suppose such function exists, then 
sort 3:2:1:undefined <= (appr order) sort 3:2:1:0:undefined (since 3:2:1:undefined <= (approximation order)  3:2:1:0:undefined)
but sort should return 
1:2:3:undefined in first case, which is not <= (approximation order) 0:1:2:3:undefined
therefor it is imposible
suppose such function exists, then 
sort 3:2:1:undefined <= (appr order) sort 3:2:1:0:undefined (since 3:2:1:undefined <= (approximation order)  3:2:1:0:undefined)
but sort should return 
1:2:3:undefined in first case, which is not <= (approximation order) 0:1:2:3:undefined
therefor it is imposible