document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #358233 by richard1234(7193) $\"\"$ $\"About$

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).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "A function f(x) is not continuous if (but not only if)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

. This is true because if a is an integer, the LHS equals 1 but the RHS equals 0. Therefore f is not continuous. \n" ); document.write( "

\n" );