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Need help with proving:
Show that (a,b) + (c,d) = (a+c, b+d) is not well-defined in the rational numbers.
[Note: (a,b) + (c,d) = (ad+bc, bd) is well-defined because (a,b) is related to (c,d) when ad = bc.)]
Show that (a,b) + (c,d) = (a+c, b+d) is not well-defined in the rational numbers.
[Note: (a,b) + (c,d) = (ad+bc, bd) is well-defined because (a,b) is related to (c,d) when ad = bc.)]