Final answer:
-n is never a positive number if n is positive, as the negative sign indicates the opposite value. Zero is neither negative nor positive, so -0 is still zero. Thus, -n is always negative when n is a positive number.
Step-by-step explanation:
The question asks whether -n is always, sometimes, or never a positive number and requires an explanation of the reasoning behind the answer. By definition, -n represents the negation or the opposite value of whatever positive value n stands for. If n is positive, then -n is negative, and vice versa.
Therefore, if n is a positive number, -n will always be a negative number.
The confusion might arise if one considers zero as a positive number; however, by definition, zero is neither negative nor positive—hence the negation of zero, -0, is still zero. As such, -n is never a positive number when n is positive.
This reasoning aligns with the inductive inference that signs of numbers are consistent with the arithmetic rules that govern them.