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Set of elements which are in a sequence.

1

$begingroup$

How to write a set in which the elements are in a sequence?

For example,
sequence of natural numbers $(i)_{iin N} = (1, 2, 3, ....)$

Now if we have to make a set A of these numbers (which are in a sequence), we write, $A={i: iin N} = {1, 2, 3, .... }$

But I am confused how to write a set of a variable which vary from k to n.

For example, sequence of outcomes of an experiment is $(w_i)_{i=1}^n = (w_1, w_2, w_3, .... ,w_n)$

Now I have to make the sample space $S= {w_i, w_2, w_3, ... ,w_n}$ which is a set of these outcomes (which are in a sequence as above) ,
So how do I write the set S?

Is N1. $S = { w_i : text{i varies from 1 to n}}$ correct?

If it is correct, then what is the way of writing it mathematically instead of writing "i varies from 1 to n",

for ex : N2. $S = { w_i : w_i in {(w_i)_{i=1}^n }}$ ; is this correct?

Or N3. $S= {w_i : 1≤i≤n , iin N }$ is correct?

Note: I mean to ask set of "elements which are in a sequence", and not set of sequence.

Thanks for your help. $_/backslash_$

elementary-set-theory notation

share|cite|improve this question

edited Mar 25 at 20:26

Andrés E. Caicedo

66.1k8160252

asked Mar 25 at 18:05

Ane SaAne Sa

62

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  ${ a_i }_{i in mathbb N}$ is a sequence.
  $endgroup$
  – Mauro ALLEGRANZA
  Mar 25 at 18:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @mauro but isn't sequence denoted by "(" $(a_i)_{i in N}$ and not by "{" . And how to write the set of elements of this sequence ?
  $endgroup$
  – Ane Sa
  Mar 25 at 18:18
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  A sequence is a set; we usually denote it as $(a_n)_{n in mathbb N}$. But a sequence of elements of $A$ is a function $f : mathbb N to A$ where we have $a_n=f(n)$ and a function is a set.
  $endgroup$
  – Mauro ALLEGRANZA
  Mar 25 at 18:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thus, it is only a matter of choosing the most perspicuous notation... The set corresponding to the sequence $(a_n)_{n in mathbb N}$ can be described also with ${ a_n }_{n in mathbb N}$
  $endgroup$
  – Mauro ALLEGRANZA
  Mar 25 at 18:59
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @mauro so that means I can write sample space $S={w_1, w_2, ... , w_n}$ as $S= {w_i}_{i=0}^n$ ?
  $endgroup$
  – Ane Sa
  Mar 25 at 20:00
  

  
  
  
  

 | 
show 4 more comments

1

$begingroup$

How to write a set in which the elements are in a sequence?

For example,
sequence of natural numbers $(i)_{iin N} = (1, 2, 3, ....)$

Now if we have to make a set A of these numbers (which are in a sequence), we write, $A={i: iin N} = {1, 2, 3, .... }$

But I am confused how to write a set of a variable which vary from k to n.

For example, sequence of outcomes of an experiment is $(w_i)_{i=1}^n = (w_1, w_2, w_3, .... ,w_n)$

Now I have to make the sample space $S= {w_i, w_2, w_3, ... ,w_n}$ which is a set of these outcomes (which are in a sequence as above) ,
So how do I write the set S?

Is N1. $S = { w_i : text{i varies from 1 to n}}$ correct?

If it is correct, then what is the way of writing it mathematically instead of writing "i varies from 1 to n",

for ex : N2. $S = { w_i : w_i in {(w_i)_{i=1}^n }}$ ; is this correct?

Or N3. $S= {w_i : 1≤i≤n , iin N }$ is correct?

Note: I mean to ask set of "elements which are in a sequence", and not set of sequence.

Thanks for your help. $_/backslash_$

elementary-set-theory notation

share|cite|improve this question

edited Mar 25 at 20:26

Andrés E. Caicedo

66.1k8160252

asked Mar 25 at 18:05

Ane SaAne Sa

62

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  ${ a_i }_{i in mathbb N}$ is a sequence.
  $endgroup$
  – Mauro ALLEGRANZA
  Mar 25 at 18:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @mauro but isn't sequence denoted by "(" $(a_i)_{i in N}$ and not by "{" . And how to write the set of elements of this sequence ?
  $endgroup$
  – Ane Sa
  Mar 25 at 18:18
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  A sequence is a set; we usually denote it as $(a_n)_{n in mathbb N}$. But a sequence of elements of $A$ is a function $f : mathbb N to A$ where we have $a_n=f(n)$ and a function is a set.
  $endgroup$
  – Mauro ALLEGRANZA
  Mar 25 at 18:57
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thus, it is only a matter of choosing the most perspicuous notation... The set corresponding to the sequence $(a_n)_{n in mathbb N}$ can be described also with ${ a_n }_{n in mathbb N}$
  $endgroup$
  – Mauro ALLEGRANZA
  Mar 25 at 18:59
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @mauro so that means I can write sample space $S={w_1, w_2, ... , w_n}$ as $S= {w_i}_{i=0}^n$ ?
  $endgroup$
  – Ane Sa
  Mar 25 at 20:00
  

  
  
  
  

 | 
show 4 more comments

$begingroup$

How to write a set in which the elements are in a sequence?

For example,
sequence of natural numbers $(i)_{iin N} = (1, 2, 3, ....)$

Now if we have to make a set A of these numbers (which are in a sequence), we write, $A={i: iin N} = {1, 2, 3, .... }$

But I am confused how to write a set of a variable which vary from k to n.

For example, sequence of outcomes of an experiment is $(w_i)_{i=1}^n = (w_1, w_2, w_3, .... ,w_n)$

Now I have to make the sample space $S= {w_i, w_2, w_3, ... ,w_n}$ which is a set of these outcomes (which are in a sequence as above) ,
So how do I write the set S?

Is N1. $S = { w_i : text{i varies from 1 to n}}$ correct?

If it is correct, then what is the way of writing it mathematically instead of writing "i varies from 1 to n",

for ex : N2. $S = { w_i : w_i in {(w_i)_{i=1}^n }}$ ; is this correct?

Or N3. $S= {w_i : 1≤i≤n , iin N }$ is correct?

Note: I mean to ask set of "elements which are in a sequence", and not set of sequence.

Thanks for your help. $_/backslash_$

elementary-set-theory notation

share|cite|improve this question

edited Mar 25 at 20:26

Andrés E. Caicedo

66.1k8160252

asked Mar 25 at 18:05

Ane SaAne Sa

62

$endgroup$

share|cite|improve this question

edited Mar 25 at 20:26

Andrés E. Caicedo

66.1k8160252

asked Mar 25 at 18:05

Ane SaAne Sa

62

share|cite|improve this question

edited Mar 25 at 20:26

Andrés E. Caicedo

66.1k8160252

asked Mar 25 at 18:05

Ane SaAne Sa

62

edited Mar 25 at 20:26

Andrés E. Caicedo

66.1k8160252

edited Mar 25 at 20:26

Andrés E. Caicedo

66.1k8160252

asked Mar 25 at 18:05

Ane SaAne Sa

62

asked Mar 25 at 18:05

Ane SaAne Sa

62