Infimun and supremum of empty set

  • Thread starter Edwinkumar
  • Start date
  • #1
23
0

Main Question or Discussion Point

Why do we define(by convention) that infimum of an empty set as [tex]\infty[/tex] and supremum as [tex]-\infty[/tex]?
 
Last edited:

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,916
17
It's not a convention -- it follows directly from the definition of the supremum as the least upper bound and the infimum as the greatest lower bound.
 
  • #3
matt grime
Science Advisor
Homework Helper
9,395
3
Remember that we say M is an upper bound for X if for all x in X.... so if X is the empty set then this is never true. Now, "false implies true is true", i.e. all possible real numbers are upper bounds for the the empty set.
 
  • #4
23
0
Thanks Hurkyl and matt grime for your replies. Yes I got it now!
 

Related Threads for: Infimun and supremum of empty set

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
7
Views
2K
Replies
2
Views
4K
  • Last Post
Replies
1
Views
2K
Replies
1
Views
3K
Replies
12
Views
9K
  • Last Post
Replies
4
Views
24K
Top