Question

Is there any way to compute min(a,b) with pure algebra?

Answer 1

This is like asking if there's any way to compute whether \[x\in S\] is true or false. So no, you cannot.

Answer 2

or, if you wish,

min(a,b) = a, if a<b
= b, otherwise

Answer 3

Thanks, this was a bit silly question :-]