Summary: All that Adam did by his willful disobedience to God’s command - infecting the human race with sin and the resulting death - Jesus undid by one sacrifice. Learn about the new race He created and how you can be a part of it.
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Sin is basically independence from God.
Genesis 2:15-17 (quickview)  The Lord God took the man and put him in the garden of Eden to work it and keep it. 16 And the Lord God commanded the man, saying, "You may surely eat of every tree of the garden, 17 but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die."
Adam’s rebellion became an infection—part of the human genome—passed down from father to son or daughter through the seed of the father (we were all “in” Adam like Levi was in Abraham when he presented tithes to Melchizedek – Hebrews 7:9-10 (quickview) ).
“All have sinned” means that our continued rebellion against God is a sign of the infection. It’s a fatal disease, 100% of the time. God did not intend for us to die. Even now, physical death seems just wrong to us, and it is wrong, but it’s a result of our rebellion. We trace the sin back to Adam because he was not deceived like Eve. He willfully and knowingly went against God (1 Tim 2:14). We have been infected with sin from Adam, but we also have responsibility because we ourselves sin (“all have sinned” 3:23).
Sin was still in the world but we came to understand it more when the Law was given, describing the character of a holy God and contrasting that with the character of sinful man.
The Law makes us accountable to sin, but we were sinners before the Law came about. It says “sin was not counted” which to me means, it was sin—we just didn’t know what to call it before the Law.
Death is the direct result of sin. Adam disobeyed a direct command of God. Those from Adam to Moses did not have the direct command but sinned anyway, and suffered death because of it. The Law helps us see our sinfulness. It’s like getting a deep cut in the middle of the night. Not seeing the wound does not make it go away. Turning on the light merely reveals the truth of the wound that was already there. The Law also gives no remedy to sin, but merely points to the remedy of Jesus.
Adam was a “type” of Christ, whom Paul calls “The Last Adam” in 1 Corinthians 15:45 (quickview) . Adam was a flawed human, Jesus is the perfect human. Adam typifies the disobedience of a fallen man in the first creation, Jesus is the obedient Son who is the first fruits of a new creation (1 Corinthians 15:20 (quickview) ).
Why is the free gift not like the trespass? It took only one act of rebellion (“trespass” is a willful violation, not a mistake or a “bad example”) against God’s command to bring sin and death to all of humanity. As Paul will say, it will take only one sacrifice to undo all of that sin and death (everyone that has ever lived has died – except Enoch and Elijah). Our problem as humans is that we want to make ourselves better by ourselves. It’s a futile endeavor.
Gal 2:16 by works of the law no one will be justified.
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The result of one man’s sin was condemnation—separation of humanity from God. But the result of Jesus sacrifice is the return of fellowship (justification—right standing before God) for ALL of humanity.