Consider the following statements,
[ 0 , 1 ] × [ 0 , 1 ] with the dictionary order is
complete.
[ 0 , 1 ] × [ 0 , 1 ) with the dictionary order is
complete.
[ 0 , 1 ) × [ 0 , 1 ] with the dictionary order is
complete.
Where the dictionary order on R × R is given by ( a , b
) < ( x , y ) if either a...