Define heresy. How can the old women be considered heretic?

Heresy is a belief or opinion contrary to orthodox doctrine. The old woman declares her love for knowledge an books which is considered heresy by the state. Montag feels horrible for the old woman yet at the same time he envies her. Here is a human being standing up for what is right and true. He, on the other hand hides behind his title and uniform. The old woman changes Montag. He liberates (steals) books from her house and stashes them to read later. Although he is upset about the terrible sin he has committed, he is actually rebelling in his own way.