I ask this question with regards to a grammar in Chosmky Normal Form. The definition states that the rules must be of the following forms:
- A $\rightarrow$ BC
- A $\rightarrow$ a
- S $\rightarrow$ $\epsilon$
And A,B and C are non-terminal symbols, B and C are different from S and a is a terminal symbol. The definition also states that the last rule can only be present if the language of the grammar accepts the empty string (source). Now if $\epsilon$ is a terminal symbol, than this is a contradiction as the second rule can be transformed to S $\rightarrow$ $\epsilon$, seeing as A must not be different from S. This leads me to conclude that $\epsilon$ is not a terminal symbol, is this correct?