This question has been around since children and heaven have been around.  Theories abound, some say Babies are born the seed of Adam and therefore bear the guilt of sin.  and are accountable, others bring in an age of accountability.  some say infant baptism is the ticket to heaven.  I wonder, what does the Bible say?

Romans 3:10
As it is written, There is none righteous, no, not one.

2 Cor. 5:10
For we must all appear before the judgement seat of Chrst; that everyone may receive the things done in his body, according to that he hath done, whether it be good or bad.

Romans 8:30
Moreover whom he did predestinate, them he also called: and whom he called, them he also justified: and whom he justified, them he also glorified.

Deut. 1:39
Moreover your little ones, which ye said should be a prey, and your children, which in that day had no knowledge between good and evil, they shall go in thither, and unto them will I give it, and they shalll possess it.
Live life with a due sense of responsibility, not as those who do not know the meaning of life but as those who do.  Ephesian 5:15
"You and I have need of the strongest spell that can be found to wake us from the evil enchantment of worldliness." CS. Lewis from The Weight of Glory
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Do Babies go to heaven??