2. 46 Insert "+" or "-" signs between the numbers $1,2,3 \cdots, 1989$, what is the smallest non-negative number that the sum can achieve?
[Solution] Except for 995, all numbers $1,2,3, \cdots, 1989$ can be divided into 994 pairs: (1, 1989), $(2,1988), \cdots,(994,996)$. Since the parity of the two numbers in each pair is the same, the result of the operation is always even regardless of how "+" or "-" signs are placed before each pair; and 995 is an odd number, so the value of the sum of the numbers $1,2,3, \cdots, 1989$ with any placement of "+" or "-" signs is always odd. Therefore, the smallest non-negative number that can be obtained is not less than 1.

On the other hand, the number 1 can be obtained in the following way:
$1=1+(2-3-4+5)+(6-7-8+9)+\cdots+(1986-1987-$ $1988+1989)$.

Therefore, the smallest non-negative number that the sum can achieve is 1.