Formal Definition of Limit

Topic:
Limits
Let be a function defined on an interval that contains , although it might not be defined at itself. The limit of as approaches is if gets really close to whenever ges really close to . To say this formally,  if for every there exists for which whenever . The construction below helps make this more intutitive. Pick to set a vertical range for around . Then set small enough that the pink brick fits inside the blue strip.