We will just define, we will make, and this is where we're defining delta as a function of epsilon. We're going to make 2 delta equal epsilon, or if you divide both sides by 2, we're going to make delta equal to epsilon over 2. If you make delta equal epsilon over 2, if you make, let me switch colors just to ease the monotony, if you make delta equal epsilon over 2, then this statement right over here becomes the absolute value of f of x minus L is less than, instead of 2 delta, it'll be less than 2 times epsilon over 2 is just going to be less than epsilon. This is the key. If someone gives you any positive number epsilon for this function, as long as you make delta equal epsilon over 2, then any x within that range, that corresponding f of x is going to be within epsilon of our limit. This tells you, say the epsilon, and remember, it has to be true for any positive epsilon, but you could see how the game could go. If someone gives you the epsilon, let's say they want to be within 0.5 of our limit.