1. The problem statement, all variables and given/known data f:ℝ→ℝ is defined as f(x)= 2x if x is rational and f(x)=4-2x if x is irrational. Is it true that lim x→1/2=1? 2. The attempt at a solution Intuitively it seems that as x gets ever closer to 1/2 from either side that the function will oscillate between numbers very close to 1 and 3 and therefore there the limit doesn't exist. Firstly is my intuition right? Secondly how does one show this using the definition of a limit or some other theorem? I thought about using the fact that all (xn)[itex]\subseteq[/itex]ℝ such that (xn)→1/2 would have to imply that (f(xn))→1. Again i can't formally show that this can't be.