I'm just stuck on this question. How can I represent the additive inverse of all continuous functions?
The additive inverse: For every $\overrightarrow{u}$ in V, there is a vector V denoted by $\overrightarrow{-u}$ such that $\overrightarrow{u}$ + ($\overrightarrow{-u}$) = $\overrightarrow{0}$.
Any help is appreciated.
This is a solution I found to a similiar problem earlier:
Describe the additive inverse of the vector space $P_3$ where $P_3$ is the set of all polynomials of degree 3 or below. Solution: $-(a_0 + a_1x + a_2x^2 + a_3x^3) = -a_0 - a_1x - a_2x^2 - a_3x^3$