I'd also point to I John 3:4 in order to derive some understanding of sin, although my view of this verse is not the one you'll commonly hear.
KJV says Sin is the transgression of the law.
"Lawkeepers" (Torah observers or Sabbathkeepers) will claim this definition, and imply that the law is talking about the Torah or the Ten Commandments, depending on what standard they uphold as being "the standard".
I believe the correct translation in this regard links behavior (sin or hamartia) with motivation (anomia or rebellion). In other words, I think what it's saying is that sin is a manifestation of rebellion.
Adam and Eve rebelled against God, basically asserting their "right" to decide what is right and wrong, rather than relying on God totally to reveal this for them. This was an act of cosmic treason; basically giving God the finger. Mankind continues to manifest this rebellious nature when they sin. Christians don't even totally escape this tendency due to the remnant of the old nature called "the flesh", and they pay the temporal results for their rebellion when they do that...God disciplines every son that he loves.
This view is consistent with the letter of I John, where the heretics it is addressing are portrayed as those who continue to live in rebellion and disobedience, and do not obey the commandments of God.
I have a commentary in the Pillar series which agrees with my view on this. I did not derive the view from the commentary, but the author (Peter O Brien) essentially agrees with it.
Some here believe that anomia should essentially be translated "transgression of the law" like the KJV translates it but I disagree with good philosophical and exegetical reasons. Either way, though, it makes no different to me. If anomia refers to "transgression of the law", my understanding would be God's moral law, but I am confident that the verse is linking behavior (hamartia or sin) with motivation (anomia or rebellion). I believe there's a consistency throughout Scripture that sin is linked with rebellion against God, and that started in the garden of Eden with our rejection of God as our source in terms of revelation, instead choosing to believe Satan or to decide for ourselves what is right and wrong. "There is a way that seems right to a man, but the end thereof is death"