If f is a real function on R[tex]^1[/tex], and holds:lim [f(x+h)-f(x-h)] = 0 for every x belongs R[tex]^1[/tex]. Does f continuous? And I thought it no. Since I considered it mentioned only the left-hand and right-hand limit are equal, but whether or not equal to f(x) was not exactly known. Will anybody provide me a suggestion? To whether my judgement is true or vice versa. Thx!