Question for the scarlet letter essay?

The Letter A is a symbol for Adultress, and also when the man carves the letter A into his chest because he too did. The symbol shows how even if it was morally wrong, they were in love. They had a daughter, who was treated by society wrongly b/c of the affair. Having to wear the letter was her punishment that everyone knew about, yet the other guy was not punished by society but by himself... I hope that helps its been 3 years sense ive read the book but i had to write a paper too about it. I cant remeber the guys name either so i hope you could understand what i was trying to say... It might not be the right answer, but maybe it will help?