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  3. consider the following statements, [ 0 , 1 ] × [

Consider the following statements, [ 0 , 1 ] × [ 0 , 1 ] with...

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Advance Math

Consider the following statements,

  1. [ 0 , 1 ] × [ 0 , 1 ] with the dictionary order iscomplete.
  2. [ 0 , 1 ] × [ 0 , 1 ) with the dictionary order iscomplete.
  3. [ 0 , 1 ) × [ 0 , 1 ] with the dictionary order iscomplete.

Where the dictionary order on R × R is given by ( a , b) < ( x , y ) if either a < x or a = x and b < y.

For each of these three statements either (i) prove it is trueor (ii) provide a counterexample to show that it is false.

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