For example, say I've already defined a function $g$. Then I'd like to write, in purely mathematical terms, "the function $f$ from $A$ to $B$ such that $f(a)$ equals $g(x)$." Sometimes, I see the full ...
2
votes
2answers
58 views

What is exactly difference between $(\partial f)/\partial x$ and $df/ dx$ , Where f=f(x,y,z)?

I have a problem about meaning partial derivative.Question is following; What are the meaning difference between $(\partial f)/\partial x$ and $df/ dx$ , Where $f=f(x, y, z)$ ? For example , $f$ is ...
1
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2answers
38 views

What does exponent notation mean in logic/discrete math?

My discrete math textbook defines an expression as: $A^C \cup (A-B)$, but I am not sure how to read $A^C$. Does anyone understand what this notation means in the context of logic/discrete math?
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2answers
74 views

Limit laws when not both limits exist

In the calculus textbooks I've come across, the limit laws are given on the condition that both individual limits exist. Is it safe to weaken that condition by saying that they are valid as long as ...
3
votes
1answer
35 views

Function / Map notation?

Please forgive my ignorance, if I've phrased my question improperly. I'm not sure what the appropriate terminology is; that's the basis of my question. So, I'm not sure if I'm even remotely close in ...
0
votes
1answer
42 views

What does $\mathbb{Z}/2\mathbb{Z} \times A_n$ mean?

I know $A_n$ is the alternating group and that $$\mathbb{Z}/2\mathbb{Z} = \{0+2n\} \cup\{1+2n\} \quad n\in\mathbb{Z}$$ But I don't understand what the $\times$ operation signifies in this case?!
0
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1answer
39 views

Basic question about notation in group theory

Am I correct in thinking that it, for the group $(G,*)$ with $x \in G$ we have $x^{n}=x*x*...*x$ (n copies of $x$), with the only exception being additive groups, where $x^{n}$ does not make sense and ...