Vector Space

  • Thread starter arunkp
  • Start date
  • #1
1
0
Please tell me one of the bases for the infinite dimenional vector space - R (the set of all real numbers) over Q (the set of all rational numbers). The vector addition, field addition and multiplication carry the usual meaning.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
619
Why do you think there is one you can describe constructively?
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,833
961
It's not JUST "infinite dimensional". Since the set of real numbers is uncountable, while the set of rational numbers is countable, any basis for the real numbers, as a vector space over the rational numbers, would have to be uncountable- so it is impossible to list them.

Theoretically, you could set of a function, say over [0, 1], such that f(x) for each x gives a "basis" number. If you figure out how to do that, please let me know!
 

Related Threads on Vector Space

  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
16
Views
4K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
15
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
4
Views
1K
Top