How do you provide a direct counterexample to show that an a

How do you provide a direct counterexample to show that an argument is invalid? How do you provide a formal counterexample?

Solution

1) Suppose the argument is \"positive integer is a sum of three squares\"..---showing the first few 1,2,3...satisfy this property.. Then 79 is a direct counterexample to show that this argument is invalid.

2) A formal counterexample is not a specific instance--for the same example above, one can directly prove that any n Mod 7 would be a (formal) counterexample.