Dave according to God the definition of sin is the transgression of the law. Your definition is not in the bible , falling short of something is not sin
I fell short of being 6 feet tall , did I sin because I'm 5:10 "
In the bible there are sins, transgressions and iniquities. In the NT sometimes they are all called "sins" but that does not remove the distinction.
Sins are every thing that fall short.
Transgressions are intentional violations of a known standard of God
Iniquities are the trans-generational bad effects of sins and transgressions.
Also - can you get yourself away from this "definition?"
Romans 14:23b ...whatever is not from faith is sin.
Even obeying the commandments can be sin if it is not done from faith. I will say it again - your definition is only partial and way too narrow.