improve: Improvement: 

When $n=0$, the expression indicates that the minimum energy of $1/2$ cannot be attained by an oscillator starting with zero energy, and vice versa, as per our assumptions. Additionally, a zero-energy oscillator cannot absorb energy packets from its surroundings due to the absence of the constant $1/2$ contribution, rendering it unable to fully encompass the range of energy configurations presented by the different energy triangles.