Express the notion of a minimum of a set of number (where numbers are defined via sets). That is, define a relation Min(S,x) using logic and set-theoretic operations such that it is true whenever x is the minimum element in S.
- I understand the definition of numbers in terms of sets. I did that in part a of this same question.
I understand what a function or relation is
But I have no idea what this is asking, nor how to answer it.
Edit: My definition of a number is as follows:
0 = {}
$n+1 = n\cup \{n\}$
So :
- 1 = {{}}
- 2 = {{}, {{}}}
- 3 = {{}, {{}}, {{}, {{}}}}