How to assign a variable to an array

I want to ask the user to enter an X amount of file names. I want to put those names into an array and then loop back through them to verify they are in the directory. 1st- How would I assign the value to an array and what is the correct syntax. 2nd- how would i reference that array after I assigned it to check to see if the file exist. Thanks.

something like

#!/bin/bash
i=0
while true   # read user input
do
   read -p "enter file name (blank if finished) : "
   [ -z "$REPLY" ] && break
   FILE[$i]=$REPLY
   ((i++))
done
for ((i=0; i<${#FILE[@]}; i++))   # check if files exist
do
   F=${FILE[$i]}
   if [ -f "$F" ]
   then echo "File $F exists"
   else echo "File $F does not exist"
   fi
done

Maybe it's better - and sure it's easier - to check files before :

#!/bin/bash
i=0
while true   # read user input and check files
do
   read -p "enter file name (blank if finished) : " F
   [ -z "$F" ] && break
   [ -f "$F" ] || { echo "File does not exist" && continue; }
   FILE[$i]=$F
   ((i++))
done
for ((i=0; i<${#FILE[@]}; i++))   # print files
do
   echo -e "File number $i\t: ${FILE[$i]}"
done

Thanks. Your example helped.