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it is like there is a wall between two parts of a function, you are facing the wall. you can only see from one side. You want to know what the function inside the wall is like, but you can't really take down the wall, so you can only use something that really resembles the point on the wall and make a guess.
Notice that sometimes you can't even shout out a guess because what you guess are self contradicting. You guess from one side of the wall and be like: hey in this wall the function might be A! and you guess from the other side of the wall and be like: hey in this wall the function is gonna be like B! You are so excited that you finally made a guess(that is not an easy job), and then you are like, so i guess inside this wall the function is gonna be like A? B? So you can't even make a guess. That guess is the limit, we use something really resembles the point inside the wall and make a conjecture.
For the limit to exist means that you should be able to reach the same "guess" regardless which side of the wall you are speaking from.
but why are you making such a guess? you are making this guess because you want to travel from this side of the wall to the other side of the wall, you will be blind-folded and will not be aware where you are going. If you make the right guess, then you wont fall. but if you made the wrong guess, you will be stuck at some point.
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