Set notation

  • #1
338
0

Main Question or Discussion Point

I'm taking a class in abstract algebra this summer, so I thought I'd get ahead by reading the book before class starts.

This is from a book called "Abstract Algebra: A Geometric Approach", chapter 1:

Applying the Principle of Mathematical Induction with a slight modification.
If [tex]S' \subset \{n \in N:n\geq n_0\}[/tex] has these properties:
(1) [tex]n_0 \in S'[/tex]
(2) If [tex]k \in S'[/tex] then [tex]k+1 \in S'[/tex]
then [tex]S'=\{n \in N:n\geq n_0\}[/tex]
If we define [tex]S=\{m \in N:m+(n_0-1) \in S'\}[/tex], we see that [tex]1 \in S[/tex] and [tex]k \in S[/tex], which leads to [tex]k+1 \in S[/tex] , and so [tex]S=N[/tex].
Thus, [tex]S'=\{n \in N: n=n_0+(m-1)[/tex] for some [tex]m \in N\}=\{n \in N:n \geq n_0\}[/tex]

I'm not sure how to interpret all that. I know the sideways U means "subset", and the sideways U with a line means "is an element of". But does something like this [tex]\{n \in N:n\geq n_0\}[/tex] mean n is an element of N only when [tex]n \geq n_0[/tex]?

What about this: [tex]S=\{m \in N:m+(n_0-1) \in S'\}[/tex]?

How do you interpret that?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
249
… I know the sideways U means "subset", and the sideways U with a line means "is an element of". But does something like this [tex]\{n \in N:n\geq n_0\}[/tex] mean n is an element of N only when [tex]n \geq n_0[/tex]?

What about this: [tex]S=\{m \in N:m+(n_0-1) \in S'\}[/tex]?

How do you interpret that?
Hi Bill! :smile:

The : means "such that" …

so that means "S is the set of all elements m of N such that m + n0 - 1 is an element of S´" :wink:
 

Related Threads for: Set notation

  • Last Post
Replies
1
Views
539
  • Last Post
Replies
8
Views
744
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
8
Views
769
Top