SOLUTION: Give an example of a function that is continuous at all non-integer values but is discontinuous at all integer values. Prove the discontinuity property of your function.

Question 549787: Give an example of a function that is continuous at all non-integer values but is discontinuous at all integer values. Prove the discontinuity property of your function.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
For example, let f(x) = 1 if x is not an integer, but f(x) = 0 if x is an integer (it is easier to write this function using piece-wise notation).

A function f(x) is not continuous if (but not only if)

. This is true because if a is an integer, the LHS equals 1 but the RHS equals 0. Therefore f is not continuous.
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