Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

Here is a wacky question for you:

Suppose you have a simple recursive function f(x)=x. Given the fact that a function f(x)=y can be rewritten as a set of ordered pairs (x, y) with x from the domain of f and y from the range of f, it would seem that the function f(x)=x can be written as the set containing the ordered pair (x, x). But does such an ordered pair, with identical elements, make any sense? After all, order is everything in ordered pairs (and tuples generally), right? But how can one distinguish order when the members of the pair are the same?

I have read somewhere that the Kuratowski definition of an ordered pair (x, y) as {{x}, {x, y}} allows ordered pairs with identical elements, namely as follows: (x, x)= {{x}, {x, x}} = {{x}, {x}} = {{x}}. But how does having the set {{x}} tell us anything about order?

What are your thoughts on this? And do you know of any literature dealing with this issue? Thanks for your answers!

Stoney

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Can an ordered pair have identical elements?

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**