Clarification: Yes, if the divorce is not in line with the fornication/adultery condition that Jesus explains.
Still yes on the remarriage.
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God divorced Israel. Did God sin?
God forbid! No, it appears that God's divorcement of Israel was on the basis of spiritual adultery. Thus, it appears to be in line with the words that Jesus spoke on the divorce subject. Further on down in that same chapter in Jeremiah, the Lord pleads for Israel to return unto Him because He is still married to the backslider.
Divorce is CAUSED BY sin.
Indeed.