A technician monitoring a high-precision chemical reaction states that the temperature, $T$ in ${}^{\circ }C$, must satisfy the constraint $54.4<T<54.5$. The technician claims that $54.5$ is the largest possible temperature within this specification.

Explain the error in the technician's statement.

A research scientist argues that there is no largest value for $T$ in the interval $54.4<T<54.5$ and provides the following proof by contradiction:

Step 1: Assume there is a largest temperature in the interval $54.4<T<54.5$ and let this largest value be $L$.

Step 2: Let $k=\frac{L+54.5}{2}$.

Step 3: $L<k<54.5$, which is a contradiction.

Step 4: Therefore, there is no largest temperature in the interval $54.4<T<54.5$.

Explain the contradiction stated in Step 3.

Using a similar method, prove that there is no smallest value of $T$ in the interval $54.4<T<54.5$.