Start with three numbers:  X Y Z

step 1)  if (X > Y) then swap (X,Y)  // now X <= Y 
step 2) if (Y > Z) then swap (Y,Z) // now Y <= Z and X <= Z too
step 3) if (X > Y) then swap (X,Y) // now X<=Y<=Z

Proof that after step 2, Y <= Z and X <= Z:

After step 1, X <= Y.

It is obvious that Y <= Z after step 2.  To see that also X <= Z after 
step 2, note the following:
In step 2, two things can happen:

  A) The test shows that Y <= Z and the swap is not performed.
     In that case, since X <= Y was made true in step 1,
     we have X <= Y and Y <= Z, which implies that X <= Z, by transitivity.

  B) The test shows that Y > Z, and the swap IS performed.  Now 
     X <= Z follows from the fact that X <= Y after step 1, and
     the swap made Y the NEW value of Z.

===
Example One:
start with: 3   2   1

after step 1:  2   3   1
after step 2:  2   1   3 
after step 3:  1   2   3

===
Example Two:
start with: 3   1   2

after step 1:  1   3   2
after step 2:  1   2   3 
after step 3:  1   2   3

===
Example Three:
start with: 2   1   3

after step 1:  1   2   3
after step 2:  1   2   3 
after step 3:  1   2   3

===
Example Four:
start with: 2   3   1

after step 1:  2   3   1
after step 2:  2   1   3 
after step 3:  1   2   3