Description of a polynomial time mapping reduction from SUBSET-SUM to PARTITION.

Given a set S = {x1,...,x_n} of positive numbers and a positive integer t 
we want to construnct a set S' of positive integers such that 
  there is a subset of S which sums to t  IF AND ONLY IF
  there is a subset in S' that has the same sum as its complement.

S' will simply be S with an additionl number which is |2t-s| where s is the 
sum of all numbers in S, and |x| is the absolute value of x).

Why does this work?
If there is a subset T of S that sums to t, then the complement set in S (that
is S-T) has sum s-t. The difference between these sum is |2t-s| so in S' we 
can simply add the new number to the T or S-T depending on which one has 
smaller sum. (More explicitly, if t <= s/2 we will add the new number which 
will be of size s-2t to T and both sets wil lhave size s-t. If t>s/2 we will 
add the new number which will be 2t-s to S-T and now both sets will sum to t.