A limit is the value that a function approaches (without necessarily being equal to) as x approaches a specific value. A limit can only exist if the limits approaching from the left and the right both exist and are equal. the analogy ive been going off is the idea of a force field or a locked door. i think im catching the basic concepts of limits, but getting a little held up on the idea of a limit being discontinuous. it might help if some one could first give a few practical examples of uses of limits in general, and then perhaps also explain the idea of a discontinuous limit please.