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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1answer
48 views

What does $C^{\text{1,stw}}(0,b)$ mean

I know that this C with the one means continoulsy differentiable functions but what does this stw stand for? Does anyone know this?
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2answers
130 views

what is $C^{-\infty}(\mathbb{R})$

Thanks in advance. what is $C^{-\infty}(\mathbb{R})$? Is that the same as the "distribution" defined in differential geometry? It would be helpful if someone can describe it in another way ...
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2answers
297 views

Proper Use Of Notation? (Determine whether the function is surjective)

Determine whether the function $f: Z×Z→Z$ is onto if a) $f(m,n)=m+n$. b) $f(m,n)=m^2+n^2$ c) $f(m,n)=m$. d) $f(m,n)=|n|$. e) $f(m,n)=m−n$. I was able to answer these ...
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3answers
144 views

Is adding a plus before a positive number a mistake?

I had a simple problem to find out the function equation from a sinusoidal graph. $$F(x)= -2\sin(2x)$$ Would it be considered a "mistake" to write it down the following way? $$F(x)= -2\sin(+2x)$$ ...
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2answers
4k views

Difference between formula and algorithm

What is the difference between the terms formula and algorithm in mathematics? I haven't seen the definition of formula anywhere. I know that algorithm means that Turing machine halts for every input. ...
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1answer
197 views

Using the Cauchy integral formula to evaluate $\int_{\gamma=(a,a)} \frac{z}{z^4-1} dz$.

I'm trying to understand how to use the Cauchy integral formula, but a bit confused as to how to use it as I cant seem to get the right answer! $$\int_{\gamma=(a,a)} \frac{z}{z^4-1} dz$$ where ...
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1answer
74 views

Problem converting matlab formula for relative frequency vector to mathematical formula

I have the following matlab code: ...
8
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1answer
112 views

If $H$ is a subgroup of $G$ and $x,y\in G$, what is $xHy$ called?

For a group $G$, its subgroup $H$ and $x,y\in G,$ we call $xH$ a left coset of $H,$ and we call $Hy$ a right coset of $H.$ Is there a special name for sets of the form $xHy$? Is there a name or ...
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1answer
36 views

How could I write the intersection of all sets in $S$ containing $E$ in symbols?

How could I write the intersection of all subsets in $S$ containing $E$ in symbols? Something like? $$\bigcap_{E\subset C}C$$
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1answer
39 views

Mathematical description of an identifier which consists of text and numbers [closed]

in my code I use an artificial identifier of the form UIxxx where xxx is in the range of 1 to 999. In my assay, where I describe this unique identifier I am not sure how to mathematically describe it. ...
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2answers
2k views

What does $\propto$ mean?

From this article: $\ldots$a maximum-a-postiori "a maximum-a-posteriori $(MAP_{x,k}^{\,\,\,\,\,1})$ estimation, seeking a pair $(\hat{x}, \hat{k})$ maximizing: $$p(x, k\mid y) \propto p(y|x, ...
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3answers
125 views

Abuse of notation in declaring a variable is a function of another?

The standard way to write $ \text{ y is a function of x} $ is $ y = f(x) $ This is taken to mean that $y$ is the value of function $f$ evaluated at $x$. For simplicity let's take $f$ to be some ...
4
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3answers
129 views

Order of calculation in all math equations

I already asked a question (Order of operations in rotation matrix notation.) about the order in which a particular equation is "processed" and now I need to generalise that and learn the rules of ...
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3answers
198 views

Order of operations in rotation matrix notation.

I'm trying to convert this equation to C# but I'm not a mathematician and I find math notation ambiguous: See the first matrix in this article: http://mathworld.wolfram.com/RotationMatrix.html ...
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1answer
235 views

What does “8.5070592e+37” mean?

When Google calc gives me numbers like this: 8.5070592e+37 How do I convert this back into a large number again. i.e ...
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2answers
33 views

Notation for the set of all $x_i$

Maybe a silly question, but what is the most compact way of clearly expressing the set of all $x_i$ if it is obvious that $i$ runs from 1 to $n$? $\{x_i\}$? $\{x_i\}_i$? $\{x_i\}_{i=1}^n$? $\{x_1, ...
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2answers
128 views

Alternative function notation?

I have a professor that uses the notation $$ \lambda (x_1,x_2,\dots ,x_n)\ . \ c_1x_1 +c_2x_n + \dots +c_nx_n \colon \ \mathbb{R}^n \longrightarrow \mathbb{R}$$ for a function $$ f \colon \ ...
3
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0answers
66 views

Define composition of small cyles and making a big graph

I am having following sub graphs and wish to compose all and make a one bigger graph (say G). After that, I want to select the closed path where it is passing along the outer vertices of that ...
2
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2answers
109 views

Is there the shortest notation for a vector obtained by projecting $\vec{A}$ onto $\vec{B}$?

Is there the shortest notation defined for a vector obtained by projecting $\vec{A}$ onto $\vec{B}$? Is there the shortest notation defined for the complementary vector of a vector obtained by ...
3
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2answers
115 views

How to write down formally number of occurences?

I want to write formally the following sentence: The sequence $S$ contains elements of the set $A$. Probability value $P(a)$ for element $a$ is defined as a number of its occurences in the ...
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1answer
50 views

A question about Riemann sums

Take: $$ (u*v)(k) = \sum_{i=-\infty}^\infty u(i)v(k-i). $$ $k$ is there, it's because you want to define $$ \ldots\ldots, (u*v)(-3), (u*v)(-2), (u*v)(-1), (u*v)(0), (u*v)(1), (u*v)(2), (u*v)(3), ...
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1answer
112 views

How to write the following expression in index notation?

I would like to know how can I write $ ||\vec{a} \times(\nabla \times \vec{a})||^2 $ and $(\vec{a} \cdot (\nabla \times \vec{a}))^2$ in index notation if $\vec{a}=(a_1,a_2,a_3)$ Thank you for ...
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5answers
275 views

What does the notation $2\mathbb{Z}$ mean?

I have an assignment that is asking to define a one-to-one correspondence between the sets $2\mathbb{Z}$ and $17\mathbb{Z}$... or in other words, define some bijective function on $$f:2\mathbb{Z}\to ...
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1answer
72 views

What is the definition of coefficient?

How to define coefficient? And what does it mean when someone says: put the $i$th term to be the coefficient of $x^i$
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3answers
217 views

Notation: Concatenate two functions (piecewise) / Concatenate two vectors, lists or tuples

Functions Given two functions $f: F\rightarrow F'$ and $g: G\rightarrow G'$ with disjount domains ($G\cap F=\emptyset$), what are common ways to denote the following function $ h: F \cup G ...
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1answer
66 views

Put the $i$th term to be the coefficient of $x^i$: A question about Mathematical notation and sequences

Take $u(x)$ and $v(x)$ to be integer polynomials, and then interpret them as sequences in the obvious way: i.e. you put the $i$th term to be the coefficient of $x^i$. $u(x)=x-2$, $v(x)=3x^2+x$. The ...
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2answers
110 views

Is there a character to depict a large number?

Does a symbol exist to depict an arbitrarily large, finite number?
0
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1answer
98 views

Notations for one-sided coset spaces

Let $G$ be a group and let $H$ be its subgroup. What notations are used for the coset spaces $\{gH\,|\,g\in G\}$ and $\{Hg\,|\,g\in G\}?$ What I've written is a bit much to type, and I will be writing ...
3
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1answer
54 views

What is $\text{Col}(\kappa,\lambda)$ in set theory

I saw somewhere thing like this: $\text{Col}(\kappa,\lambda)$. What is this?
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2answers
164 views

What is the meaning of the expression $\liminf f_n$?

I am a little confused as to what $\liminf f_n$ means for a sequence $f_n$ of functions converging to $f$. I can not locate a definition anywhere.
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3answers
127 views

Is $f:\mathbb{Z}_{30}\longrightarrow\mathbb{Z}_{30}$ defined by $f([a])=[7a]$ well defined?

To tell the truth, I'm not even sure what this means. The professor gave an example saying that $\mathbb{Z}_m=\{[0],[1],[2],\dots,[m-1]\}$, and I sort of understand that.. but I have no idea what ...
5
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4answers
731 views

Sequence Notation — Which brackets to use?

I'm teaching sequences at the moment. I've always put sequences in round brackets, for example $(1,2,3,4,5)$ is a sequence whose first member is $1$, whose second member is $2$, and so on. I've also ...
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0answers
73 views

Simple notation question for the optimization problems

Let $f_\alpha:X\to \Bbb R$ be any collection of functions with any indexing $\alpha\in A$. I am interested in $\inf_X f_\alpha$ and $\sup_X f_\alpha$. For the shorthand for the former case it is ...
4
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1answer
188 views

Ideas for denoting parameters of a function, as opposed to variables, in the list of arguments?

In general, the list of arguments of a function includes only variables, not parameters. In some specific cases, a parameter could be incorporated into the function name, like $y$ in $$\log_y (x)$$ ...
0
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0answers
35 views

What is the most appropriate means of differentiating two sets of the same equations?

First, I should mention, I am not a mathematician, but I am trying to be respectful of mathematical conventions. My problem is this: I have two sets of the same equations, one attributed to one group, ...
1
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1answer
262 views

Lipschitz and Holder continuous

Let a function $f(t,x)$, which is Lipshitz continuous in $x$ and $1/2$-Holder continuous in $t$. Is there any "official" and widely accepted way to denote the class of such functions ? I am ...
0
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1answer
162 views

Math notation for histogram selection process

Suppose you have values and classify them in a histogram. In pseudo code this may look like this: ...
2
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2answers
50 views

Is there a notation for a given order-preserving bijection?

Let $A,B$ be sets and $G,H$ be order-relation for $A,B$ respectively. Say, i proved existence of an isomorphism $\psi$ such that [$(x,y)\in G$ iff $(\psi(x),\psi(y))\in H$]. However, "$A\cong B$" ...
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3answers
107 views

What is the term for a graph on $n$ vertices with no edges?

What is the term for a graph comprised of $n$ pairwise disconnected vertices? I could call these $1$-colorable graphs or something like that, but I would rather use standard terminology if it ...
3
votes
1answer
104 views

Set theory: notation

I have a question w.r.t. notation that appears dealing with product sets. Let $T$ be any index set and $X$ and $Y$ be any two sets. Then $X^T = \{f:T\to X\} $ and $Y^T = \{g:T\to Y\}$. Let $A\subset ...
5
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2answers
449 views

The notation for partial derivatives

Today, in my lesson, I was introduced to partial derivatives. One of the things that confuses me is the notation. I hope that I am wrong and hope the community can contribute to my learning. In ...
1
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1answer
58 views

Notation Confusion

This is an extremely soft question. This is a definition from Ramsey Theory: $n\to (l_1,\ldots, l_r)^k$ if for every $r$-coloring of $[n]^k$, there exists $i$, $1\le i\le r$, and a set $T$, ...
2
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1answer
93 views

A question concerning multi-indices

I am having difficulties understanding the following formula : $$(x_1+\cdots+x_n)^k=\sum_{\alpha,|\alpha|=k}\frac{|\alpha|!}{\alpha!}x^\alpha $$ where $\alpha$ is a multi-index. I find this notation ...
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4answers
817 views

Why doesn't Spivak ever write $dx$ in an integral?

I've noticed that Spivak, and many other analysis books I read like Munkres, do not use $dx$ when they integrate. Why is that? This is a serious question.
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1answer
286 views

Meaning of the bar over $\bf{c}'$ in $\bf{\bar{c}}'=\bf c' -\bf c'_B \bf B^{-1} \bf A\geq \bf 0$?

I am trying to understand the page 87 Bertimas about Linear Programming. The author uses bolding and bars -- now I am starting to think that the bar means something else to vector, bolding apparently ...
5
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3answers
2k views

“Such that” symbol “$\mid$”

I know the "such that" symbol $\mid$ from the definition of sets: $$\{x \mid x \in \Bbb N \land x < 3\}$$ Is it OK to use this symbol outside of sets. For instance, if I want to define a function ...
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0answers
95 views

Nomenclature and/or notation for the intersection of a set with its boundary.

Is there standard nomenclature and/or notation for the expression $A \cap \partial A$?
2
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2answers
98 views

Functions, domains and codomains

I am refreshing a bit my basic knowledge of mathematics, and I have some doubts, I am sure you can help me with. Let's take this function in python: ...
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1answer
137 views

Graph decomposition and union by mathematical notation

(I guess, readers might misguided by my original post, So I modify it) If I have an undirected graph, Could you please help me to describe Decomposing a undirected graph into cycles Cycle breaking ...
2
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2answers
108 views

Correct notation or operator to remove elements from sequence

I'm currently using the following notation to denote a sequence (i.e. ordered list of elements): $\langle x_n | x \in \mathbb{N} \rangle$ E.g. $S = \langle 1,3,5,7 \rangle$ and $S_2 = 3$ I know ...