Not meaning to hound anyone--but I am wondering how it is God knows a remnant will be saved. I have been told God knows group averages, and also that God can determine who is saved and who is not saved. I have been told that this is an estimate, and that this means "all who will be saved, will be saved," i.e. the remnant is just whoever will be saved.
None of these, I find satisfactory, for a remnant means relatively few, and these being saved is God's sentence on earth, not his observation, nor some form of estimate.
A remnant will return, a remnant of Jacob will return to the Mighty God. Though your people, O Israel, be like the sand by the sea, only a remnant will return. Destruction has been decreed, overwhelming and righteous. (Isaiah 10:21-22)
And then later, "all Israel will be saved," so such predictions are not simply based on human recalcitrance--this is another answer I have been given.