• Support PF! Buy your school textbooks, materials and every day products Here!

Nested Ordered Pair

  • #1
50
1

Homework Statement


One way of modeling tuples in set theory is through nested ordered pairs. A notation I'm not familiar with (I'm assuming it means that the following elements are nested into the last one) is used. (a1, a2, a2,... an) = (a1(a2, a3,..., an)). I have never seen the second "(" in the latter part of the equation. My question is what is a nested ordered pair? What are its properties? How can the second element in the latter part of the equation, have lots of elements; while, the whole thing still be an ordered pair? Nested generally means something in something, and an ordered pair is a couple or two tuple, but I can't seem to put the two together.

Homework Equations


None that I know of

The Attempt at a Solution


I've spent about 30 minutes searching and I still can't find a definition.[/B]
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,805
932
I have never seen that notation before. I have seen the ordered pair defined as the un ordered pair (a, (a, b)).
The point is simply that the un ordered pair (a, (a, b)) tells you that there are two objects, a and b, and that a is being treated differently from b since it is named twice.
 
  • #3
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
32,710
5,029
I would guess it means as ##(a_1, (a_2, (a_3, (...))))##. This is an ordered pair. The second element is an ordered pair. The second element of that is an ordered pair...
Having written that I did a quick search and found http://en.wikipedia.org/wiki/Tuple#Tuples_as_nested_ordered_pairs. This adds the interesting clean-up of making the the innermost ordered pair ##(a_n, \phi)##, which is neater than finishing with ##(a_{n-1}, a_n)##.
 

Related Threads on Nested Ordered Pair

  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
7
Views
2K
Replies
3
Views
1K
Replies
6
Views
734
Replies
4
Views
5K
Replies
3
Views
12K
  • Last Post
Replies
16
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
9
Views
732
Top