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.
Algebra ->
Sequences-and-series
-> 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.
Log On
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.