1
vote
1answer
49 views

What is meant by $ab$ on words $a$ and $b$ in $\{ab\ |\ a,b \in Σ^*\}$?

Given language $L$ := $\{ab\ |\ a,b \in Σ^*\}$, $Σ := \{blue, green\}$. Is the notation "$ab$" above taken to be word concatenation, such that $\{bluegreen\} \subset L$? What occurs when $L$ := ...
0
votes
4answers
42 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
2answers
40 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.
3
votes
0answers
23 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 ...
-1
votes
0answers
39 views

Common character to substitute union ∪ and intersection ∩

When writing set expressions on a computer without access to the proper symbols (∪, ∩, etc.), what non-letter symbols found on a English US keyboard are commonly used as substitutes? The three ...
1
vote
1answer
35 views

Set Theory notation verification

In set theory, the notation $$\bigcup X$$ means the union of all elements of $X$. For example, $\bigcup\{ a,b \}=a \cup b$. I encounter the following notation $$\bigcup X \subseteq X$$ in the book ...
2
votes
3answers
52 views

Does the set given by $\{(1/n)\}_{n=1}^\infty$ include $0$?

Is there some sort of consensus on whether or not $$0 \in \{(1/n)\}_{n=1}^\infty?$$
2
votes
2answers
64 views

What does the notation $\bigcup_{n\in\mathbb N} A_n$ mean in sets?

$$\bigcup\limits_{n\in\mathbb N} A_n$$ The book is asking me to prove that $f(\bigcup\limits_{n\in\mathbb N} A_n) = \bigcup\limits_{n\in\mathbb N} A_n$. I'm able to prove that f(the notation ...
0
votes
1answer
21 views

Notation: Building a set from sequences of random variables, some a.s. equal

For $1 \leq i \leq n$ let $(\psi_{ij})_{1 \leq j \leq n_i}$ be sequences of random variables. Is there a better notation than $$\{\psi_{ij} : 1 \leq i \leq n, 1 \leq j \leq n_i\}$$ to build a set ...
0
votes
3answers
83 views

How to formulate “The $n$ smallest”

I know how to formulate the set of all $x$ with minimal distance to $y$ with $d(x,y)$ being the distance function: $\{x \mid \arg\min d(x,y)\}$ But how do I formulate the set of the $n$ closest $x$ ...
1
vote
3answers
81 views

Set notation and mappings question

Good evening. I have a question. Suppose I have two sets, $A=\{1,2,3,4\}$ and $B=\{5,6\}$. I want to write the notation for a function that takes each element in $A$ and assigns to it a value in $B$. ...
0
votes
0answers
32 views

Terms for particular equivalence relation and partition?

Let $T$ be a set of sets. Let $\equiv$ be an equivalence relation on $\bigcup T$ defined by the formula $$a\equiv b \Leftrightarrow \forall X\in T:(a\in X\Leftrightarrow b\in X).$$ Let $S$ be a ...
0
votes
2answers
46 views

What is the notation for the number of elements in a set?

Let's say S = {1, 2, 3}. There are 3 elements in S. How do I express this in notation? I tried using google but I could not find what I was looking for.
3
votes
2answers
66 views

In composition of two mappings, can the outer mapping access the arguments of the inner mapping?

In composition of two mappings, can the outer mapping access the arguments of the inner mapping? Here is an example to illustrate my question and my thought. E.g. $f: \cup_{n \in \mathbb N} \mathbb ...
3
votes
0answers
67 views

Can $\mathbb A=\{f(x)\mid x\in\mathbb R\}$ be shortened as $\mathbb A=f(\mathbb R)$?

Can $\mathbb A=\{f(x)\mid x\in\mathbb R\}$ be shortened as $\mathbb A=f(\mathbb R)$? I saw this notation in the IMO olympiad training materials (the solution to the Problem 16 (IMO 1999 Problem ...
0
votes
1answer
78 views

What are sets and classes in maths, and how are they related to $O()$ and $o()$ notation?

Are there many definitions of sets and classes in mathematics, as given in Formal definion of the notations used in measuring time complexity? And in particular, why the notation given in Fedja's ...
0
votes
1answer
24 views

Notation of list expansion to a tuple

I have a set $S$ that I want to expand to a $|S|$-tuple. How is the notation for that? Currently I have something like that: $$ T = (f(x) : x \in S) $$ An example: $$ S = (A,B,C)\\ T = (f(A), f(B), ...
3
votes
1answer
57 views

What does $F = 2^W$ mean?

I'm reading the book Reasoning about uncertainty and having some problems with the notation. $F = 2^W$ where $W$ is a set and $F$ an algebra. What this mean?
0
votes
1answer
48 views

How to write the union of sets

This is just a question about notation(and I can not write it pretty well in Latex either). Is $X=(0,+\infty)\subset\Bbb{R}$ and $Y=\Bbb{R}$. Then $X\times Y= (0,+\infty)\times \Bbb{R} =$ ? ...
0
votes
3answers
78 views

What is $X^{\omega}$ where $X$ is a set?

I fail to find a duplicate. If it exists, please link me in the comments and I will delete the question. In my recently bought topology book, they use $X^{\omega}$ where $X$ is a set. However, this ...
0
votes
0answers
17 views

Notation for mimimal sum when choosing elements from two sets

I'd be grateful for any pointers on the following I am wondering if there is any standard notation (or neat suggestions) for the following. I have two sets $\{t_1, t_2, \ldots , t_k\}$ and $\{s_1, ...
0
votes
1answer
48 views

Is $\sup\{t>0:F(t)>0 \in [0,t]\}$ an incorrect math expression?

I saw the following in a journal paper and the notation looks wrong - am I right? $$t_1 = \sup\{t>0:F(t)>0 \in [0,t]\}$$ I would like to translate this into an English sentence, but I don't ...
6
votes
2answers
440 views

Meaning of a set in the exponent

Let $ D = 2^\mathbb{N} $, i.e., D is the set of all sets of natural numbers. What's the meaning of this definition? Intuitively, I would suggest that $ D = \{1,2,4,...\} $ but the explanation ...
0
votes
2answers
45 views

Combinaision of two functions

Let us denote $X_0 = \{x, y\}$ and $X_1 = \{a, b\}$ two disjoint sets of variables; let us denote $V$ a set of values. I have two functions $f_0 : X_0 \rightarrow V$ and $f_1 : X_1 \rightarrow V$, ...
0
votes
0answers
24 views

Is there accepted notation and/or terminology for the smallest cover of $S$ with cells from $P$?

Let $X$ denote a set. Then for $S \subseteq X$ and $P$ a partitioning of $X$, define $P \diamond S$ as the smallest cover of $S$ with cells from $P$. Explicitly: $$P \diamond S = \bigcup\{Q \in P ...
0
votes
0answers
31 views

Product of tuples vs cartesian product of set

If $\left ( X_{i} \right )_{1\leq i\leq n}$ is an ordered n-tuple of sets their Cartesian product is defined as: $$\prod_{i=1}^{n}X_{i}:=\left \{ (x_{i})_{1\leq i\leq n} :x_{i}\in (X_{i}) \; \text{ ...
1
vote
1answer
51 views

Count of matched items in multiple sets

I do apologize if this is a duplication. I did find a question that appears close to describing something of what I'm looking for, but I'm just not "seeing" the complete picture (maybe): Counting ...
1
vote
3answers
39 views

Notation: the set of two-element subsets of $\Bbb N$

Let $\{a,b\}\subseteq \Bbb N$. Is there a special name or notation for sets of this type, for example $\Bbb N^{2\ge}$? Any subset size may be used, but the specific size and denoting that order does ...
0
votes
1answer
46 views

tuple of tuples notation

Is the following notation right for indicating a $\mathit{m}-$tuple of $\mathit{n_{j}}-$tuples (I mean that each tuple of the $\mathit{m}-$tuple has a different number of elements)? ...
0
votes
2answers
78 views

$\Bbb Z^\ast$ What is this notation?

What does $\Bbb Z^\ast$ mean? I would think some subset of the integers but I cannot find a definition. Thank you.
1
vote
0answers
30 views

Set-builder defining set size and valid elements? Notation help.

I'm working on some documentation for a system that uses an arbitrary waveform generator that accepts data with a number of requirements. I would like to include some formal definitions of the ...
0
votes
2answers
26 views

Cannot understand a mapping function which include some sets

I have kept a screenshot of my problem below which describes about the various sets. At the last line, there is an expression where a function delta uses those sets and maps them into another. I am ...
2
votes
2answers
74 views

Element of a Singleton (set with one element) notation

I was wondering what the notations are for indicating the element of a singleton (or unit set, or set with cardinality 1). This would be the inverse of set construction: $$X = \{y\} \tag{1}$$ $$y = ...
1
vote
1answer
73 views

correct Set theory notations.

What is correct notation for the following, I have seen both in some books. To show an empty set, is it Φ(phi) or Ø(slash O) or both. To show an Universal set, is it ε(epsilon) or U or both. I am ...
2
votes
1answer
56 views

$A \setminus B \cup C = A \setminus (B \cup C)$? [duplicate]

$A \setminus B \cup C$ or $A \setminus (B \cup C)$? Sorry as this is a very soft question, but I couldn't find the answer anywhere. Are these two things generally considered the same?
1
vote
1answer
27 views

Small notation question about union of chains (Set Theory)

The question is derived from this question I encountered: Let $A$ be a set, and let there be a function $f: A \rightarrow A$, so that for every $a \in A$, $f(a) \neq a$. Define $S=\{X \subseteq A: ...
0
votes
1answer
30 views

Reading set notation for the flow number

Could someone please help me to understand the following notation: Flow Number: In case of need, S refers to a set of flows, C(s) is called congestion and D(S) is dilation. How would you put in ...
0
votes
1answer
21 views

Notation for a collection of sets under a certain condition

I am looking for the notation to describe "A collection of sets that are the union of a finite number of intervals". Is this correct - $A = \{A_i\}_{i \in I}$ where each $A_i = \bigcup_{n \in N} ...
0
votes
2answers
29 views

How do you write the set where $2$ numbers are chosen

A = the event that the sum of outcomes of $2$ dice being thrown So do I say $A = \{14;41;23;32\}$ That looks like I'm saying $41$ (the number) not $4$ from one die and $1$ from the other which ...
0
votes
0answers
31 views

Notations for elementary set theory

I wish to understand the following notations which defined for every cardinals, $a,b$: $P(a,b) = \left| In(A,B) \right|$ $C(a,b) = \left| P_b(A) \right|$ $E(ab) = \left| Eq(A,B) \right|$ ...
1
vote
2answers
91 views

What does $\vee$ mean in set theory?

The following proof is from Probability by Davar Khoshnevisan. There is a symbol $\vee$ in the third sentence of the proof. What does this symbol mean, please? There seems no definition about it in ...
2
votes
3answers
119 views

Notation for a space of finite sequences

For a given set $X$, what is the notation for the space of all finite $X$-valued sequences? I realise that the space of $n$-tuples is written as $X^n$, and the space of infinite sequences is ...
1
vote
1answer
25 views

Is there notation or a name for the complement of the unbounded face of a planar graph?

Let $G$ be a finite graph embedded in $\mathbb{C}$. Let $F$ denote denote its unbounded face. Is there notation or a name for $F^c$ without referring directly to $F$. Of course this is equivalent ...
2
votes
1answer
27 views

Domain of a composite function

I was given the question: Find the domain of the function $f(x)=\ln(\ln(\ln x))$ I found the answer by inspection: $\qquad D(\ln x)=(0,\infty)$ $\therefore\quad D(\ln(\ln x))=(1,\infty)$ ...
1
vote
0answers
24 views

element subset for adjacency matrix

I am trying to create an element of a matrix that is a subset of a larger matrix. However, I am told that my subscripts do not match. I wanted other people's opinion as to what I am doing wrong and ...
0
votes
1answer
26 views

Understanding the definition of the d-dimensional Hyperube

Please see the picture bellow about the definition of the nodes of the d-dimensional Hypercube. Could anyone please tell me what does that notation means. I get confused with the superscript after the ...
3
votes
1answer
38 views

Notation for a set of objects expressed by symbols

I have two questions about set notation The first one is how you would write down a set of objects expressed by symbols? Let's say we have $n$ persons identified by $p_i$. Can I write: $$P = \{p_1, ...
3
votes
3answers
103 views

Notation for choosing the k smallest elements from a set of integer

Is there any specific notation for picking $k$ elements from a set which are the smallest? Ex: {$1,3,5,7,9,11$} with $k = 3 \Rightarrow$ We want $1,3,5$
0
votes
3answers
67 views

Set question - $ ℤ^+ = ℕ$ [duplicate]

I am not sure whether the following statement is true: $ ℤ^+ = ℕ$ if not, why? Thank you in advance! I appreciate your help!
1
vote
1answer
31 views

Set Theory Elementhood Notation

From How to Prove it: Given $A=\{n^2|n \in N\}$ where $N$ is the set of all natural numbers. I want to express A in terms of elementhood test notation. Velleman says $A=\{x| \exists n \in N ...